What Weights Work for You? Adapting Weights for Any Pareto Front Shape in Decomposition-Based Evolutionary Multiobjective Optimisation

Li, Miqing; Yao, Xin

doi:10.1162/evco_a_00269

Cited by 126 publications

(74 citation statements)

References 76 publications

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“…has been considered in a few studies [2,19], and we will discuss it in great detail in latter sections. However, how to position reference sets as search targets has not yet been explored in literature.…”

Section: Motivationmentioning

confidence: 99%

“…A population size of 100 is used for 2 objectives, as recommended by [5]. A population size of 105, and 200 is used for 3 objectives, according to the suggestion in [3,19,38]. For scalable WFG problems, the population size is set according to [3].…”

Section: Simulation Setupmentioning

confidence: 99%

“…Many existing decomposition-based algorithms use points on a unit simplex as references [6,42]. This reference setting works well for problems with a PF similar to the unit simplex, but has been increasingly reported to be ineffective for problems with other types of PFs, such as degeneracy [12] and disconnectedness [19].…”

Section: Introductionmentioning

confidence: 99%

“…The use of an indicator to guide the adaptation of references has recently been studied in [31]. Other adaptive approaches include improved reference set adaptation [19] and sampling [38]. Note that reference utilisation is similar to preference articulation [26,27], where preference information from the decision maker is incorporated into algorithms so as to find only preferred regions on the PF.…”

Section: Introductionmentioning

confidence: 99%

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AREA: An adaptive reference-set based evolutionary algorithm for multiobjective optimisation

Jiang

Guo

et al. 2020

Information Sciences

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Population-based evolutionary algorithms have great potential to handle multiobjective optimisation problems. However, these algorithms depends largely on problem characteristics, and there is a need to improve their performance for a wider range of problems. References, which are often specified by the decision maker's preference in different forms, are a very effective method to improve the performance of algorithms but have not been fully explored in literature. This paper proposes a novel framework for effective use of references to strengthen algorithms. This framework considers references as search targets which can be adjusted based on the information collected during the search. The proposed framework is combined with new strategies, such as reference adaptation and adaptive local mating, to solve different types of problems. The proposed algorithm is compared with state of the arts on a wide range of problems with diverse characteristics. The comparison and extensive sensitivity analysis demonstrate that the proposed algorithm is competitive and robust across different types of problems studied in this paper.

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Section: Motivationmentioning

confidence: 99%

Section: Simulation Setupmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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AREA: An adaptive reference-set based evolutionary algorithm for multiobjective optimisation

Jiang

Guo

et al. 2020

Information Sciences

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“…Decomposition-based evolutionary multiobjective optimization (EMO) algorithms decomposes a multiobjective optimization problem (MOOP) [2] into a number of single-objective optimization problems using a set of weight vectors [10]. Each subproblem or weight vector is associated with a solution in the population, and the diversity of the evolutionary population is controlled explicitly by a set of weight vectors [6]. Thus, an appropriate set of weights can increase the quality of the final solution.…”

Section: Introductionmentioning

confidence: 99%

MOEA/D with uniformly randomly adaptive weights

Farias

Braga

Bassani

et al. 2018

Proceedings of the Genetic and Evolutionary Computation Conference

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When working with decomposition-based algorithms, an appropriate set of weights might improve quality of the final solution. A set of uniformly distributed weights usually leads to well-distributed solutions on a Pareto front. However, there are two main difficulties with this approach. Firstly, it may fail depending on the problem geometry. Secondly, the population size becomes not flexible as the number of objectives increases. In this paper, we propose the MOEA/D with Uniformly Randomly Adaptive Weights (MOEA/D-URAW) which uses the Uniformly Randomly method as an approach to subproblems generation, allowing a flexible population size even when working with many objective problems. During the evolutionary process, MOEA/D-URAW adds and removes subproblems as a function of the sparsity level of the population. Moreover, instead of requiring assumptions about the Pareto front shape, our method adapts its weights to the shape of the problem during the evolutionary process. Experimental results using WFG41-48 problem classes, with different Pareto front shapes, shows that the present method presents better or equal results in 77.5% of the problems evaluated from 2 to 6 objectives when compared with state-of-the-art methods in the literature.

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Multi‐objective Firefly algorithm for enhanced balanced exploitation and exploration capabilities

Liu

2023

Concurrency and Computation

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SummaryThe multi‐objective Firefly algorithm has a single strategy for finding the best in the evolutionary process, which is easy to fall into the local optimum and leads to poor distribution and convergence of the population. To address this problem, this article proposes an enhanced multi‐objective Firefly algorithm with balanced exploitation and exploration capability (MOFA‐EBE). The convergence evaluation index is introduced to divide the population into two sub‐regions according to the difference of convergence, namely, the development area and exploration area, and each sub‐region is assigned its learning strategy to maximize the utilization of population information. Since the individuals in the development region are far from the Pareto front, the Lévy flights mechanism is added to expand the search area and make them approach the Pareto front quickly under the guidance of the convergent global optimal particles to improve the convergence of the algorithm; since the individuals in the exploration region already have better convergence, they are assigned the most diverse and convergent global individuals for guidance and the Cauchy The variation mechanism is added to the Pareto frontier for continuous exploration to improve the distributivity of the algorithm. In the experimental part, the algorithm is compared with some multi‐objective optimization algorithms on 19 benchmark test functions, and the effectiveness of the added strategy of MOFA‐EBE is verified. The results show that MOFA‐EBE is significantly superior to several other algorithms in terms of improving population convergence and distributivity.

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What Weights Work for You? Adapting Weights for Any Pareto Front Shape in Decomposition-Based Evolutionary Multiobjective Optimisation

Cited by 126 publications

References 76 publications

AREA: An adaptive reference-set based evolutionary algorithm for multiobjective optimisation

AREA: An adaptive reference-set based evolutionary algorithm for multiobjective optimisation

MOEA/D with uniformly randomly adaptive weights

Multi‐objective Firefly algorithm for enhanced balanced exploitation and exploration capabilities

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