Constrained Test Problems for Multi-objective Evolutionary Optimization

Deb, Kalyanmoy; Pratap, Amrit; Meyarivan, T.

doi:10.1007/3-540-44719-9_20

Cited by 273 publications

(152 citation statements)

References 7 publications

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“…To examine the effectiveness of our proposed schemes, we use six complex problems with irregular Pareto fronts instead of some well-known test suites such as ZDT (Zitzler et al, 2000) or DTLZ (Deb et al, 2005) for empirical comparison. Some of them have been tested in (Jiang and Yang, 2015) and , showing that the original MOEA/D faces difficulties in solving these kinds of problems due to their complex characteristics.…”

Section: Experimental Settingsmentioning

confidence: 99%

“…The weighted Tchebycheff approach has received intensive research interest due to its ability to approximate both convex and concave POFs. Despite its great success for solving standard benchmark problems like ZDT (Zitzler et al, 2000) or DTLZ (Deb et al, 2005), some recent investigations have revealed that this approach has difficulties in uniformly distributing solutions on boundary regions of the POF for complex problems (Qi et al, 2014;Jiang and Yang, 2015). On the other hand, the PBI approach gains a firm foothold in MOEA/D because it can provide a more uniform distribution of POF than the weighted Tchebycheff for three-and higher-dimensional problems (Li et al, 2015a;Zhang and Li, 2007;Deb and Jain, 2014;Gomez and Coello Coello, 2015).…”

Section: Introductionmentioning

confidence: 99%

“…Probably due to the lack of complicated POF characteristics in the well-known ZDT (Zitzler et al, 2000), DTLZ (Deb et al, 2005) and WFG (Huband et al, 2006) test suites in the field of multiobjective optimization, PBI has been rarely or even not deeply examined on problems with complicated POFs. However, real-world MOPs often have irregular POF geometries Osycza and Kundu, 1995;Wang et al, 2013), where the shape can be extremely convex and/or concave.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Improving the multiobjective evolutionary algorithm based on decomposition with new penalty schemes

Yang

Jiang

2016

Soft Comput

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It has been increasingly reported that the multiobjective optimization evolutionary algorithm based on decomposition (MOEA/D) is promising for handling multiobjective optimization problems (MOPs). MOEA/D employs scalarizing functions to convert an MOP into a number of single-objective subproblems. Among them, penalty boundary intersection (PBI) is one of the most popular decomposition approaches and has been widely adopted for dealing with MOPs. However, the original PBI uses a constant penalty value for all subproblems and has difficulties in achieving a good distribution and coverage of the Pareto front for some problems. In this paper, we investigate the influence of the penalty factor on PBI, and suggest two new penalty schemes, i.e., adaptive penalty scheme (APS) and subproblem-based penalty scheme (SPS), to enhance the spread of Pareto optimal solutions. The new penalty schemes are examined on several complex MOPs, showing that PBI with the use of them is able to provide a better approximation of the Pareto front than the original one. The SPS is further integrated into two recently developed MOEA/D variants to help balance the population diversity and convergence. Experimental results show that it can significantly enhance the algorithm's performance.

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Section: Experimental Settingsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Improving the multiobjective evolutionary algorithm based on decomposition with new penalty schemes

Yang

Jiang

2016

Soft Comput

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“…In order to test DCMMIOA's characteristics, three dynamic constrained multi-objective evolutionary algorithms reported are selected to compare against it, i.e., DMEA [6] and two similar versions of DNSGAII-A and DNSGAII-B [2]. In addition, we give seven DCMO problems DCTP1 to DCTP7 acquired by introducing a time-varying Rastrigin function into the seven static benchmark problems CTP1 to CTP7 [18], and two dynamic engineering design problems DSR and DPVM gained through modifying the coefficients of the two original versions [19,20]; more details can be found below. Such dynamic problems are utilized to examine the inherent properties of these four approaches.…”

Section: Experimental Studymentioning

confidence: 99%

“…Deb et al designed a series of static constrained multiobjective test problems, i.e., CTP1 to CTP7 [18]. We modify their common function g(x) into the following time-varying Rastrigin's multimodal function, and correspondingly, the static problems are extended in order into dynamic multi-objective multimodal problems DCTP1 to DCTP7.…”

Section: Benchmark Problems and Experimental Analysismentioning

confidence: 99%

Immune Optimization Approach for Dynamic Constrained Multi-Objective Multimodal Optimization Problems

Zhang¹,

Liao²,

Wang³

2012

AJOR

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This work investigates one immune optimization approach for dynamic constrained multi-objective multimodal optimization in terms of biological immune inspirations and the concept of constraint dominance. Such approach includes mainly three functional modules, environmental detection, population initialization and immune evolution. The first, inspired by the function of immune surveillance, is designed to detect the change of such kind of problem and to decide the type of a new environment; the second generates an initial population for the current environment, relying upon the result of detection; the last evolves two sub-populations along multiple directions and searches those excellent and diverse candidates. Experimental results show that the proposed approach can adaptively track the environmental change and effectively find the global Pareto-optimal front in each environment.

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Surrogate-assisted multicriteria optimization: Complexities, prospective solutions, and business case

Allmendinger

Emmerich

Hakanen

et al. 2017

J. Multi-Crit. Decis. Anal.

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Complexity in solving real-world multicriteria optimization problems often stems from the fact that complex, expensive, and/or time-consuming simulation tools or physical experiments are used to evaluate solutions to a problem. In such settings, it is common to use efficient computational models, often known as surrogates or metamodels, to approximate the outcome (objective or constraint function value) of a simulation or physical experiment. The presence of multiple objective functions poses an additional layer of complexity for surrogate-assisted optimization.For example, complexities may relate to the appropriate selection of metamodels for the individual objective functions, extensive training time of surrogate models, or the optimal use of many-core computers to approximate efficiently multiple objectives simultaneously. Thinking out of the box, complexity can also be shifted from approximating the individual objective functions to approximating the entire Pareto front. This leads to further complexities, namely, how to validate statistically and apply the techniques developed to real-world problems. In this paper, we discuss emerging complexity-related topics in surrogate-assisted multicriteria optimization that may not be prevalent in nonsurrogate-assisted single-objective optimization. These complexities are motivated using several real-world problems in which the authors were involved. We then discuss several promising future research directions and prospective solutions to tackle emerging complexities in surrogate-assisted multicriteria optimization. Finally, we provide insights from an industrial point of view into how surrogate-assisted multicriteria optimization techniques can be developed and applied within a collaborative business environment to tackle real-world problems.

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Constrained Test Problems for Multi-objective Evolutionary Optimization

Cited by 273 publications

References 7 publications

Improving the multiobjective evolutionary algorithm based on decomposition with new penalty schemes

Improving the multiobjective evolutionary algorithm based on decomposition with new penalty schemes

Immune Optimization Approach for Dynamic Constrained Multi-Objective Multimodal Optimization Problems

Surrogate-assisted multicriteria optimization: Complexities, prospective solutions, and business case

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