An Algorithm Based on Differential Evolution for Multi-Objective Problems

Santana‐Quintero, Luis V.; Coello, Carlos A. Coello

doi:10.5019/j.ijcir.2005.32

Cited by 63 publications

(37 citation statements)

References 29 publications

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“…Many subsequent approaches (PDEA [8], MODE [9], NSDE [10], GDE2 [11], DEMO [12], GDE3 [13] and NSDE-DCS [14]) used nondominated sorting and/or the crowding distance metric to calculate the fitness of individuals. Only recently, new algorithms that do not follow the environmental selection of NSGA-II were proposed (ε-MyDE [15] and DEMORS [16]). To our best knowledge, no algorithms that combine DE with the environmental selection of SPEA2 or IBEA have been presented so far.…”

Section: Related Workmentioning

confidence: 99%

Differential Evolution versus Genetic Algorithms in Multiobjective Optimization

Tušar

Filipič

Lecture Notes in Computer Science

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Abstract. This paper presents a comprehensive comparison between the performance of state-of-the-art genetic algorithms NSGA-II, SPEA2 and IBEA and their differential evolution based variants DEMO NS-II , DEMO SP2 and DEMO IB . Experimental results on 16 numerical multiobjective test problems show that on the majority of problems, the algorithms based on differential evolution perform significantly better than the corresponding genetic algorithms with regard to applied quality indicators. This suggests that in numerical multiobjective optimization, differential evolution explores the decision space more efficiently than genetic algorithms.

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Section: Related Workmentioning

confidence: 99%

Differential Evolution versus Genetic Algorithms in Multiobjective Optimization

Tušar

Filipič

Lecture Notes in Computer Science

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“…It is well-known that DE algorithms have a fast convergence rate but they often reach the vicinity of the true Pareto front [17], [42]. To overcome this problem and maintain the convergence rate, a twophase scheme has been proposed in [43].…”

Section: Outputmentioning

confidence: 99%

Multiobjective controller design by solving a multiobjective matrix inequality problem

Chiu

2014

IET Control Theory & Applications

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In this study, linear matrix inequality (LMI) approaches and multiobjective (MO) evolutionary algorithms are integrated to design controllers. An MO matrix inequality problem (MOMIP) is first defined.A hybrid MO differential evolution (HMODE) algorithm is then developed to solve the MOMIP. The hybrid algorithm combines deterministic and stochastic searching schemes. In the solving process, the deterministic part aims to exploit the structures of matrix inequalities, and the stochastic part is used to fully explore the decision variable space. Simulation results show that the HMODE algorithm can produce an approximated Pareto front (APF) and Pareto-efficient controllers that stabilize the associated controlled system. In contrast with single-objective designs using LMI approaches, the proposed MO methodology can clearly illustrate how the objectives involved affect each other, i.e., a broad perspective on optimality is provided. This facilitates the selecting process for a representative design, and particularly the design that corresponds to a nondominated vector lying in the knee region of the APF. In addition, controller gains can be readily modified to incorporate the preference or need of a system designer.W.-Y. Chiu is with the Multiobjective Control Lab,

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“…Several variants of DE have been proposed in the literature also for multiobjective optimization, by many authors including Abbass (2002), Babu and Jehan (2003), Kukkonen and Lampinen (2005), Robic and Filipic (2005), Santana-Quintero and Coello (2005). For a review, see, for example, Price et al (2005), Santana-Quintero and Coello (2005).…”

Section: Introductionmentioning

confidence: 99%

“…For a review, see, for example, Price et al (2005), Santana-Quintero and Coello (2005). The existing multiobjective variants of DE have also proven successful in solving many of the multiobjective test problems available (Kukkonen and Lampinen 2006;Zhang et al 2009a).…”

Section: Introductionmentioning

confidence: 99%

A new hybrid mutation operator for multiobjective optimization with differential evolution

et al. 2011

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Differential evolution has become one of the most widely used evolutionary algorithms in multiobjective optimization. Its linear mutation operator is a simple and powerful mechanism to generate trial vectors. However, the performance of the mutation operator can be improved by including a nonlinear part. In this paper, we propose a new hybrid mutation operator consisting of a polynomial-based operator with nonlinear curve tracking capabilities and the differential evolution's original mutation operator, for the efficient handling of various interdependencies between decision variables. The resulting hybrid operator is straightforward to implement and can be used within most evolutionary algorithms. Particularly, it can be used as a replacement in all algorithms utilizing the original mutation operator of differential evolution. We demonstrate how the new hybrid operator can be used by incorporating it into MOEA/D, a winning evolutionary multiobjective algorithm in a recent competition. The usefulness of the hybrid operator is demonstrated with extensive numerical experiments showing improvements in performance compared with the previous state of the art.

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An Algorithm Based on Differential Evolution for Multi-Objective Problems

Cited by 63 publications

References 29 publications

Differential Evolution versus Genetic Algorithms in Multiobjective Optimization

Differential Evolution versus Genetic Algorithms in Multiobjective Optimization

Multiobjective controller design by solving a multiobjective matrix inequality problem

A new hybrid mutation operator for multiobjective optimization with differential evolution

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