Decomposition-Based Multiobjective Optimization Algorithms With Adaptively Adjusting Weight Vectors and Neighborhoods

The decomposition-based multiobjective optimization algorithm (MOEA/D) is an effective method of solving a multiobjective optimization problem (MOP). The main idea of MOEA/D is that the objectives are weighted through different vectors to form different subproblems, and an optimal solution set is obtained by co-evolution in a certain neighborhood. However, with the increase of objectives, the number of nondominated solutions increases exponentially, resulting in the deteriorated capability of searching for optimal solutions. In addition, for an optimization problem with the complex Pareto front (PF), the selection pressure of nondominated solutions is insufficient. To make evolution more efficient, an MOEA/D with adaptively adjusting weight vectors and neighborhoods (MOEA/D-AAWNs) is developed in this article. First, the evolutionary direction of each subproblem is analyzed and the Sparsity function (Spa) is proposed to measure the population density on the PF. By using Spa, a method of generating uniform vectors is presented to improve the diversity of solutions. Besides, a method of adaptively adjusting neighborhoods is given. It adjusts neighborhoods according to the number of iterations and the Spa value of its corresponding subproblem. In this way, the computational resource can be effectively allocated, leading to the improvement in evolutionary efficiency. The proposed algorithm is applied to solve a series of benchmark optimization instances, and the experimental results show that the proposed algorithm outperforms comparison algorithms in runtime, convergence, and diversity.