Adaptive Offspring Generation for Evolutionary Large-Scale Multiobjective Optimization

Offspring generation plays an important role in evolutionary multiobjective optimization. However, generating promising candidate solutions effectively in high-dimensional spaces is particularly challenging. To address this issue, we propose an adaptive offspring generation method for large-scale multiobjective optimization. First, a preselection strategy is proposed to select a balanced parent population, and then these parent solutions are used to construct direction vectors in the decision spaces for reproducing promising offspring solutions. Specifically, two kinds of direction vectors are adaptively used to generate offspring solutions. The first kind takes advantage of the dominated solutions to generate offspring solutions toward the Pareto optimal set (PS) for convergence enhancement, while the other kind uses those nondominated solutions to spread the solutions over the PS for diversity maintenance. The proposed offspring generation method can be embedded in many existing multiobjective evolutionary algorithms (EAs) for large-scale multiobjective optimization. Experiments are conducted to reveal the mechanism of our proposed adaptive reproduction strategy and validate its effectiveness. Experimental results on some large-scale multiobjective optimization problems have demonstrated the competitive performance of our proposed algorithm in comparison with five state-of-the-art large-scale EAs.

I. Introduction

Multiobjective optimization problems (MOPs), commonly seen in real-world applications [1]–[5], refer to the optimization of multiple conflicting objectives simultaneously, which can be mathematically formulated as follows:

$$\begin{align*} \text {Minimize}&~F\left ({\mathbf {x}}\right)=\left ({f_{1}\left ({\mathbf {x}}\right),f_{2}\left ({\mathbf {x}}\right), {\dots },f_{M}\left ({\mathbf {x}}\right)}\right) \\ \text {subject to}&~\mathbf {x}\in X\tag{1}\end{align*}$$ where is the search space of decision variables with denoting the decision vector [6]. Due to the conflicting nature of the objectives, the Pareto dominance is used to distinguish the qualities of two solutions [7]. Suppose and are two solutions of an MOP, is said to Pareto dominate (denoted as ) iff two criteria are satisfied: 1) for all the objectives, () and 2) there exists at least one objective that [8]. Sequentially, if is not Pareto dominated by any other solutions in , is called the Pareto optimal solution, , is called the Pareto optimal set (PS), and is called the Pareto optimal front (PF).