The Collaborative Local Search Based on Dynamic-Constrained Decomposition With Grids for Combinatorial Multiobjective Optimization

Cai, Xinye; Xia, Chao; Zhang, Qingfu; Mei, Zhiwei; Hu, Han; Wang, Lisong; Hu, Jun

doi:10.1109/tcyb.2019.2931434

Cited by 28 publications

(5 citation statements)

References 57 publications

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“…Associate each solution in Q with an unit reference vector in V according to Definition 2; (6) for i � 1 ⟶ |new A| do (7) Find the neighborhood reference vectors of new A i among V and store as NRV i ; (8) For i � 1 ⟶ |V| do (9) if no solution is associated to V i then (10) V←V/V i ; (11) (17) Remove all the solutions that own the same neighborhood reference vectors with new A k in new A; ALGORITHM 2: Reference vector adjustment.…”

Section: Environmental Selectionmentioning

confidence: 99%

“…According to their environmental selection strategies, the existing algorithms can be roughly divided into four categories: (1) Paretodominance-based; (2) decomposition-based; (3) indicatorbased; and (4) others. Pareto-dominance-based algorithms [4,7,8] often divide solutions into different nondominated levels and use a second criterion to select solutions in the last level; decomposition-based MOEAs [9][10][11][12][13] decompose the original MOP into multiple subproblems and solve them in a cooperative way; for indicator-based MOEAs and MaOEAs, such as hypervolume-based many-objective (HypE) [14] and indicator-based multiobjective evolutionary algorithm with reference point adaptation (AR-MOEA) [15], it tends to develop an indicator to evaluate the overall performance and sort the individuals according to their indicator values.…”

Section: Introductionmentioning

confidence: 99%

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An Adaptive Reference Vector Adjustment Strategy and Improved Angle‐Penalized Value Method for RVEA

Qiu

Zhu

et al. 2021

Complexity

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Decomposition-based evolutionary multiobjective algorithms (MOEAs) divide a multiobjective problem into several subproblems by using a set of predefined uniformly distributed reference vectors and can achieve good overall performance especially in maintaining population diversity. However, they encounter huge difficulties in addressing problems with irregular Pareto fronts (PFs) since many reference vectors do not work during the searching process. To cope with this problem, this paper aims to improve an existing decomposition-based algorithm called reference vector-guided evolutionary algorithm (RVEA) by designing an adaptive reference vector adjustment strategy. By adding the strategy, the predefined reference vectors will be adjusted according to the distribution of promising solutions with good overall performance and the subspaces in which the PF lies may be further divided to contribute more to the searching process. Besides, the selection pressure with respect to convergence performance posed by RVEA is mainly from the length of normalized objective vectors and the metric is poor in evaluating the convergence performance of a solution with the increase of objective size. Motivated by that, an improved angle-penalized distance (APD) method is developed to better distinguish solutions with sound convergence performance in each subspace. To investigate the performance of the proposed algorithm, extensive experiments are conducted to compare it with 5 state-of-the-art decomposition-based algorithms on 3-, 5-, 8-, and 10-objective MaF1–MaF9. The results demonstrate that the proposed algorithm obtains the best overall performance.

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Section: Environmental Selectionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

An Adaptive Reference Vector Adjustment Strategy and Improved Angle‐Penalized Value Method for RVEA

Qiu

Zhu

et al. 2021

Complexity

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“…• Travelling salesman problem (TSP): Given a weighted and undirected complete graph, TSP is one of the most famous routing problems that aims to find the shortest Hamiltonian cycle covering all nodes [250]. Several MOEA/D variants have been developed mainly with dedicated reproduction operators (e.g., SA [61,62], EDAs [251] and ACO [168]) and local search strategies (e.g., guided local search [177] and collaborative local serach [252]). In addition to reproduction operators, [253] proposed a hybrid selection mechanism alternating between non-dominated sorting and decomposition for combinatorial optimization problems including TSPs.…”

Section: Applications On Routing Problemsmentioning

confidence: 99%

Decomposition Multi-Objective Evolutionary Optimization: From State-of-the-Art to Future Opportunities

2021

Preprint

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Decomposition has been the mainstream approach in the classic mathematical programming for multi-objective optimization and multi-criterion decision-making. However, it was not properly studied in the context of evolutionary multi-objective optimization until the development of multi-objective evolutionary algorithm based on decomposition (MOEA/D). In this article, we present a comprehensive survey of the development of MOEA/D from its origin to the current state-of-the-art approaches. In order to be self-contained, we start with a step-by-step tutorial that aims to help a novice quickly get onto the working mechanism of MOEA/D. Then, selected major developments of MOEA/D are reviewed according to its core design components including weight vector settings, subproblem formulations, selection mechanisms and reproduction operators. Besides, we also overviews some further developments for constraint handling, computationally expensive objective functions, preference incorporation, and real-world applications. In the final part, we shed some lights on emerging directions for future developments.

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“…Usually, multi-objective evolutionary algorithms (MOEAs) [4][5] [6] and Multiobjective particle swarm optimizations (MOPSOs) [7][8] [9] are considered to be alternatives for tackling MOPs, which attempt to search for a Pareto optimal set (POS) consisting of the best possible tradeoffs among the objectives. The mapping of the POS in the objective space is called the Pareto optimal front (POF).…”

Section: Introductionmentioning

confidence: 99%

A dynamic multi-objective particle swarm optimization algorithm based on adversarial decomposition and neighborhood evolution

Zheng

Zhang

Zou

et al. 2022

Swarm and Evolutionary Computation

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The Collaborative Local Search Based on Dynamic-Constrained Decomposition With Grids for Combinatorial Multiobjective Optimization

Cited by 28 publications

References 57 publications

An Adaptive Reference Vector Adjustment Strategy and Improved Angle‐Penalized Value Method for RVEA

An Adaptive Reference Vector Adjustment Strategy and Improved Angle‐Penalized Value Method for RVEA

Decomposition Multi-Objective Evolutionary Optimization: From State-of-the-Art to Future Opportunities

A dynamic multi-objective particle swarm optimization algorithm based on adversarial decomposition and neighborhood evolution

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