A self-organizing map approach for constrained multi-objective optimization problems

Abstract

There exist many multi-objective optimization problems (MOPs) containing several inequality and equality constraints in practical applications, which are known as CMOPs. CMOPs pose great challenges for existing multi-objective evolutionary algorithms (MOEAs) since the difficulty in balancing the objective minimization and constraint satisfaction. Without loss of generality, the distribution of the Pareto set for a continuous m-objective CMOP can be regarded as a piecewise continuous manifold of dimension (m − 1). According to this property, a self-organizing map (SOM) approach for constrained multi-objective optimization problems is proposed in this article. In the proposed approach, we adopt the strategy of two population evolution, in which one population is evolved by considering all the constraints and the other population is used to assist in exploring the areas. In the evolutionary stage, each population is assigned a self-organizing map for discovering the population distribution structure in the decision space. After the topological mapping, we utilize the extracted neighborhood relationship information to generate promising offspring solutions. Afterwards, the neuron weight vectors of SOM are updated by the objective vectors of the surviving offsprings. Through the proposed approach, we can make the population efficiently converge to the feasible region with suitable levels of diversity. In the experiments, we compare the proposed method with several state-of-the-art approaches by using 48 benchmark problems. The evaluation results indicate that the overwhelmingly superior performance of the proposed method over the other peer algorithms on most of the tested problems. The source code is available at https://github.com/hccccc92918/CMOSMA.

A multi-objective collaborative optimization method for excavator working devices based on knowledge engineering

“…To confirm the superiority of the proposed knowledge-based multiobjective optimization algorithm discussed in Section ''Knowledge-guided algorithm for multiobjective collaborative optimization'' for addressing the multiobjective optimization problem of the excavator working device, a comparison is conducted with prominent multiobjective optimization algorithms. The Reference Point Dominance-based NSGA-II (RPDNSGA2), 33 MOEA/D with Covariance Matrix Adaptation evolution strategy (MOEA/D-CMA), 34 Competitive mechanism based Multi-Objective Particle Swarm Optimizer (CMOPSO), 35 RVEA-iGNG, 18 and CMOSMA 19 are employed in the excavator multiobjective optimization. The parameters for each algorithm, including population size and maximum evolution generation, are set to be the same.…”

“…18 He et al proposed a self-organizing map approach for constrained multiobjective optimization problems (CMOSMA), which adopts the strategy of two population evolution to consider the constraints and explore the areas. 19 In summary, multiobjective optimization algorithms typically utilize the non-dominated relationship or the Pareto front to obtain a set of non-dominated solutions and select the final solution. However, as the number of subobjectives in real-world engineering problems increases to more than five subobjectives, it becomes challenging to determine the dominant relationships between different solutions.…”

“…18 He et al proposed a self-organizing map approach for constrained multiobjective optimization problems (CMOSMA), which adopts the strategy of two population evolution to consider the constraints and explore the areas. 19…”

A dual-population constrained multi-objective evolutionary algorithm with variable auxiliary population size

“…Generally speaking, CHTs and the internal mechanism used by CMOEAs play a decisive role in the performance of the algorithms. From this perspective, CMOEAs can be divided into the following categories: (1) The penalty function method [12][13][14]; (2) The methods that consider constraints and objectives separately [15][16][17]; (3) the method of using two-stage [18][19][20]; and (4) the method based on dual-population [21][22][23].…”

“…Many optimization problems in the real world usually contain multiple objective functions and complex constraints, which can be collectively referred to as constrained multi-objective optimization problems (CMOPs) [1][2][3]. Generally, CMOPs can be defined by the following formula [4]:…”