multi -modalmulti -objective problems (MMOPs) have gained much attention during the last decade. These problems have two or more global or local Pareto optimal sets (PSs), some of which map to the same Pareto front (...
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multi -modalmulti -objective problems (MMOPs) have gained much attention during the last decade. These problems have two or more global or local Pareto optimal sets (PSs), some of which map to the same Pareto front (PF). This article presents a new affinity propagation clustering (APC) method based on the multi -modalmultiobjective differential evolution (MMODE) algorithm, called MMODE_AP, for the suit of CEC'2020 benchmark functions. First, two adaptive mutation strategies are adopted to balance exploration and exploitation and improve the diversity in the evolution process. Then, the affinity propagation clustering method is adopted to define the crowding degree in decision space (DS) and objective space (OS). Meanwhile, the non -dominated sorting scheme incorporates a particular crowding distance to truncate the population during the environmental selection process, which can obtain welldistributed solutions in both DS and OS. Moreover, the local PF membership of the solution is defined, and a predefined parameter is introduced to maintain of the local PSs and solutions around the global PS. Finally, the proposed algorithm is implemented on the suit of CEC'2020 benchmark functions for comparison with some MMODE algorithms. According to the experimental study results, the proposed MMODE_AP algorithm has about 20 better performance results on benchmark functions compared to its competitors in terms of reciprocal of Pareto sets proximity (rPSP), inverted generational distances (IGD) in the decision (IGDX) and objective (IGDF). The proposed algorithm can efficiently achieve the two goals, i.e., the convergence to the true local and global Pareto fronts along with better distributed Pareto solutions on the Pareto fronts.
Even if a multi-modalmulti-objective Evolutionary Algorithm (MMOEA) is designed to find solutions well spread over all locally optimal approximation sets of a multi-modal multi-objective optimization Problem (MMOP), ...
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ISBN:
(纸本)9783031147210;9783031147203
Even if a multi-modalmulti-objective Evolutionary Algorithm (MMOEA) is designed to find solutions well spread over all locally optimal approximation sets of a multi-modal multi-objective optimization Problem (MMOP), there is a risk that the found set of solutions is not smoothly navigable because the solutions belong to various niches, reducing the insight for decision makers. To tackle this issue, a new MMOEAs is proposed: the multi-modal Bezier Evolutionary Algorithm (MM-BezEA), which produces approximation sets that cover individual niches and exhibit inherent decision-space smoothness as they are parameterized by Bezier curves. MM-BezEA combines the concepts behind the recently introduced BezEA and MO-HillVallEA to find all locally optimal approximation sets. When benchmarked against the MMOEAs MO Ring PSO SCD and MO-HillVallEA on MMOPs with linear Pareto sets, MM-BezEA was found to perform best in terms of best hypervolume.
In this paper, the mathematical model of Vehicle Routing Problem with Time Windows (VRPTW) is established based on the directed graph, and a 3-stage multi-modalmulti-objective differential evolution algorithm (3S-MMD...
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In this paper, the mathematical model of Vehicle Routing Problem with Time Windows (VRPTW) is established based on the directed graph, and a 3-stage multi-modalmulti-objective differential evolution algorithm (3S-MMDEA) is proposed. In the first stage, in order to expand the range of individuals to be selected, a generalized opposition-based learning (GOBL) strategy is used to generate a reverse population. In the second stage, a search strategy of reachable distribution area is proposed, which divides the population with the selected individual as the center point to improve the convergence of the solution set. In the third stage, an improved individual variation strategy is proposed to legalize the mutant individuals, so that the individual after variation still falls within the range of the population, further improving the diversity of individuals to ensure the diversity of the solution set. Based on the synergy of the above three stages of strategies, the diversity of individuals is ensured, so as to improve the diversity of solution sets, and multiple equivalent optimal paths are obtained to meet the planning needs of different decision-makers. Finally, the performance of the proposed method is evaluated on the standard benchmark datasets of the problem. The experimental results show that the proposed 3S-MMDEA can improve the efficiency of logistics distribution and obtain multiple equivalent optimal paths. The method achieves good performance, superior to the most advanced VRPTW solution methods, and has great potential in practical projects.
multi-modal multi-objective optimization is to locate (almost) equivalent Pareto optimal solutions as many as possible. Some evolutionary algorithms for multi-modal multi-objective optimization have been proposed in t...
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multi-modal multi-objective optimization is to locate (almost) equivalent Pareto optimal solutions as many as possible. Some evolutionary algorithms for multi-modal multi-objective optimization have been proposed in the literature. However, there is no efficient method for multi-modal many-objectiveoptimization, where the number of objectives is more than three. To address this issue, this paper proposes a niching indicator-based multi-modalmulti- and many-objectiveoptimization algorithm. In the proposed method, the fitness calculation is performed among a child and its closest individuals in the solution space to maintain the diversity. The performance of the proposed method is evaluated on multi-modalmulti-objective test problems with up to 15 objectives. Results show that the proposed method can handle a large number of objectives and find a good approximation of multiple equivalent Pareto optimal solutions. The results also show that the proposed method performs significantly better than eight multi-objective evolutionary algorithms.
multi-modal multi-objective optimization problems have multiple equivalent Pareto sets, each of which is mapped to the entire Pareto front. A number of multi-modalmulti-objective algorithms have been proposed to find...
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ISBN:
(数字)9781665467087
ISBN:
(纸本)9781665467087
multi-modal multi-objective optimization problems have multiple equivalent Pareto sets, each of which is mapped to the entire Pareto front. A number of multi-modalmulti-objective algorithms have been proposed to find all equivalent Pareto sets. Their performance is evaluated by computational experiments on multi-modalmulti-objective test problems. A common feature of those test problems is that a single point on the Pareto front in the objective space corresponds to multiple clearly separated Pareto optimal solutions in the decision space. In this paper, we propose a new type of multi-modalmulti-objective test problems where a single point on the Pareto front corresponds to an infinite number of Pareto optimal solutions (i.e., a subset of the decision space). This means that the mapping from the Pareto set in the decision space to the Pareto front in the objective space is a set-to-point mapping. For example, all points on a line in the decision space are mapped to the same single point on the Pareto front. As a result, the dimensionality of the Pareto set is larger than that of the Pareto front. We examine the search behavior of multi-modalmulti-objective algorithms using the proposed test problems. Some interesting observations are reported.
multimodality is often observed in practical optimization problems. Therefore, multi-modalmulti-objective evolutionary algorithms (MMEA) have been developed to tackle the multimodality of these problems. However, mos...
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ISBN:
(纸本)9781728124858
multimodality is often observed in practical optimization problems. Therefore, multi-modalmulti-objective evolutionary algorithms (MMEA) have been developed to tackle the multimodality of these problems. However, most of the existing studies focused on population diversity in either an objective or a decision space. A double-niched evolutionary algorithm (DNEA) is a state-of-the-art MMEA that employs a niche-sharing method to improve the population in both the objective and decision spaces. However, its performance has been evaluated solely for real-coded problems and not for binary-coded ones. In this study, the performance of DNEA is evaluated on a multi-objective 0/1 knapsack problem, and the population diversity in both the objective and decision spaces is evaluated using a pure diversity measure. The experimental results suggest that DNEA is effective for multi-objective 0/1 knapsack problems to improve the decision space diversity;further, its performance is significantly affected by its control parameter, niche radius.
Local Pareto optimal solutions may exist in multi-modal multi-objective optimization problems. Traditional multi-objective evolutionary algorithms usually try to escape from local Pareto optima. However, these solutio...
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ISBN:
(纸本)9781728121536
Local Pareto optimal solutions may exist in multi-modal multi-objective optimization problems. Traditional multi-objective evolutionary algorithms usually try to escape from local Pareto optima. However, these solutions may be good enough for the decision makers and are additional options if Pareto optimal solutions are infeasible. In this paper, we modify our previous double-niched evolutionary algorithm (DNEA) to search for local Pareto optimal solutions. The new version is termed as DNEA-L. We apply DNEA-L to 3- and 4-objective polygon-based problems with local Pareto optima. The experimental results show that DNEA-L is efficient to find a large number of local Pareto optimal solutions with good diversity.
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