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Multiple Objective Optimization with Vector Evaluated Genetic Algorithms.
... To verify the effectiveness of NSICA, we selected some multiobjective test problems from several significant past studies in this area, which we have described in Table 1. We used the hypervolume [28] indicator as the performance criterion in this subsection. The hypervolume indicator appeals to researchers because it is compatible with multiple objectives, does not require prior knowledge of the actual Pareto-optimal front, and can be used as both proximity and diversity metric without the need for separate calculations. ...
... Objective Functions Variable Bounds n SCH [28] f1 Old anterior myocardial infarction 15 04 ...
This study proposes a multi-objective, non-dominated, imperialist competitive algorithm (NSICA) to solve optimal feature selection problems. The NSICA is a multi-objective and discrete version of the original Imperialist Competitive Algorithm (ICA) that utilizes the competition between colonies and imperialists to solve optimization problems. This study focused on solving challenges such as discretization and elitism by modifying the original operations and using a non-dominated sorting approach. The proposed algorithm is independent of the application, and with customization, it could be employed to solve any feature selection problem. We evaluated the algorithm's efficiency using it as a feature selection system for diagnosing cardiac arrhythmias. The Pareto optimal selected features from NSICA were utilized to classify arrhythmias in binary and multi-class forms based on three essential objectives: accuracy, number of features, and false negativity. We applied NSICA to an ECG-based arrhythmia classification dataset from the UCI machine learning repository. The evaluation results indicate the efficiency of the proposed algorithm compared to other state-of-the-art algorithms.
... A multi-objective optimization algorithm refers to an algorithm used to solve multi-objective optimization problems. Schaffer [29] proposed an algorithm based on vector evaluation to solve related multi-objective optimization problems, which is the first time that an evolutionary algorithm has been applied to the field of multi-objective optimization. Then, more and more researchers became able to solve the multi-objective optimization problem based on evolutionary algorithms. ...
Inter-domain routing systems are important complex networks on the Internet. It has been paralyzed several times in recent years. The researchers pay close attention to the damage strategy of inter-domain routing systems and think it is related to the attacker's behavior. The key to the damage strategy is knowing how to select the optimal attack node group. In the process of selecting nodes, the existing research seldom considers the attack cost, and there are some problems, such as an unreasonable definition of attack cost and an unclear optimization effect. To solve the above problems, we designed an algorithm to generate damage strategies for inter-domain routing systems based on multi-objective optimization (PMT). We transformed the damage strategy problem into a double-objective optimization problem and defined the attack cost related to the degree of nonlinearity. In PMT, we proposed an initialization strategy based on a network partition and a node replacement strategy based on partition search. Compared with the existing five algorithms, the experimental results proved the effectiveness and accuracy of PMT.
... Genetic Algorithm (VEGA), was the first algorithm created to deal with MOPs (Schaffer, 1984). After this, many other derivations attempting to offer improvements were developed: (i) the Vector Optimized Evolution Strategy (VOES) (Kursawe, 1991), (ii) the Lexigraphic ...
In order to solve challenging engineering problems, the state‐of‐the‐art in multi‐objective optimization shows a trend toward using meta‐heuristics and a posteriori decision‐making methods. This encourages the search for algorithms better able to find Pareto fronts with more convergence, coverage, and lower computational cost. This work shows the creation and validation of the Multi‐objective Sunflower Optimization (MOSFO), a hypercubic and constrained multi‐objective meta‐heuristic inspired by the phototropic life cycle of sunflowers around the sun. Having a much simpler programming model than most evolutionary algorithms, MOSFO was validated using the most difficult set of test functions in the literature (CEC 2009) and applied to ten constrained multi‐objective optimization problems (CEC 2021). The proposed algorithm was compared with ten other powerful algorithms: MOGWO, MOPSO, NSGA‐II, MOEA/D, NSGA‐III, CCMO, ARMOEA, ToP, TiGE 2, and AnD. Inverted General Distance, Spacing, Maximum Spread, and Hyper volume were used as comparison metrics to evaluate the convergence and coverage capabilities of the algorithms. MOSFO had the best average IGD value in 8 of the 10 test functions when compared with the other algorithms. In terms of MS, MOSFO had the highest average value of MS for 7 of the test functions. In summary, MOSFO showed substantial convergence and coverage capabilities and proved to be very competitive among the algorithms used, which were carefully selected to be popular and recent. The method is even more promising for problems with three or more objectives.
... These methods perform poorly on the Pareto-optimality since only a single optimal solution can be found in each simulation run. To obtain different trade-off solutions and provide flexibility in decision making, many multi-objective optimization evolutionary algorithms (MOEAs) have been proposed (Schaffer 1985). Collectively, there are about three kinds of MOEAs, namely the Pareto-based MOEAs, the decomposition-based MOEAs, and the performance indicator-based MOEAs (He et al 2017). ...
We study a multi-user multiple-input single-output downlink system aided by a reconfigurable intelligent surface (RIS). Users’ sum rate and transmit power are two important performance indicators in such systems. However, most existing works only optimize one of them, resulting in severe performance degradation of the other. Motivated by this, in this paper, we formulate a multi-objective optimization problem to maximize the sum rate of users and minimize the transmit power simultaneously. According to our early work on fitness landscape analysis of sum rate maximization problems, the proposed problem is inferred to be multi-modal. To solve this non-convex and multi-modal problem, we propose a novel multi-objective evolutionary hybrid beamforming (MEHB) framework to find different trade-off solutions between the two conflicting objectives. In particular, we employ different kinds of multi-objective evolutionary algorithms and multi-modal multi-objective evolutionary algorithms as the baseline of MEHB framework, so as to design the passive beamforming. And the active beamforming at the base station is optimized by the classical zero-forcing method. The simulation results have verified the effectiveness of the dominance-based evolutionary algorithms in handling hybrid beamforming problems.
... GA is an algorithm for searching optimized solutions that draws on natural selection and genetic mechanisms in biology, and outperforms traditional mathematical optimization algorithms such as linear programming, nonlinear programming and stochastic dynamic programming in terms of convergence speed, diversity of solution set space and optimality seeking ability, and is the first evolutionary algorithm applied to the field of optimized operation (Wang et al. 2022). The first generation of GAs is the Vector Evaluated Genetic Algorithm (VEGA) (Schaffer 1985), which evaluates each subpopulation for different objectives and enables the first application of genetic algorithms to multi-objective optimization problems. However, VEGA is prone to converge on solutions that are particularly good on one objective but poor on others. ...
The main objective of most hydropower systems is to pursue the efficient use of water resources and maximize economic benefits. At the same time the protection of ecological environment should not be neglected. In this study, a coordination model of power generation and ecological flow for the operation of cascade hydropower system was first established using a multi-objective optimization method. Multi-objective genetic algorithms (MOGAs) are widely used to solve such multi-objective optimization problems because of their excellent performance in terms of convergence speed, diversity of solution set space and optimality seeking ability. However, the adaptability of MOGAs to a particular optimized operation problem sometimes varies widely. It is of great significance to investigate the adaptability of different algorithms for a new optimized operation problem and to recommend a more suitable solution algorithm. Three MOGAs namely NSGA-II, NSGA-III and RVEA are selected to solve the proposed optimized operation model. Numerical experiments were conducted to evaluate the performance of the algorithms using real-world data from a cascade hydropower system located in the lower Yalong River. The results show that the Pareto fronts corresponding to NSGA-II and NSGA-III significantly dominate the Pareto fronts corresponding to the RVEA. The Pareto fronts corresponding to the NSGA-III algorithm are slightly better than those of NSGA-II. In terms of the four performance metrics, NSGA-III has certain advantages over NSGA-II and RVEA. NSGA-III is recommended as the solution algorithm for the established coordination model of power generation and ecological flow.
... These research methods all need to set complex weights. In order to avoid the above problems, NSGA-II and its improved algorithm [17][18][19][20][21][22][23][24][25], as a solution to the multi-objective optimization problem, have successfully solved the multi-objective optimization problem in several research fields. However, there are few related researches in the field of online learning resource recommendation. ...
Due to the characteristics of online learning resource recommendation such as large scale, uneven quality and diversity of preferences, how to accurately obtain various personalized learning resource lists has become an urgent problem to be solved in the field of online learning resource recommendation. This paper proposes an online learning resource recommendation model based on the improved NSGA-Ⅱ algorithm, which integrates the Tabu search algorithm to improve the local search ability of NSGA-Ⅱ algorithm. It takes background fitness, cognitive fitness and diversity as the objective functions for optimization. The dynamic updating of crowding degree is used to avoid the risk that the individuals with low crowding degree in the same area are deleted at the same time. Meanwhile, an adaptive genetic algorithm is applied to assign the optimal crossover rate and the mutation rate according to individual adaptability level, which ensures the convergence of genetic algorithm and the diversity of population. The experimental results show that the proposed model is superior to the traditional recommendation algorithm in terms of accuracy index, mean fitness, recall rate, F1 mean, HV, GD and IGD, etc., thus verifying the feasibility and effectiveness of the algorithm.
... Further, various standard test functions, considered in this paper for the evaluation of proposed approaches. Test functions, ZDTi (i = 1, 2, 3, 4, 6) [57], SCH [49], FON [22], and KUR [36] are unconstrained optimization problems, whereas BINH2 [59], CEX [16], OZY [45], and TNK [51] are optimization problems subjected to constraints. 3. Quality Indicators: Multi-objective optimization algorithms are quantitatively analyzed by considering two factors. ...
The presence of RF components in mixed-signal circuits make it a challenging task to resolve tradeoffs among performance specifications. In order to ease the process of circuit design, these tradeoffs are being analyzed using multi-objective optimization methodologies. This paper presents a hybrid multi-objective optimization framework (MHPSO), a combination of particle swarm optimization and simulated annealing. The framework emphasizes on preserving nondominated solutions in an external archive. The multi-dimensional space excluding the archive is divided into several sub-spaces according to a velocity-temperature mapping scheme. Further, the solutions in each sub-space are optimized using simulated annealing for generation of a Pareto front. The framework is extended by incorporating crowding distance comparison operator (MHPSO-CD) to maintain nondominated solutions in the archive. The effectiveness of proposed methodologies is demonstrated for performance space exploration of three electronic circuits, i.e., a two-stage operational amplifier, a folded cascode operational amplifier, and a low noise amplifier with inductive source degeneration. Additionally, the performance of proposed algorithms (MHPSO, MHPSO-CD) are evaluated on various test functions, and the results are compared with standard multi-objective evolutionary algorithms.
div class="section abstract"> Further advancing key technologies requires the optimization of increasingly complex systems with strongly interacting parameters—like efficiency optimization in engine development for optimizing the use of energy. Systematic optimization approaches based on metamodels, so-called Metamodel-Based Design Optimization (MBDO), present one key solution to these demanding problems. Recent advanced methods either focus on Single-Objective Optimization (SoO) on local metamodels with online adaptivity or Multiobjective Optimization (MoO) on global metamodels with only limited adaptivity. In the scope of this work, a fully online adaptive (“in the loop”) optimization approach, capable of both SoO and MoO, is developed which automatically approximates the global system response and determines the (Pareto) optimum. A combination of a new Design of Experiment (DoE) method for sampling points, Neural Networks as metamodel/Response Surface Model (RSM), and a Genetic Algorithm (GA) for global optimization performed on the RSM enables very high flexibility. Key features of the presented MBDO methodology are as follows: A new fully online, adaptive approach working in iterative loops combined with successive refinements of the RSM; Two novel boundary treatment approaches for handling arbitrarily complex constraints; A novel approach to automatically adapt the number of neurons of the Neural Network to the system complexity; An innovative uncertainty-based DoE method to maximize information gain for each new sample point; Comprehensive additional sampling strategies. Detailed benchmarks to popular DoE methods and MBDO approaches from the literature are conducted. The benchmarks show comparable to slightly better performance to current state-of-the-art SoO MBDO approaches with the significant benefit that a global RSM is obtained, providing valuable insight into the system behavior. Compared to state-of-the-art MoO MBDO approaches, the benchmark highlights a considerably better performance in terms of the needed number of samples (i.e., simulations or experiments), significantly fewer resources required, and high accuracy approximation of the Pareto front.
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