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Nondominated sorting and diversity estimation procedures are an essential part of many multiobjective optimization algorithms. In many cases these procedures are the com-putational bottleneck of the entire algorithm. We present the methods to decrease the cost of these procedures for multiobjective differential evolution (DE) algorithms. Our approa...
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... Big O Notation is one of the most necessary mathematical notations used in computer science to measure an algorithm's efficiency. Big O notation represents the upper bound running time complexity of an algorithm and can be used to describe the worst-case scenario of an algorithm (Drozdik et al., 2013). In this study, the computational complexity of the proposed algorithms is analyzed by the Big O notation (Nopiah et al., 2010;Yahia et al., 2020;Wardoyo and Afifa, 2018;Drozdik et al., 2013). ...
... Big O notation represents the upper bound running time complexity of an algorithm and can be used to describe the worst-case scenario of an algorithm (Drozdik et al., 2013). In this study, the computational complexity of the proposed algorithms is analyzed by the Big O notation (Nopiah et al., 2010;Yahia et al., 2020;Wardoyo and Afifa, 2018;Drozdik et al., 2013). Moreover, the Total Running Time (T( )) of the proposed algorithms for estimating the DSR in the study area has been evaluated and presented in Table 8. ...
Accurate estimating the solar radiation (SR) in a region is an essential issue in hydrological studies, energy engineering, architecture, and agricultural planning. In the current study, the conventional multiple linear regression (MLR), multilayer perceptron neural network (MLPNN), and adaptive neuro-fuzzy inference system (ANFIS) improved using evolutionary algorithms, the particle swarm optimization algorithm (PSO), differential evolution (DE), ant colony optimization for continuous domains (ACOR), and genetic algorithm (GA), as well as three different ensemble techniques, including simple average ensemble (SAE), weighted average ensemble (WAE), and neural network ensemble (NNE) were applied to model daily solar radiation (DSR) in Belleville station in Illinois, USA. For this purpose, the DSR data for eleven stations collected from 2015 to 2019 were obtained from ISWS (the Institute of Illinois State Water Survey). Seven models were then run using three distinct input datasets to estimate the DSR in the study area. The findings indicated that the evolutionary algorithms are significantly effective in boosting the performance of the ANFIS model when the number of inputs increases. It was also found that ensemble methods can improve the performance of the single models in estimating daily solar radiation. Overall, the results indicated that the ANFIS-GA had the best performance for the selected inputs (R2=0.947, RMSE=2.010 (MJ m−2 day −1), MAPE=15.61, NSE=0.947). The results of the complexity analysis showed that although the ANFIS-GA algorithm had the highest accuracy in estimating daily solar radiation in the study area, it has more complexity than ANFIS-PSO and ANFIS-DE algorithms.
... In this algorithm, a new acceptance function based on a probability computation is used to utilize simulated annealing for better guiding the search towards better regions. Another technique that aims at reducing the complexity of multiobjective differential evolution by computing the domination ranks and crowding distance is presented in Drozdik (2014). A memetic search that used probabilistic solution principles in the differential evolution algorithm is introduced in Kumar et al. (2014). ...
Developing efficient algorithms for solving multi-objective optimization problems is a challenging and essential task in many applications. This task involves two or more conflicting objectives that need to be simultaneously optimized. Many real-world problems fall into this category. We introduce an improved version of multi-objective differential evolution (DE) algorithm, namely MOnDE that uses a new mutation strategy and a normalization method to select non-dominated solutions. The new mutation strategy “DE/rand-to-nbest” uses the best normalized individual in terms of all the objectives to guide the search towards the true pareto optimal solutions. As a result, the probability of producing superior solutions is increased and a faster convergence is achieved. Summation of normalized objective values method is used instead of non-domination sorting to overcome the high computational complexity and overhead problems of sorting non-dominated solutions. The performance of our approach is tested on a set of benchmark problems that consist of two to five objectives. Different combinations of multi-objective evolutionary programming and multi-objective differential evolution algorithms have been used for comparisons. The results affirm the efficiency and robustness of the proposed approach among other well-known algorithms from the literature.
... These operations do not affect the computational complexity between RCGA and MRGA. For DE, its computational complexity is ( + + ( + )) where all the notations are described above [29]. Therefore, MABC has the same complexity as that of the original ABC. ...
The modernization of smart devices has emerged in exponential growth in data traffic for a high-capacity wireless network. 5G networks must be capable of handling the excessive stress associated with resource allocation methods for its successful deployment. We also need to take care of the problem of causing energy consumption during the dense deployment process. The dense deployment results in severe power consumption because of fulfilling the demands of the increasing traffic load accommodated by base stations. This paper proposes an improved Artificial Bee Colony (ABC) algorithm which uses the set of variables such as the transmission power and location of each base station (BS) to improve the accuracy of localization of a user equipment (UE) for the efficient energy consumption at BSes. To estimate the optimal configuration of BSes and reduce the power requirement of connected UEs, we enhanced the ABC algorithm, which is named a Modified ABC (MABC) algorithm, and compared it with the latest work on Real-Coded Genetic Algorithm (RCGA) and Differential Evolution (DE) algorithm. The proposed algorithm not only determines the optimal coverage of underutilized BSes but also optimizes the power utilization considering the green networks. The performance comparisons of the modified algorithms were conducted to show that the proposed approach has better effectiveness than the legacy algorithms, ABC, RCGA, and DE.
... These operations do not affect the computational complexity between RCGA and MRGA. For DE, its computational complexity is ( + + ( + )) where all the notations are described above [29]. Therefore, MABC has the same complexity as that of the original ABC. ...
The exponential growth in data traffic due to the modernization of smart devices has resulted in the need for a high-capacity wireless network in the future. To successfully deploy 5G network, it must be capable of handling the growth in the data traffic. The increasing amount of traffic volume puts excessive stress on the important factors of the resource allocation methods such as scalability and throughput. In this paper, we define a network planning as an optimization problem with the decision variables such as transmission power and transmitter (BS) location in 5G networks. The decision variables lent themselves to interesting implementation using several heuristic approaches, such as differential evolution (DE) algorithm and Real-coded Genetic Algorithm (RGA). The key contribution of this paper is that we modified RGA-based method to find the optimal configuration of BSs not only by just offering an optimal coverage of underutilized BSs but also by optimizing the amounts of power consumption. A comparison is also carried out to evaluate the performance of the conventional approach of DE and standard RGA with our modified RGA approach. The experimental results showed that our modified RGA can find the optimal configuration of 5G/LTE network planning problems, which is better performed than DE and standard RGA.
... In addition, even if the hypervolume could be computed fast, there would still be the need to determine the non-dominated individuals because the hypervolume is computed from them. This paper is a significant revision and extension of our previous work [1], in which we were restricted to differential evolution [16] algorithms. In this work we generalize our method to any multi-objective evolutionary algorithm (MOEA) which uses non-dominated sorting. ...
... (4) This definition is slightly more strict than in our previous work [1]. We can see an illustration of both upper and lower reference areas for several different choices of reference individual in Fig. 8. ...
... There is also no mechanism for fast insertion in logarithmic time such as with RB trees or skip-lists. This is again a slight modification to our previous work [1] where we used skip-lists. In order to remove or insert an individual into these lists while maintaining the ordering we use an alternative mechanism. ...
Many multi-objective evolutionary algorithms rely on the non-dominated sorting procedure to determine the relative quality of individuals with respect to the population. In this paper we propose a new method to decrease the cost of this procedure. Our approach is to determine the non-dominated individuals at the start of the evolutionary algorithm run and to update this knowledge as the population changes. In order to do this efficiently we propose a special data structure called the M-front, to hold the non-dominated part of the population. The M-front uses the geometric and algebraic properties of the Pareto dominance relation to convert orthogonal range queries into interval queries using a mechanism based on the nearest neighbor search. These interval queries are answered using dynamically sorted linked lists. Experimental results show that our method can perform significantly faster than the state of the art Jensen-Fortin’s algorithm, especially in many-objective scenarios. A significant advantage of our approach is that if we change a single individual in the population we still know which individuals are dominated and which are not.
Missing data are a major problem that affects data analysis techniques for forecasting. Traditional methods suffer from poor performance in predicting missing values using simple techniques, e.g., mean and mode. In this paper, we present and discuss a novel method of imputing missing values semantically with the use of an ontology model. We make three new contributions to the field: first, an improvement in the efficiency of predicting missing data utilizing Particle Swarm Optimization (PSO), which is applied to the numerical data cleansing problem, with the performance of PSO being enhanced using K-means to help determine the fitness value. Second, the incorporation of an ontology with PSO for the purpose of narrowing the search space, to make PSO provide greater accuracy in predicting numerical missing values while quickly converging on the answer. Third, the facilitation of a framework to substitute nominal data that are lost from the dataset using the relationships of concepts and a reasoning mechanism concerning the knowledge-based model. The experimental results indicated that the proposed method could estimate missing data more efficiently and with less chance of error than conventional methods, as measured by the root mean square error.
The complexity of multi-objective evolutionary algorithms based on the non-dominated principles mainly depends on finding non-dominated fronts. In order to reduce complexity and improve construction efficiency, this paper introduces a non-dominated set construction algorithm based on Two Dimensional Sequence (TSNS). When the non-dominated set closes to the Pareto optimal front, it always maintains one dimension by ascending order while the other dimension by descending order. In order to verify the effectiveness of the proposed algorithm, we integrate the algorithm into GA, DE, PSO, then we tested and compared it with classical benchmark functions. The experimental results indicate that the proposed algorithm performs better than NSGA-II in terms of the quality of solutions and the speed of convergence.
In cellular network cost involved in location management is higher but this issue is more common, crucial and complex problem. Although location management issues have been emerged in the field of communications no specific definition has been devised for it. Wireless network area is usually consisting of location area and paging area. The cost involved when a mobile subscriber moving in a particular service area. Since during a call the exact location of the subscriber must be known to the network the management of the network is to track the subscriber when a call comes to mobile device. For the same some cost is incurred that is location update cost and paging cost of the subscriber during the movement in a location service area. This study proposes a new evolutionary approach named Binary Differential Evolution (BDE) minimizes the total cost involved in wireless network. This technique is a stochastic, population-based optimization strategy proposed for combinatorial optimization problem to solve the location management issue. Here the given cellular network is partitioned into reporting cell and non-reporting cell so as to optimize the location area of a given cellular area. BDE is a meta-heuristic strategy presented to be a very powerful widely used technique based on evolutionary algorithms with some specific characteristics. Among the various evolutionary strategies BDE is one of the biological global optimization approach with reduced complexity has received a wide attraction from many fields such as computer science, economics and engineering fields. With the help of the realistic data for generating the test network simulation are carried out in different networks and the results are demonstrated and discussed in this work. The objective of this work is to define the best values to the Differential Evolution (DE) configuration by considering various parameters using realistic network.
