Multiobjective evolutionary algorithms: a comparative case study and the strength Pareto approach

Zitzler, Eckart; Thiele, Lothar

doi:10.1109/4235.797969

Cited by 7,024 publications

(3,312 citation statements)

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“…In this paper, we propose a new mating scheme for simultaneously improving the convergence speed and the diversity. The effect of the proposed mating scheme on the performance of the SPEA [21] and the NSGA-II [4] is examined through computational experiments on knapsack problems in Zitzler & Thiele [21]. Experimental results show that the search ability of those EMO algorithms on the two-objective and three-objective knapsack problems is significantly improved by the proposed mating scheme.…”

Section: Introductionmentioning

confidence: 93%

“…While mating restriction has been often discussed in the literature, its effect has not been clearly demonstrated. As a result, it is not used in many EMO algorithms as pointed out in some reviews on EMO algorithms [6,17,21]. The aim of this paper is to clearly demonstrate that the search ability of EMO algorithms can be improved by appropriately choosing parent solutions.…”

Section: Introductionmentioning

confidence: 99%

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A Similarity-Based Mating Scheme for Evolutionary Multiobjective Optimization

Ishibuchi

Shibata

2003

Lecture Notes in Computer Science

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Abstract. This paper proposes a new mating scheme for evolutionary multiobjective optimization (EMO), which simultaneously improves the convergence speed to the Pareto-front and the diversity of solutions. The proposed mating scheme is a two-stage selection mechanism. In the first stage, standard fitness-based selection is iterated for selecting a pre-specified number of candidate solutions from the current population. In the second stage, similarity-based tournament selection is used for choosing a pair of parents among the candidate solutions selected in the first stage. For maintaining the diversity of solutions, selection probabilities of parents are biased toward extreme solutions that are different from prototypical (i.e., average) solutions. At the same time, our mating scheme uses a mechanism where similar parents are more likely to be chosen for improving the convergence speed to the Paretofront. Through computational experiments on multi-objective knapsack problems, it is shown that the performance of recently proposed well-known EMO algorithms (SPEA and NSGA-II) can be improved by our mating scheme.

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Section: Introductionmentioning

confidence: 93%

Section: Introductionmentioning

confidence: 99%

A Similarity-Based Mating Scheme for Evolutionary Multiobjective Optimization

Ishibuchi

Shibata

2003

Lecture Notes in Computer Science

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“…Different measurements are used when dealing with multiple objectives such as: spacing [57], hypervolume ratio [58], S-and FS-metrics [59], accuracy [60], stability [60], variable space generational distance [61] and maximum spread [61].…”

Section: Measurementsmentioning

confidence: 99%

A survey of swarm intelligence for dynamic optimization: Algorithms and applications

Mavrovouniotis

Yang

2017

Swarm and Evolutionary Computation

490

213

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Swarm intelligence (SI) algorithms, including ant colony optimization, particle swarm optimization, bee-inspired algorithms, bacterial foraging optimization, firefly algorithms, fish swarm optimization and many more, have been proven to be good methods to address difficult optimization problems under stationary environments. Most SI algorithms have been developed to address stationary optimization problems and hence, they can converge on the (near-) optimum solution efficiently. However, many real-world problems have a dynamic environment that changes over time. For such dynamic optimization problems (DOPs), it is difficult for a conventional SI algorithm to track the changing optimum once the algorithm has converged on a solution. In the last two decades, there has been a growing interest of addressing DOPs using SI algorithms due to their adaptation capabilities. This paper presents a broad review on SI dynamic optimization (SIDO) focused on several classes of problems, such as discrete, continuous, constrained, multi-objective and classification problems, and real-world applications. In addition, this paper focuses on the enhancement strategies integrated in SI algorithms to address dynamic changes, the performance measurements and benchmark generators used in SIDO. Finally, some considerations about future directions in the subject are given.

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“…It is possible to rank a given algorithm over another based on the number of times the resulting Pareto approximation fronts dominate (strong, regular or weakly) each other. The second approach relies on quality indicators, mainly the hypervolume I H and the Epsilon indicators that were already introduced in Zitzler and Thiele 73 and Zitzler et al 70 , respectively. Quality indicators usually transform a full Pareto approximation set into a real number.…”

Section: Multi-objective Quality Measuresmentioning

confidence: 99%