An Immune-Inspired Resource Allocation Strategy for Many-Objective Optimization

Recently, a number of resource allocation strategies have been proposed for evolutionary algorithms to efficiently tackle multiobjective optimization problems (MOPs). However, these methods mainly allocate computational resources based on the convergence improvement under the decomposition-based framework, which may become ineffective with the increased number of optimization objectives. To address this problem, this article suggests an immune-inspired resource allocation strategy, which breaks through the decomposition-based framework and can better balance convergence and diversity for many-objective optimization. In our method, the diversity distances of solutions are defined by the Euclidean distances of their projected points on the unit hyperplane. Then, based on the diversity distances, resource allocation is realized by using an immune cloning operator to encourage exploring sparse regions of the search space. Moreover, to provide high-quality solutions in coordination with this immune cloning operator, a novel archive update mechanism is designed. When compared to most well-known resource allocation strategies, our method is advantageous for many-objective optimization. The experimental results also validate the superiority of our method over several state-of-the-art evolutionary algorithms for solving two sets of complicated MOPs having 5 to 15 objectives.

I. Introduction

Multiobjective optimization problems (MOPs) involve the optimization of multiple objectives simultaneously [1], [2], [3], [4], which can be mathematically defined by $$\begin{align*} {\mathrm{ minimize}}&F\left ({{\mathbf{x}}}\right)=\left ({f_{1} \left ({{\mathbf{x}}}\right),\ldots,f_{m} \left ({{\mathbf{x}}}\right)}\right) \\ {\mathrm{ subject~to}}&{\mathbf{x}}\in \Omega\tag{1}\end{align*}$$ where is a decision vector in search space ( means the number of decision variables) and defines objective functions. When is larger than three, (1) is called a many-objective optimization problem (MaOP). As one single solution generally cannot optimize all objectives, a set of tradeoff optimal solutions called Pareto-optimal set (PS) can be obtained and its mapping to the objective space is called Pareto-optimal front (PF) [5]. In recent decades, multiobjective evolutionary algorithms (MOEAs) have become very popular and effective for solving MOPs. Most MOEAs can be divided into three main categories based on the adopted population update mechanisms, i.e., Pareto-based MOEAs [6], [7], [8], [9], [10], decomposition-based MOEAs [11], [12], [13], and indicator-based MOEAs [14], [15], [16], [17], [18], which have been validated to be effective for solving MOPs with two or three objectives.