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A new mutation operator for real coded genetic algrithms
Abstract
In this paper, a new mutation operator called power mutation (PM) is introduced for real coded genetic algorithms (RCGA). The performance of PM is compared with two other existing real coded mutation operators taken from literature namely: non-uniform mutation (NUM) and Makinen, Periaux and Toivanen mutation (MPTM). Using the various combinations of two crossovers (Laplace crossover [Kusum Deep, Manoj Thakur, A new crossover operator for real coded genetic algorithms, Applied Mathematics and Computations, accepted for publication, doi:10.1016/j.amc.2006.10.047] and Heuristic crossover [Z. Michalewicz, Genetic Algorithms + Data Structures = Evolution Programs, Springer-Verlag, New York, 1992; A.H. Wright, Genetic algorithms for real parameter optimization, in: G.J.E. Rawlins (Ed.), Foundations of Genetic Algorithms I, Morgan Kaufmann, San Mateo, 1991, pp. 205–218]) and three mutation operators (the newly defined mutation in this paper, PM, NUM and MPTM) six generational real coded GAs are compared on a set of 20 benchmark global optimization test problems. Various performance criterion are used to judge the efficiency, accuracy and reliability of all the RCGAs. The results show that the RCGA using the proposed power mutation, when used in conjunction with the earlier defined Laplace crossover, outperforms all other GAs considered in this study.
... The breaking points for these matrices, which are used to define subsets of chromosomes for exchange between parent individuals, are selected randomly. At the same time, there are decision variables that are floatingpoint type, which require the use of real-coded crossover and mutation operators, such as SBX-crossover [54], LXcrossover [55] and Power Mutation [56], for obtaining more accurate results. This is especially relevant when large search ranges are given for these decision variables (i.e., there are high accuracy requirements for the mantissa). ...
... is a proposed genetic algorithm designed to solve an agent-based model of controlled trade interactions. RCGA (Real-Coded Genetic Algorithm) is an evolutionary algorithm that utilizes real-coded genetic operators, such as the Simulated Binary Crossover (SBX) [49] and Power Mutation [56], as heuristic operators for generating offspring individuals. The benefit of RCGA lies in the absence of the requirement for binary representation and, consequently, encoding and decoding of decision variable values, as well as the associated costs of performing bitwise crossover and mutation operations. ...
The article discusses the development and study of a new matrix-based hybrid genetic algorithm (MBHGA) for solving an agent-based model of firms’ behavior with controlled trade interactions. The proposed model employs symmetric strategies optimized using the MBHGA algorithm. This algorithm combines evolutionary search with real-coded crossover and matrix binary-coded crossover as genetic operators, creating a hybrid approach. The aim of the designed system is to assist decision-makers in selecting optimal strategies for their firms in situations where some companies impose restrictions on interactions. As demonstrated by the results of optimization experiments, the MBHGA algorithm significantly outperformed other methods, such as RCGA, PSO, GWO, SPEA2, and NSGA-II, in terms of both accuracy (measured by deviations from reference values) and the quality of the Pareto front approximation (measured by LHV, IGD, and CPF) when solving an agent-based model of firms’ behavior. As demonstrated in this study, the performance of MBHGA significantly depends on the size of the model (i.e., the number of agents), and it can be enhanced by parallelizing the evolutionary search process, including matrix crossover operations for decision variables. Optimization experiments using a genetic algorithm were conducted to maximize utility functions for agent companies under trade restrictions. The results showed that trade restrictions have a negative impact on the utility function values in both single- and multi-objective optimization, for selected countries and for all countries’ firms. However, an optimization-based approach using the MBHGA algorithm can help minimize the negative consequences of trade restrictions by providing the ability to find nondominated solutions and the best possible trade-offs.
... The last step is the mutation operator, which prevents the search from converging to local optima, by making random changes to the individuals. The used function is the Power mutation [40,53]: ...
... where M i is the mutated individual, x i is the ith gene of the individual, α and β are the lower and upper bounds of the genes respectively, t is the scaled distance of x i from the ith component of the lower bound (α i ) of the doses and s is given by [53]: ...
The application of the achievements of mathematics and informatics greatly helped the development of medicine. Designing personalized therapies using different algorithms is crucial, especially during chemotherapy, to minimize the toxic effects on the patient and avoid resistance, thus ensuring a higher quality of life. In this work, we present an LSTM neural network that can quickly and accurately estimate the parameters of the tumor dynamics model based on noisy virtual patient data. In addition, we present a genetic algorithm designed for therapy optimization, which is able to predict the most appropriate personalized therapy based on the estimated parameters. In this work, we focus on finding the optimal hyperparameters of this genetic algorithm. Optimizing the hyperparameters is of fundamental importance in designing the best possible personalized therapy.
... The SM process consists of switching the allocated and unallocated positions of the offspring solutions. To augment the algorithm's exploration capacity, power mutation (PM) (Deep & Thakur, 2007), in conjunction with swap mutation, is integrated into the current solution framework. Subsequently, the repair mechanism is reapplied to rectify any infeasible offspring solutions generated. ...
... The use of a repair mechanism to handle these combinatorial constraints is reported to be more effective than the application of other constrainthandling techniques (Coello, 2021). The effectiveness of using the repair mechanism has also been demonstrated in other studies (Deep & Thakur, 2007;Woldesenbet et al., 2009). ...
The outset of this manuscript involves introducing an analytical formula for the credibility of coherent trapezoidal fuzzy numbers, which represent an extended version of the traditional trapezoidal fuzzy numbers. With this formula, we present a precise counterpart to compute the credibilistic mean, semivariance, and skewness of coherent trapezoidal fuzzy numbers. Leveraging these analytical formulations, we construct a novel tri-objective portfolio selection problem, integrating credibilistic mean, semivariance, and skewness as objectives, along with some practical constraints. When used with the returns of the portfolio as a whole, the derived analytical expressions help to overcome the otherwise computationally expensive approach involving the simulation of results using individual assets’ returns. The proposed model is solved by adapting an efficient multiobjective genetic algorithm. The algorithm has been specifically designed to solve portfolio selection models of this type. The efficiency of the proposed model is then demonstrated by taking a real-world scenario of financial stock market datasets from the NSE India. Based on the results of this study, it appears that the proposed novel tri-objective portfolio selection model produces promising results compared to the baseline model and the NIFTY 50 Index considered as a benchmark.
... chromosome [11]. The new values of the genes, representing wavenumber positions in spectra, are then rounded to the nearest integer. ...
... The standard deviation of this distribution is the parameter called "scale" which is equal to 1 in the first generation, but this parameter is controlled during the next generations by another parameter called "shrink." The standard deviation at the t th generation, t is the same at all coordinates of the parent chromosome, and is given by the recursive formula [11]: ...
Microelectronics production failure analysis is an important step in improving product quality and development. In fact, the understanding of the failure mechanisms and therefore the implementation of corrective actions on the cause of the failure depend on the results of this analysis. These analyses are saved under textual features format. Then such data need first to be preprocessed and vectorized (converted to numeric). Second, to overcome the curse of dimensionality caused by the vectorisation process, a dimension reduction is applied. A two-stage variable selection and feature extraction is used to reduce the high dimensionality of a feature space. We are first interested in studying the potential of using an unsupervised variable selection technique, the genetic algorithm, to identify the variables that best demonstrate discrimination in the separation and compactness of groups of textual data. The genetic algorithm uses a combination of the K-means or Gaussian Mixture Model clustering and validity indices as a fitness function for optimization. Such a function improves both compactness and class separation. The second work looks into the feasibility of applying a feature extraction technique. The adopted methodology is a Deep learning algorithm based on variational autoencoder (VAE) for latent space disentanglement and Gaussian Mixture Model for clustering of the latent space for cluster identification. The last objective of
this paper is to propose a new methodology based on the combination between variational autoencoder (VAE) for the latent space disentanglement, and genetic algorithm (GA) to find, in an unsupervised way, the latent variables allowing the best discrimination of clusters of failure analysis data. This methodology is called VAE-GA. Experiments on textual datasets of failure analysis demonstrate the effectiveness of the VAEGA proposed method which allows better discrimination of textual classes compared to the use of GA or VAE separately or the combination of PCA with GA (PCA-GA) or a simple Auto-encoders with GA (AE-GA).
... 6. Population update: New individuals replace the old ones, and the process repeats until a specified stopping criterion is reached, such as a maximum number of generations or a certain performance level. The learning process can be presented in more detail with a flowchart in Figure 2. From this flowchart, it is evident that tournament selection [8] is used as the selection operator, simulated binary crossover (SBX) [9] is applied as the crossover operator, and the mutation operator is implemented using the Power mutation method [10]. ...
This research explores a method of optimizing neural networks for vehicle control in a simulation environment using a real-coded genetic algorithm (RCGA). The study focuses on applying RCGA in conjunction with multiple genetic operators, including simulated binary crossover (SBX), power mutation (PM), and tournament selection, to evolve neural network weights and biases, enhancing control performance for simulated vehicles. By utilizing RCGA to adjust neural network parameters, the approach enables adaptive and efficient vehicle control. The experiments demonstrate that combining sensor data with neuroevolutionary optimization in a simulation leads to a highly reliable control system, achieving performance metrics comparable to human operators. These findings suggest that RCGA-based optimization methods can be effectively applied to complex dynamic systems in various technical fields.
... Mutation is usually carried out with a single parent and plays an important role in increasing the population diversity. Various mutation operators have been developed for different solution representations, for example, Gaussian and uniform mutation for binary coding (Fogel and Atmar, 1990), swap and insertion for integer coding (Larrañaga et al., 1999), polynomial and power mutation for real coding (Deep and Thakur, 2007;Deb and Deb, 2012). Some mutation operators are problem-dependent, such as greedy sub tour mutation for traveling salesman problems (Albayrak and Allahverdi, 2011) and energy mutation for multicast routing problems (Karthikeyan et al., 2013). ...
The performance of different mutation operators is usually evaluated in conjunc-tion with specific parameter settings of genetic algorithms and target problems. Most studies focus on the classical genetic algorithm with different parameters or on solving unconstrained combinatorial optimization problems such as the traveling salesman problems. In this paper, a subpopulation-based genetic al-gorithm that uses only mutation and selection is developed to solve multi-robot task allocation problems. The target problems are constrained combinatorial optimization problems, and are more complex if cooperative tasks are involved as these introduce additional spatial and temporal constraints. The proposed genetic algorithm can obtain better solutions than classical genetic algorithms with tournament selection and partially mapped crossover. The performance of different mutation operators in solving problems without/with cooperative tasks is evaluated. The results imply that inversion mutation performs better than others when solving problems without cooperative tasks, and the swap-inversion combination performs better than others when solving problems with cooperative tasks.
... And polynomial mutation operator proposed by Deb is one of the most widely used mutation operator [13]. A comprehensive introduction to mutation operator can be seen from [14]. In a word, it is very important to choose or design appropriate select, crossover and mutation operators of GAs, when dealing with different optimization problems. ...
Increasing nature-inspired metaheuristic algorithms are applied to solving the real-world optimization problems, as they have some advantages over the classical methods of numerical optimization. This paper has proposed a new nature-inspired metaheuristic called Whale Swarm Algorithm for function optimization, which is inspired by the whales behavior of communicating with each other via ultrasound for hunting. The proposed Whale Swarm Algorithm has been compared with several popular metaheuristic algorithms on comprehensive performance metrics. According to the experimental results, Whale Swarm Algorithm has a quite competitive performance when compared with other algorithms.
... We also create P mut = 28 children from mutation using adaptive power mutation. Power mutation involves selecting a single parent, p, for each child, c, and then applying a mutation based on increasing or decreasing each component by an amount equal to a uniform draw raised to a power (Deep and Thakur, 2007), scaled by each component's distance to the boundary. Adaptive power mutation indicates the strength of mutation -the power -varies depending on whether a candidate has fitness greater than or below average fitness. ...
Trade imbalances significantly alter the welfare implications of tariffs. Using an illustrative model, we show that trade deficits enhance a country's ability to alter its terms of trade, and thereby benefit from tariffs. Greater trade deficits imply higher optimal, or welfare maximizing, tariffs. We compute optimal unilateral and Nash equilibrium tariffs between the United States and China \unicode{x2014} the countries with the largest bilateral trade imbalance \unicode{x2014} using a multi-region, multi-sector applied general equilibrium model with service sectors and input-output linkages, a computationally complex task. We find the United States gains from such a trade war with China, albeit minimally.
... A power mutation operator [39] was applied for the mutation operation. The algorithm of the operator mutates parent x, as follows: ...
Accurate forecasting of ship encounter positions is crucial for preventing collisions at sea. This paper presents a framework for predicting a ship’s trajectory using a sparse Gaussian process. The proposed method effectively addresses the limitations of existing full Gaussian processes, specifically the significant storage requirements and time complexity associated with data training. The model is trained using Automatic Identification System (AIS) data on trajectories, with hyperparameters optimized through a genetic algorithm. Experimental analysis demonstrates that the proposed model reduces average time complexity by 61.3 s and improves average prediction error to 9.2 m compared to full Gaussian-process-based models.
... The mutation operator prevents the search from converging to local optima, by implementing random changes to the individuals. This mutation function is similar to the crossover function and is proven to work on this problem [7,49]: ...
The application of engineering in medical practice has a long history; however, these systems are generally used for diagnosis. The cyber-medical system approach combines engineering and biology to enhance the treatment of patients. For example, artificial pancreas systems have proved that the achievements of modern technology can be successfully applied in treating chronic diseases. The chapter discusses the application of control theory in the treatment of cancer. Therapy optimization comprises the steps of modeling, parameter identification for personalization, and therapy optimization based on control theory and mathematical optimization. The sections of the chapter discuss these problems with the current solutions being used in the Physiological Controls Research Center of Óbuda University.
... According to Equations (7)-(11), the updated gains K K K are recorded in the database as K K K (t ), enabling DD-PID to calculate the newly optimised PID gains K K K new (t ). In this study, the Nelder-Mead [26] method is employed for the optimisation process; however, other optimisation methods, such as real-coded genetic algorithms [27] may also be applied. ...
In industrial process control, the proportional–integral–derivative (PID) control scheme is well‐recognized and widely utilized. However, due to the distinctive characteristics of real systems, their control design primarily aims at achieving optimal production performance, constrained by uncertainty and variations. This paper initially discusses a database‐driven PID (DD‐PID) control scheme that was previously proposed. This scheme combines the DD‐PID with the cerebellar model articulation control to minimise computational and memory requirements for industrial application. Subsequently, a hydraulic system is introduced, detailing its characteristics and control necessities. Furthermore, both the DD‐PID and the proposed cerebellar model articulation control memory‐based DD‐PID control schemes are implemented and evaluated through experimental examples on a hydraulic system. Lastly, as a practical validation of the theoretical approach, a quantitative assessment compares the two methods, discussing the practicality and efficacy of the proposed scheme in reducing computation and memory consumption.
... Thus, this paper introduces a hybrid optimization methodology incorporating the TLBO and the WOA for SHE in a three-phase 11-level MLI with modified reduced switch topology [48]. This hybrid method has been implemented in MATLAB®/Simulink environment and applied to experimental prototype for seeking to offer a versatile and efficient solution to the challenge of harmonic minimization in MLIs [49]. ...
This study presents an innovative hybrid optimization approach that combines teaching-learning based optimization (TLBO) with the whale optimization algorithm (WOA) for selective harmonic elimination (SHE) technique in a modified reduced switch topology three phase multilevel inverter (MLI). The proposed topology requires fewer switches than a conventional cascaded H-bridge MLI and another reduced switch topology in a single phase MLI. Once applied to an 11-level inverter, this hybrid strategy effectively tackles the issues of harmonic reduction and total harmonic distortion (THD) on the line-to-line voltage, significantly improving the quality of the output power through the optimal determination of switching angles. The study leverages the TLBO and WOA to solve the non-linear set of equations associated with the SHE controls technique, aiming to overcome the limitations of classical methods prone to local optimal solutions and dependent on initial controlling parameters. This method has been performed in two steps, during the first step TLBO has been executed and in the next step the solutions derived from TLBO has been used as an initial guess for WOA which ensures the attainment of the precisely converged solution. By using MATLAB®/Simulink software environment, the performance of the hybrid TLBO with WOA method has been simulated and benchmarked against traditional standalone metaheuristic techniques. The simulation results reveal that proposed hybrid approach becomes advantageous in terms of SHE and output voltage quality across various modulation indices. The experimental results verified that the proposed algorithm has been validated through the implementation of a three-phase 11-level inverter. This study highlights the significant potential of the hybrid optimization method in progressing harmonic minimization techniques within the multilevel inverters.
... If P > P m the gene stays the same and does not undergo any mutation, otherwise if P ≤ P m mutation occurs and a random gene from the range of potential values will substitute the original gene. The literature also presents various techniques for mutation, such as Uniform mutation [97], Power [98], Non-uniform [99], Shrink [100], Gaussian [101], etc. The mutation operator introduces the concept of ergodicity to genetic algorithms used in space exploration. ...
This thesis explores the Anaerobic Digestion (AD) process model, focusing on
optimizing productivity. The International Water Association’s Anaerobic Digestion Model No.1
(ADM1) is a key model in this field. The main challenge is identifying uncertain parameters.
To tackle this, a methodology using genetic algorithms (GA) is introduced to fine-tune the
parameters of a simplified model, AM2HN. The GA minimizes the proposed objective function
on two scales: linear and logarithmic. This methodology, validated through computer simulation,
shows significant improvement over traditional techniques. Furthermore, The reduced model AM2 is used to formulate and test a robust control, demonstrating its efficacy and potential. This study contributes significantly to AD process modeling and control.
... To compare the performance of different algorithms, them are evaluated by using the Performance Index (PI) (Deep and Thakur 2007). PI is a positive indicator that takes into account the algorithm's runtime. ...
A multi-objective coyote optimization algorithm based on hybrid elite framework and Meta-Lamarckian learning strategy (MOCOA-ML) was proposed to solve the optimal power flow (OPF) problem. MOCOA-ML adds external archives with grid mechanism on the basis of elite non-dominated sorting. It can guarantee the diversity of the population while obtaining the Pareto solution set. When selecting elite coyotes, there is a greater probability to select the elite in sparse areas, which is conducive to the development of sparse areas. In addition, combined with Meta-Lamarckian learning strategy, based on four crossover operators (horizontal crossover operator, longitudinal crossover operator, elite crossover operator and direct crossover operator), the local search method is adaptively selected for optimization, and its convergence performance is improved. First, the simulation is carried out in 20 test functions, and compared with MODA, MOPSO, MOJAYA, NSGA-II, MOEA/D, MOAOS and MOTEO. The experimental results showed that MOCOA-ML achieved the best inverted generational distance value and the best hypervolume value in 11 and 13 test functions, respectively. Then, MOCOA-ML is used to solve the optimal power flow problem. Taking the fuel cost, power loss and total emissions as objective functions, the tests of two-objective and three-objective bechmark problems are carried out on IEEE 30-bus system and IEEE 57-bus system. The results are compared with MOPSO, MOGWO and MSSA algorithms. The experimental results of OPF demonstrate that MOCOA-ML can find competitive solutions and ranks first in six cases. It also shows that the proposed method has obtained a satisfactory uniform Pareto front.
... As a heuristic algorithm, the Genetic Algorithm simulates the evolution process of biological species in nature, demonstrating commendable optimization capabilities, and therefore is widely utilized [30]. However, standard genetic algorithms still suffer from various issues, such as premature convergence [31][32][33]. To address this, we propose an enhanced multi-population Genetic Algorithm in this paper, combining variable neighborhood search (VNS) information for optimal individual selection. ...
The flexible job-shop scheduling problem (FJSP) with parallel batch processing machine (PBM) is one of those long-standing issues that needs cutting-edge approaches. It is a recent extension of standard flexible job shop scheduling problems. Despite their wide application and prevalence in practical production, it seems that current research on these types of combinatorial optimization problems remains limited and uninvestigated. More specifically, existing research mainly concentrates on the flow shop scenarios in parallel batch machines for job shop scheduling but few literature emphasis on the flexible job shop integration in these contexts. To directly address the above mentioned problems, this paper establishes an optimization model considering parallel batch processing machines, aiming to minimize the maximum completion time in operating and production environments. The proposed solution merges variable neighborhood search with multi-population genetic algorithms, conducting a neighborhood search on the elite population to reduce the likelihood of falling into local optima. Subsequently, its applicability was evaluated in computational experiments using real production scenarios from a partnering enterprise and extended datasets. The findings from the analyses indicate that the enhanced algorithm can decrease the objective value by as much as 15% compared to other standard algorithms. Importantly, the proposed approach effectively resolves flexible job shop scheduling problems involving parallel batch processing machines. The contribution of the research is providing substantial theoretical support for enterprise production scheduling.
... Real-Coded Genetic Algorithms (RCGAs) are populationbased bio-inspired evolutionary algorithms indented for solving large-scale singleobjective and multiobjective optimization problems. Unlike classic genetic algorithms suggested firstly in [54] and [55], RCGAs uses real-coded heuristic operators, such as a crossover (e.g., the simulatedbinary crossover (SBX), Laplace crossover (LX), etc.) and a mutation (e.g., non-uniform mutation (NUM), power mutation (PM), etc.) to generate new potential decisions [56], [57], [58], [59], [60], [61]. The first important advantage of RCGAs is the possibility of searching in continuous decision space without necessary of using encoding and decoding operations for decision variables providing a more precision of obtained solutions (i.e., the level of accuracy after a decimal point) in less computational expenses. ...
There are many reasons for traffic congestions such as the "stop-and-go wave effect", periodic increase in intensity of vehicle and pedestrian traffic ("rush hours"), frequent maneuvering, uncontrolled pedestrians’ movement on road crossings and other factors. This paper considers the problem of biobjective optimization and rebalancing of vehicles’ and pedestrians’ flows with the use of Manhattan road networks (MRNs) with smart traffic lights (STLs) as the case study of intelligent transportation system (ITS). For this purpose, we have studied the possibilities of applying STLs to control of traffic in large-scale road networks providing a speed harmonization and traffic prioritization between vehicles and pedestrians. The considered multiagent system (MAS) includes agent vehicles, agent pedestrians and agent lights that interact with each other according with given rules (e.g., V2V, V2P, V2I). Such STLs use information on the traffic structure and its density to switch signals at each moment in time. In the non-stationary mode with a periodic traffic intensity to provide the analysis of traffic flows done by STLs it has been suggested to use the fuzzy clustering algorithm aggregated with the density-based spatial clustering algorithm (FCA-DBSCAN). At the uniform motion fixed durations of phases set up for STLs that computed individually with use of the suggested parallel hybrid biobjective real-coded genetic algorithm (BORCGA-BOPSO). The approach allows to improve significantly the time-efficiency of seeking optimal individualised STLs’ characteristics while keeping up their quality. Moreover, the ITS based on STLs with parameters optimized with the BORCGA-BOPSO provides significant traffic improvement in MRNs in contrast to the case of uncontrolled pedestrian crossings and using usual (i.e., non-smart) traffic lights.
... Appendix B.2 shows the detailed procedure of the swap mutation. [73] is employed along with the swap mutation in the proposed solution framework to enhance the exploration abilities of the modified algorithm. This mutation operator applied here provides a slight perturbation to an active asset that results in a localized search in the neighborhood of the existing value with satisfying asset bounds. ...
Financial portfolio formation is usually a multi-objective decision-making problem concerning return and risk on the investment. In this study, we make use of an extension of regular triangular fuzzy numbers, known as coherent triangular fuzzy numbers, to describe portfolio returns in a credibility-based framework. The paper's novelty lies in proposing and deriving a crisp equivalent for computing the coherent triangular fuzzy number-based credibilistic semivariance, credibilistic skewness, and credibilistic semikurtosis. Using these analytical expressions, we propose three multi-objective portfolio optimization models involving the practical constraints related to investment decisions. All the proposed analytical expressions, when used with the returns of the portfolio as a whole, help to overcome the computationally expensive process of simulating results using the returns of individual assets. The proposed models differ with respect to different risk measures, viz. semivariance, Mean-Absolute-Semi-Deviation (MASD), and Conditional Value-at-Risk (CVaR). These models are solved using an adaptation of an efficient Multi-Objective Genetic Algorithm (MOGA) specifically designed to solve portfolio optimization problems with practical constraints. Data from the National Stock Exchange (NSE) in Mumbai, India and the New York Stock Exchange (NYSE) in New York, USA, are used to demonstrate the effectiveness of the proposed portfolio optimization models and solution methodology. All the proposed models are compared with respect to each other and the benchmarks considered in this study to bring out the performance stability.
... Some of the Mutation operators are: 1. Displacement mutation: A sub string of the main gene string is displaced from its original position such that the obtained combination is legal. 3 Power mutation: This method of mutation was proposed in 2007 in [67]. The distribution function: 4. f (x) = a * x b where b=a-1 and a is a random power that the user chooses. 5. ...
INTRODUCTION: The Evolutionary algorithms created back in 1953, have gone through various phases of development over the years. It has been put to use to solve various problems in different domains including complex problems such as the infamous problem of Travelling Salesperson (TSP).OBJECTIVES: The main objective of this research is to find out the advancements in Evolutionary algorithms and to check whether it is still relevant in 2023.METHODS: To give an overview of the related concepts, subdomains, pros, and cons, the historical and recent developments are discussed and critiqued to provide insights into the results and a better conception of the trends in the domain. RESULTS: For a better perception of the development of evolutionary algorithms over the years, decade-wise trend analysis has been done for the past three decades.CONCLUSION: Scope of research in the domain is ever expanding and to name a few EAs for Data mining, Hybrid EAs are still under development.
... This property is believed to generate a better solution with their parents' best qualities. A real coded GA operator called Laplace crossover is introduced by Deep and Thakur (2007). In the Laplacian operator, instead of one, two off springs are generated which are supposed to have the parents' qualities. ...
... Mutation introduces minor random alterations to individual chromosomes, promoting diversity and empowering the algorithm to explore different regions of the search space (Eshelman and Schaffer, 1993;Goldberg, 1989;Katoch et al., 2021). By iteratively applying these genetic operators, GA adeptly navigates complex and high-dimensional search spaces, establishing a robust framework for solving optimization problems (Deep and Thakur, 2007;McCall, 2005). ...
Expansive soils exhibit excessive volume increases upon contact with water, which can pose a serious threat to stability of structures and foundations. Therefore, it is essential to determine the swelling properties, e.g. maximum swelling pressure, of these problematic soils. We employed a feed-forward neural network algorithm trained with Levenberg-Marquardt, Bayesian regularization, scaled conjugate gradient, and genetic algorithm to build a network model capable of determining the maximum swelling pressure of clayey soils over a wide range of conditions. The models were developed based on a sufficiently large experimental dataset that takes into account key factors that influence the soil swelling. The results show that the feed-forward neural network algorithm trained with Bayesian regularization has the highest overall accuracy, as its predictions agree well with the experimental data. Besides, a simplified network model was developed to be used in cases of limited data availability. The developed model provides accurate predictions over a wide range of conditions and can serve as a valuable tool for researchers and engineers dealing with expansive soils.
... A mixed-integer real-coded genetic algorithm (RCGA) (Deep et al. 2009) was developed by using Laplace crossover (Deep and Thakur 2007a) and power mutation (Deep and Thakur 2007b). A constriction PSO algorithm (Clerc and Kennedy 2002) is also developed to solve the proposed problem. ...
In the real market, the item’s demand is substantially affected by the item’s selling price and frequency of advertising. This study focuses on an optimal ordering policy followed by advertising, pricing, and preservation policies. The present study incorporates the quantity-dependent ordering cost and time-dependent holding cost. A partial prepayment scheme is developed for inventory purchase decisions. The spoilage impact can be effectively reduced by an optimal investment in refrigeration. The optimal decision policy has been proposed by using three metaheuristic algorithms, namely particle swarm optimization, real-coded genetic algorithm, and differential evolution algorithm. A comparison is made for these metaheuristic schemes based on the numerical illustrations. The parameter sensitivity is performed to get insights of the variability in the indicators of the inventory model.
In literature, there is an abundance of nature inspired optimization algorithms. These algorithms can be best utilized effectively when applied to real world problems. Marine Predator Algorithm is one such algorithm which has been recently proposed and has been used to solve many engineering problems. In this study, we are considering some optimization problems from electrical, medicine and computer vision world. We have applied an improved version of MPA by increasing its exploration ability. The results obtained from the experiments conclude the remark that improved version of MPA has successfully solved these problems.
This study presents a novel approach of intelligent parameter identification (IPI) for a high‐cycle accumulation (HCA) model of sand, which reduces the subjective errors on manual parameter calibration and makes the use of the HCA model more accessible. The technique is based on optimization theory and adopts the cuckoo search algorithm (CSA). To improve search ability and convergence speed of CSA, several enhancements are implemented. First, the improved CSA (ICSA) incorporates quasi‐opposition learning to expand the search space and replaces the original search strategy with a Cauchy random walk to enhance global search ability. Second, an adaptive scaling factor is introduced in the algorithm's control parameters to achieve a better balance between exploration speed and accuracy. Third, a dynamic inertia weight is used to balance the search between global and local spaces when generating new nest positions after abandoning old ones. The performance of the ICSA‐based IPI approach is evaluated by comparing it with the original CSA‐based IPI and manual calibration in determining the HCA model parameters. A comprehensive analysis is also conducted to assess the effectiveness and superiority of each improvement strategy introduced in the ICSA over the original CSA. All comparisons demonstrate that the proposed ICSA‐based IPI method is more powerful and efficient in finding optimal parameters.
In this study, three empirical formulas—Hargreaves and Samani (HS, 1985), Priestley and Taylor (PT, 1972), and the World Meteorological Organization (WMO, 1966)—representing temperature-, solar radiation-, and mass-transfer-based approaches, respectively, were evaluated. To achieve this objective, meteorological data
from five synoptic stations situated in the Samsun province in the Black Sea region of Türkiye, were utilized.
Three methods, namely the traditional method, regression analysis, and genetic algorithm, were employed to estimate the local calibration coefficients of empirical equations based on the Penman-Monteith 56 equation. Finally, the outcomes were evaluated based on four criteria: root-mean-square error, coefficient of determination, mean bias error, and percentage error of estimate. T
District Cooling Systems are progressively becoming a standard feature of smart cities. This is attributed to their inherent feature of low operating cost and high energy efficiency. Given the constantly increasing energy prices worldwide and the target of the Conference of the Parties-28th Session for reducing emissions, the District Cooling System technology is quite promising in this direction. Various studies are available that have particularly focused on the design phase optimization of the systems, while in-process operational optimization is still in its miniature phase. This paper presents a model-based metaheuristic optimization approach to cooling water system towards an inceptive control strategy to explore and exploit the energy-saving potential using a Real Coded Genetic Algorithm. The Algorithm is implemented in MATLAB to search for high-performance settings in real-time scenarios. The results showed that an energy saving from 9.66% to 26.54% can be obtained across 6 cases in the study, compared to the supervisory control.
Practical application
District cooling technology is expected to gain more credibility as the most sustainable alternative to air conditioning in the upcoming decades due to the world’s rapidly expanding need for cooling combined with the need to reduce carbon dioxide emissions. The current research and development efforts are yielding promising results for the fifth generation of this technology. Meanwhile, the study validates the enormous potential of operational optimization with contemporary artificial intelligence tools. This paper paves the way for future research by showing how the operation of a large-scale district cooling plant can be solved for energy saving.
Real-Coded Genetic Algorithms (RCGAs) are a significant area of focus in evolutionary algorithm research. Structural bias (SB), a recently recognized attribute in metaheuristic algorithms, leads populations to repeatedly exploit specific region(s) of the search space without acquiring new information. This behavior not only escalates the computational cost but also slows the convergence rate. While recent studies have revealed an inclination toward the center of the search space in basic Genetic Algorithms (GA), similar investigations for RCGA variants remain unexplored. This study addresses this gap by examining the bias in popular and widely used crossovers and mutations in RCGAs. The BIAS toolbox, a recently developed tool, is used for a preliminary assessment of biases in these variants. Furthermore, GST, a simple yet effective methodology, is utilized for a more thorough analysis, quantifying, and scrutinizing biases in RCGA variations. The outcomes of this research aim to deepen our theoretical understanding of RCGAs, thus enhancing their practical applications and contributing to the future development of more equitable and unbiased algorithms.
This work presents an improved parallel biobjective hybrid real-coded genetic algorithm (MORCGA-MOPSO-II). The approach is based on the combined use of the parallel Multi-Objective Real-Coded Genetic Algorithm (MORCGA) and the Multi-Objective Particle Swarm Optimization (MOPSO). At the same time, clustering-based selection techniques are used to form subpopulations of parent individuals. Using well-known clustering algorithms (e.g., k-Means, hierarchical clustering, c-means, and DBSCAN) in combination with the proposed clustering-based mutation (the CL-mutation) directed toward the obtained cluster centers allows for improving the quality of the Pareto fronts’ approximations. The results of the MORCGA-MOPSO-II were compared with other well-known multi-objective evolutionary algorithms (e.g., SPEA2, NSGA-II, FCGA, MOSPO, etc.). Moreover, the MORCGA-MOPSO-II was integrated with the previously developed agent-based model of a goods exchange through the objective functions. As a result, the Pareto fronts have been obtained for the agent-based model of a goods exchange in different configurations of the initial distribution of agents.
As an environment-friendly and renewable energy source, biomethane plays a significant role in the supply of sustainable energy. To determine location of hubs, reactors and condensers and allocate feedstocks, biomethane and liquefied biomethane to these facilities in a biomethane production system by minimizing the supply chain cost, a mathematical model is developed in this article. Constraints, such as the limited workforce, the reactors’ demand on the residues, and the deterioration of the residues in the hubs are considered. Genetic algorithm for solving mixed integer nonlinear programming model is proposed. Genetic algorithm finds better solutions than Lingo when applied to the given problems but the speed of obtaining the solution is slower. Biomethane supply chain has been designed in Khorasan Razavi using the developed mathematical model and genetic algorithm.
A growing trend of introducing new metaheuristic algorithms and their improvements is observed with almost the same inherited weaknesses. The main reason is that a few studies have been performed to analyze the algorithms and their variants before improving them. This paper aims to review and analyze the moth-flame optimization (MFO) algorithm and its variants to show the structural reviewing, performance evaluation, and statistical analysis required before improving a metaheuristic algorithm. First, the MFO is described, and then its eligible variants are selected and reviewed in three categories: improved, hybrid, and adapted. Then, the outstanding developments of the eligible MFO variants are reviewed from a structural point of view. Next, to show the weaknesses and strengths of the MFO, its behavior, convergence, and balance ability are qualitatively analyzed. This paper quantitatively measures the performance of the MFO and its state-of-the-art variants. It also uses well-regarded criteria to conduct statistical tests among the algorithms. The results show that IMFO achieves the highest solution quality in dimensions 10 and 30, while m-DMFO achieves the highest in dimension 100. Overall, m-DMFO outperforms MFO and its state-of-the-art variants, with an overall effectiveness of 39.08%. Moreover, the results show that CMFO is the quickest MFO variant among the other algorithms regarding execution time. The findings of this study demonstrate that despite their claims, most MFO variants have not tackled the weaknesses and still inherently suffer from the same shortcomings. Thus, it is recommended to consider structural reviewing, performance evaluation, and statistical analysis performed in this study before improving other metaheuristic algorithms.
This paper aims to present the methods of independent variables selection into multiple linear regression equations. It provides details about the independent variable selection algorithms, advantages, and limitations of independent variable selection methods, and trends in studies and research related to the independent variable selection methods into regression equations. The independent variable selection methods can be divided into two groups of methods: the general group of methods that is widely used. In this paper, we will discuss only Stepwise Regression and the metaheuristic group of methods which in this paper will discuss only Tabu Search, Genetic Algorithm, and Simulated Annealing. Each method is suitable for use in different situations.
In the process planning of metal cutting operations, economic milling is attempted to achieve by obtaining optimal values of cutting parameters such as feed rate, cutting speed, and depth of cut that minimizes the total machining cost/time involved in the cutting process. Due to the nature of different machining operations and various constraints acting on machining processes, these considered machining models are non-convex and nonlinear in nature. The objective for all the considered models is of minimization type subject to various constraints. In the present work, the effect of employing a Real Coded Genetic Algorithm (RCGA) termed Laplace Crossover Power Mutation (LXPM) Genetic Algorithm for optimizing the machining parameters occurring in single and multi-pass turning is investigated. The numerical analysis demonstrates the efficiency of LXPM over other approaches by analyzing the results.KeywordsTurning operationOptimizationReal coded genetic algorithm
In this paper, we proposed simplex crossover (SPX), a multi-parent recombination operator for real-coded genetic algorithms. SPX generates offspring vector values by uniformly sampling values from simplex formed by m (2 ≤ m ≤ number of parameters + 1) parent vectors. The SPX features an independence from of coordinate systems. Experimental results using test functions, which are commonly used in studies of evolutionary algorithms, showed SPX works well on functions having multimodality and/or epistasis with a medium number of parents: 3-parent on a low dimensional function or 4 parents on high dimensional functions.
The incorporation of contemporary directed mutation techniques into traditional genetic algorithms has shown significant potential and garnered many promising results. While such findings are important, the utility of directed mutation in a generic sense is limited by either a reliance on domain specific knowledge or an increase in complexity with respect to both parameter size and the functions required for random number generation. Thus, this paper presents a new approach to mutation that utilises a co-evolving set of simple directions for each chromosome that dictate the result of gene mutations. In addition to biasing mutation towards promising areas of the search space, the Pointed Directed (PoD) mutation technique requires no increase in a priori information about the domain, nor does it come at a significant cost to system complexity. Moreover, results show that PoD mutation offers significant advantages over gaussian mutation across a range of complex problem areas, maximising performance by utilising adaptation to tune both directions and emergent system momentum.
We study five penalty function-based constraint handling techniques to be used with genetic algorithms in global optimization. Three of them, the method of superiority of feasible points, the method of parameter free penalties and the method of adaptive penalties have already been considered in the literature. In addition, we introduce two new modifications of these methods. We compare all the five methods numerically in 33 test problems and report and analyze the results obtained in terms of accuracy, efficiency and reliability. The method of adaptive penalties turned out to be most efficient while the method of parameter free penalties was the most reliable.
Genetic algorithms are adaptive methods based on natural evolution that may be used for search and optimization problems. They process a population of search space solutions with three operations: selection, crossover, and mutation. Under their initial formulation, the search space solutions are coded using the binary alphabet, however other coding types have been taken into account for the representation issue, such as real coding. The real-coding approach seems particularly natural when tackling optimization problems of parameters with variables in continuous domains.
A problem in the use of genetic algorithms is premature convergence, a premature stagnation of the search caused by the lack of population diversity. The mutation operator is the one responsible for the generation of diversity and therefore may be considered to be an important element in solving this problem. For the case of working under real coding, a solution involves the control, throughout the run, of the strength in which real genes are mutated, i.e., the step size.
This paper presents TRAMSS, a Two-loop Real-coded genetic algorithm with Adaptive control of Mutation Step Sizes. It adjusts the step size of a mutation operator applied during the inner loop, for producing efficient local tuning. It also controls the step size of a mutation operator used by a restart operator performed in the outer loop, for reinitializing the population in order to ensure that different promising search zones are focused by the inner loop throughout the run. Experimental results show that the proposal consistently outperforms other mechanisms presented for controlling mutation step sizes, offering two main advantages simultaneously, better reliability and accuracy.
In this paper, a computational algorithm, named RST2ANU algorithm, has been developed for solving integer and mixed integer global optimization problems. This algorithm, which primarily is based on the original controlled random search approach of Price [22i], incorporates a simulated annealing type acceptance criterion in its working so that not only downhill moves but also occasional uphill moves can be accepted. In its working it employs a special truncation procedure which not only ensures that the integer restrictions imposed on the decision variables are satisfied, but also creates greater possibilities for the search leading to a global optimal solution. The reliability and efficiency of the proposed RST2ANU algorithm has been demonstrated on thirty integer and mixed integer optimization problems taken from the literature. The performance of the algorithm has been compared with the performance of the corresponding purely controlled random search based algorithm as well as the standard simulated annealing algorithm. The performance of the method on mathematical models of three realistic problems has also been demonstrated.
In a canonical genetic algorithm, the reproduction operators (crossover and mutation) are random in nature. The direction of the search carried out by the GA system is driven purely by the bias to fitter individuals in the selection process. Several authors have proposed the use of directed mutation operators as a means of improving the convergence speed of GAs on problems involving real-valued alleles. This paper proposes a new approach to directed mutation based on the momentum concept commonly used to accelerate the gradient descent training of neural networks. This mutation-with- momentum operator is compared against standard Gaussian mutation across a series of benchmark problems, and is shown to regularly result in rapid improvements in performance during the early generations of the GA. A hybrid system combining the momentum-based and standard mutation operators is shown to outperform either individual approach to mutation across all of the benchmarks.
A new recombination operator, called fuzzy recombination (FR) is introduced for continuous genes. The performance of the operator is analyzed by means of the equation describing the response to selection. The operator is evaluated according to a new design criterion: maximizing the product of heritability and standard deviation. The breeder genetic algorithm BGA with FR converges linearly for a test suite of benchmark functions.
Evolutionary computation techniques have received a great deal of attention regarding their potential as optimization techniques for complex numerical functions. However, they have not produced a significant breakthrough in the area of nonlinear programming due to the fact that they have not addressed the issue of constraints in a systematic way. Only recently have several methods been proposed for handling nonlinear constraints by evolutionary algorithms for numerical optimization problems; however, these methods have several drawbacks, and the experimental results on many test cases have been disappointing.
In this paper we (1) discuss difficulties connected with solving the general nonlinear programming problem; (2) survey several approaches that have emerged in the evolutionary computation community; and (3) provide a set of 11 interesting test cases that may serve as a handy reference for future methods.
In this paper a new genetic algorithm called the Breeder Genetic Algorithm (BGA) is introduced. The BGA is based on artificial selection similar to that used by human breeders. A predictive model for the BGA is presented that is derived from quantitative genetics. The model is used to predict the behavior of the BGA for simple test functions. Different mutation schemes are compared by computing the expected progress to the solution. The numerical performance of the BGA is demonstrated on a test suite of multimodal functions. The number of function evaluations needed to locate the optimum scales only as n ln(n) where n is the number of parameters. Results up to n = 1000 are reported.
Abstract Three main streams of Evolutionary Algorithms (EAs), i.e. probabilistic optimization algorithms based on the model of natural evolution, are compared with each other in this article: Evolution Strategies (ESs), Evolu- tionary Programming (EP), and Genetic Algorithms (GAs). The comparisonis performed with respect to certain characteristic components of EAs, i.e. the representation scheme of object variables, mutation, recombination, and the selection operator. Furthermore, each algorithm is formulated in a high-level notation as an instance of the general, unifying basic algorithm, and the fundamental theoretical results on the algorithms are presented. Finally, after presenting experimental results for three test functions representing a unimodal and a multimodal case as well as a step function with discontinuities, similarities and differences of the algorithms are elaborated, and some hints to open research questionsare sketched.
Due to increasing interest in solving real-world optimization problems using evolutionary algorithms (EAs), researchers have recently developed a number of real-parameter genetic algorithms (GAs). In these studies, the main research effort is spent on developing an efficient recombination operator. Such recombination operators use probability distributions around the parent solutions to create an offspring. Some operators emphasize solutions at the center of mass of parents and some around the parents. In this paper, we propose a generic parent-centric recombination operator (PCX) and a steady-state, elite-preserving, scalable, and computationally fast population-alteration model (we call the G3 model). The performance of the G3 model with the PCX operator is investigated on three commonly used test problems and is compared with a number of evolutionary and classical optimization algorithms including other real-parameter GAs with the unimodal normal distribution crossover (UNDX) and the simplex crossover (SPX) operators, the correlated self-adaptive evolution strategy, the covariance matrix adaptation evolution strategy (CMA-ES), the differential evolution technique, and the quasi-Newton method. The proposed approach is found to consistently and reliably perform better than all other methods used in the study. A scale-up study with problem sizes up to 500 variables shows a polynomial computational complexity of the proposed approach. This extensive study clearly demonstrates the power of the proposed technique in tackling real-parameter optimization problems.
Despite the existence of a number of procedures for real-parameter optimization using evolutionary algorithms, there is still a need of a systematic and unbiased comparison of different approaches on a carefully chosen set of test problems. In this paper, we develop a steady-state, population-based optimization algorithm which allows the main search principles to be independently designed. The algorithm so developed is applied to a set of 25 test problems and results on 10 and 30 dimensions are presented. Although the proposed procedure cannot find the exact optimum within the specified number of function evaluations, in most problems, the algorithm shows steady progress towards the optimum. Moreover, it is also observed that the performance of the algorithm does not get affected by the rotation of the functions, discontinuity and embedded noise in function description
. The genetic algorithm behaviour is determined by the exploitation and exploration relationship kept throughout the run. Adaptive genetic algorithms have been built for inducing exploitation/exploration relationships that avoid the premature convergence problem and improve the final results. One of the most widely studied adaptive approaches are the adaptive parameter setting techniques. In this paper, we study these techniques in depth, based on the use of fuzzy logic controllers. Furthermore, we design and discuss an adaptive realcoded genetic algorithm based on the use of fuzzy logic controllers. Although suitable results have been obtained by using this type of adaptive technique, we report some reflections on open problems that still remain. Keywords. Exploitation/exploration relationship, adaptive genetic algorithms, fuzzy logic controllers. 1 Introduction GA behaviour is strongly determined by the balance between exploiting what already works best and exploring possibilities t...
This paper is concerned with the application of genetic algorithms to optimization problems over several real parameters. It is shown that k-point crossover (for k small relative to the number of parameters) can be viewed as a crossover operation on the vector of parameters plus perturbations of some of the parameters. Mutation can also be considered as a perturbation of some of the parameters. This suggests a genetic algorithm that uses real parameter vectors as chromosomes, real parameters as genes, and real numbers as alleles. Such an algorithm is proposed with two possible crossover methods. Schemata are defined for this algorithm, and it is shown that Holland's Schema theorem holds for one of these crossover methods. Experimental results are given that indicate that this algorithm with a mixture of the two crossover methods outperformed the binary-coded genetic algorithm on 7 of 9 test problems.
In this paper we show how a simple inheritance mechanism is capable of learning...
Genetic algorithms are adaptive methods which may be used as approximation heuristic for search and optimization problems. Genetic algorithms process a population of search space solutions with three operations: selection, crossover, and mutation. A great problem in the use of genetic algorithms is the premature convergence, a premature stagnation of the search caused by the lack of diversity in the population and a disproportionate relationship between exploitation and exploration. The crossover operator is considered one of the most determinant elements for solving this problem. In this article we present two types of crossover operators based on fuzzy connectives for real-coded genetic algorithms. The first type is designed to keep a suitable sequence between the exploration and the exploitation along the genetic algorithm's run, the dynamic fuzzy connectives-based crossover operators, the second, for generating offspring near to the best parents in order to offer diversity or convergence in a profi
This paper discusses the application of genetic algorithms to constrained optimiza-tion problems for convex continuous parameter spaces. We present a set of six genetic operators for GAs based on oating point representation. Various experi-ments indicate the importance of these operators at dierent stages of the evolution process.
The selection of the initial population in a population-based heuristic optimizationmethod is important, since it affects the search for several iterations and often has an influence on the final solution. If no a priori information about the optima is available, the initial population is often selected randomly using pseudorandom numbers. Usually, however, it is more important that the points are as evenly distributed as possible than that they imitate random points. In this paper, we study the use of quasi-random sequences in the initial population of a genetic algorithm. Sample points in a quasi-random sequence are designed to have good distribution properties. Here a modified genetic algorithm using quasi-random sequences in the initial population is tested by solving a large number of continuous benchmark problems from the literature. The numerical results of two implementations of genetic algorithms using different quasi-random sequences are compared to those of a traditional implementation using pseudorandom numbers. The results obtained are promising.
Self-adaption is one of the most promising areas of research in evolutionary computation as it adapts the algorithm to the problem while solving the problem. In this paper we extend self-adaption to operate on more than one aspect of evolutionary computation and at more than one level of adaption. We developed a genetic algorithm which selfadapts both mutation strength and population size; the results indicate that the approach works quite well.
This paper presents a real-coded genetic algorithm (RCGA) with new genetic operations (crossover and mutation). They are called the average-bound crossover and wavelet mutation. By introducing the proposed genetic operations, both the solution quality and stability are better than the RCGA with conventional genetic operations. A suite of benchmark test functions are used to evaluate the performance of the proposed algorithm. Application examples on economic load dispatch and tuning an associative-memory neural network are used to show the performance of the proposed RCGA.
In this paper, a new real coded crossover operator, called the Laplace Crossover (LX) is proposed. LX is used in conjunction with two well known mutation operators namely the Makinen, Periaux and Toivanen Mutation (MPTM) and Non-Uniform Mutation (NUM) to define two new generational genetic algorithms LX–MPTM and LX–NUM respectively. These two genetic algorithms are compared with two existing genetic algorithms (HX–MPTM and HX–NUM) which comprise of Heuristic Crossover operator and same two mutation operators. A set of 20 test problems available in the global optimization literature is used to test the performance of these four genetic algorithms. To judge the performance of the LX operator, two kinds of analysis is performed. Firstly a pair wise comparison is performed between LX–MPTM and HX–MPTM, and then between LX–NUM and HX–NUM. Secondly the overall comparison of performances of all the four genetic algorithms is carried out based on a performance index (PI). The comparative study shows that Laplace crossover (LX) performs quite well and one of the genetic algorithms defined (LX–MPTM) outperforms other genetic algorithms.
Evolutionary computation techniques have been receiving increasing attention regarding their potential as optimization techniques for complex problems. Recently these techniques were applied in the area of industrial engineering; the most-known applications include scheduling and sequencing in manufacturing systems, computer-aided design, facility layout and location problems, distribution and transportation problems, and many others. Industrial engineering problems usually are quite hard to solve due to a high complexity of the objective functions and a significant number of problem-specific constraints; often an algorithm to solve such problems requires incorporation of some heuristic methods. In this paper we concentrate on constraint handling heuristics for evolutionary computation techniques. This general discussion is followed by three test case studies: truss structure optimization problem, design of a composite laminated plate, and the unit commitment problem. These are typical highly constrained engineering problems and the methods discussed here are directly transferrable to industrial engineering problems.
Genetic Algorithms are a class of powerful, robust search techniques based on genetic inheritance and the Darwinian metaphor of “Natural Selection”. These algorithms maintain a finite memory of individual points on the search landscape known as the “population”. Members of the population are usually represented as strings written over some fixed alphabet, each of which has a scalar value attached to it reflecting its quality or “fitness”. The search may be seen as the iterative application of a number of operators, such as selection, recombination and mutation, to the population with the aim of producing progressively fitter individuals.
These operators are usually static, that is to say that their mechanisms, parameters, and probability of application are fixed at the beginning and constant throughout the run of the algorithm. However, there is an increasing body of evidence that not only is there no single choice of operators which is optimal for all problems, but that in fact the optimal choice of operators for a given problem will be time-variant i.e. it will depend on such factors as the degree of convergence of the population. Based on theoretical and practical approaches, a number of authors have proposed methods of adaptively controlling one or more of the operators, usually invoking some kind of “meta-learning” algorithm, in order to try and improve the performance of the Genetic Algorithm as a function optimiser.
In this paper we describe the background to these approaches, and suggest a framework for their classification, based on the learning strategy used to control them, and what facets of the algorithm are susceptible to adaptation. We then review a number of significant pieces of work within the context of this setting, and draw some conclusions about the relative merits of various approaches and promising directions for future work.
In this paper we introduce interval-schemata as a tool for analyzing real-coded genetic algorithms (GAs). We show how interval-schemata are analogous to Holland's symbol-schemata and provide a key to understanding the implicit parallelism of real-valued GAs. We also show how they support the intuition that real-coded GAs should have an advantage over binary coded GAs in exploiting local continuities in function optimization. On the basis of our analysis we predict some failure modes for real-coded GAs using several different crossover operators and present some experimental results that support these predictions. We also introduce a crossover operator for real-coded GAs that is able to avoid some of these failure modes.
Thesis (Ph. D.)--University of Michigan, 1975. Includes bibliographical references (leaves 253-256). Photocopy.
David Goldberg's Genetic Algorithms in Search, Optimization and Machine Learning is by far the bestselling introduction to genetic algorithms. Goldberg is one of the preeminent researchers in the field--he has published over 100 research articles on genetic algorithms and is a student of John Holland, the father of genetic algorithms--and his deep understanding of the material shines through. The book contains a complete listing of a simple genetic algorithm in Pascal, which C programmers can easily understand. The book covers all of the important topics in the field, including crossover, mutation, classifier systems, and fitness scaling, giving a novice with a computer science background enough information to implement a genetic algorithm and describe genetic algorithms to a friend.
The unimodal normal distribution crossover (UNDX) for the
real-coded genetic algorithms (RCGA) proposed by Ono et al. (1997, 1998)
shows an excellent performance in optimization problems of multi-modal
and highly epistatic fitness functions in continuous search space.
Further, theoretical analysis of the UNDX shows that the UNDX is a
crossover operator that preserves the statistics such as the mean vector
and the covariance matrix of the population well. The present paper
proposes some design guidelines for crossover operators for RCGA. Then,
based on these guidelines, a multi-parental extension of the UNDX is
proposed so as to enhance its exploration ability. Performance of the
extended UNDX is evaluated by numerical experiments
By considering the function variables rather than the binary-bits
as genes, new mutation operators can be devised for GAs used to optimise
numeric functions. We implement Gaussian mutation operators for genetic
algorithms used to optimise numeric functions and show it is superior to
bit-flip mutation for most of the test functions. Gaussian mutation is a
fundamental operator of both evolutionary strategies (ES) and
evolutionary programming (EP). We also implement self-adaptive Gaussian
mutation (also used in evolutionary strategies and evolutionary
programming) which allows the GA to vary the mutation strength during
the run, this gives further improvement on some of the functions. The
performance of our GA using a simple implementation of self-adaptive
Gaussian mutation is now comparable to ESs. This shows the importance of
mutation and the importance of using appropriate mutation
operators
With this paper modal mutation schemes for evolutionary algorithms
as a generalization of the breeder genetic algorithm mutation scheme are
introduced and analyzed for multimodal continuous parameter optimization
problems. A new scaling rule for multiple mutations is formalized and
compared with a new step-size scaling for evolution strategies. A
performance comparison of the multivalued evolutionary algorithm with
modal mutations with recently published results concerning the
performance of Bayesian/sampling and very fast simulated reannealing
techniques for global optimization is given
The conventional understanding of genetic algorithms depends upon analysis by schemata and the notion of intrinsic parallelism. For this reason, only k-ary string representations have had any formal basis and non-standard representations and operators have been regarded largely as heuristics, rather than principled algorithms. This paper extends the analysis to general representations through identification of schemata as equivalence classes induced by implicit equivalence relations over the space of chromosomes.
This paper presents a theory of convergence for real-coded genetic algorithms---GAs that use floating-point or other high-cardinality codings in their chromosomes. The theory is consistent with the theory of schemata and postulates that selection dominates early GA performance and restricts subsequent search to intervals with above-average function value, dimension by dimension. These intervals may be further subdivided on the basis of their attraction under genetic hillclimbing. Each of these subintervals is called a virtual character, and the collection of characters along a given dimension is called a virtual alphabet. It is the virtual alphabet that is searched during the recombinative phase of the genetic algorithm, and in many problems this is sufficient to ensure that good solutions are found. Although the theory helps suggest why many problems have been solved using real-coded GAs, it also suggests that real-coded GAs can be blocked from further progress in those situations whe...
This paper introduces a new method of performing mutation in a real-coded Genetic Algorithm (GA), a method driven by Principal Component Analysis (PCA). We present both theoretical and empirical results which show that our mutation operator attains higher levels of diversity in the search space, as compared to other mutation operators, meaning that by employing our mutation operator we maintain diverse populations that increase the chances of finding better solutions during evolution of the GA. The performances of the real-coded GA with PCAmutation were checked on the problem of designing IIR filters by Deczky method, which is a well known direct design method of IIR filters. Results obtained show that our PCA-mutation GA has been more successful in keeping diverse populations during search, the consequence being the finding of better solutions to the filter design problem, compared to solutions found using GA with classical mutation operators. 1. INTRODUCTION Genetic Algorithms (GAs)...
Self-adaption is one of the most promising areas of research in evolutionary computation as it adapts the algorithm to the problem while solving the problem. In this paper we extend self-adaption to operate on more than one aspect of evolutionary computation and at more than one level of adaption. We developed a genetic algorithm which self-adapts both mutation strength and population size; the results indicate that the approach works quite well. 1 Introduction Since evolutionary algorithms implement the idea of evolution, it is more than natural to expect some self-adapting characteristics of these techniques. Apart from evolutionary strategies, which incorporate some of its control parameters in the solution vectors, most other techniques use fixed representations, operators, and control parameters. Some of the promising research areas based on the inclusion of self adapting mechanisms are: ffl representation of individuals (as proposed by Shaefer (1987); the Dynamic Parameter Enco...
this paper, an approximation for the Pareto set of optimal solutions is obtained by using a genetic algorithm (GA). The first objective function is the drag coefficient. As a constraint, it is required that the lift coefficient is above a given value. The CFD analysis solver is based on the finite volume discretization of the inviscid Euler equations. The second objective function is equivalent to the integral of the transverse magnetic radar cross section (RCS) over a given sector. The computational electromagnetics (CEM) wave field analysis requires the solution of a two-dimensional Helmholtz equation which is obtained using a fictitious domain method. Numerical experiments illustrate the above evolutionary methodology on an IBM SP2 parallel computer. c fl ??? John Wiley & Sons, Inc.
Genetic algorithms rely on two genetic operators - crossover and mutation. Although there exists a large body of conventional wisdom concerning the roles of crossover and mutation, these roles have not been captured in a theoretical fashion. For example, it has never been theoretically shown that mutation is in some sense "less powerful" than crossover or vice versa. This paper provides some answers to these questions by theoretically demonstrating that there are some important characteristics of each operator that are not captured by the other.
During the last two years several methods have been proposed for handling constraints by genetic algorithms for numerical optimization problems. In this paper we review these methods, test them on five selected problems, and discuss their strengths and weaknesses.
The success of binary-coded genetic algorithms (GAs) in problems having discrete search space largely depends on the coding used to represent the problem variables and on the crossover operator that propagates building-blocks from parent strings to children strings. In solving optimization problems having continuous search space, binary-coded GAs discretize the search space by using a coding of the problem variables in binary strings. However, the coding of real-valued variables in finite-length strings causes a number of difficulties---inability to achieve arbitrary precision in the obtained solution, fixed mapping of problem variables, inherent Hamming cliff problem associated with the binary coding, and processing of Holland's schemata in continuous search space. Although, a number of real-coded GAs are developed to solve optimization problems having a continuous search space, the search powers of these crossover operators are not adequate. In this paper, the search power...
Controlled random search technique and their applications
- Bharti
Bharti, Controlled random search technique and their applications. Ph.D. Thesis. Department of Mathematics, University of Roorkee, Roorkee, India, 1994.