An Adaptive Reference Vector-Based Interval Multiobjective Evolutionary Algorithm

In some real-world optimization problems, the parameters of an objective function may be expressed as intervals, such as the benefit of a project and the driving speed of a robot. An optimization problem involving interval parameters and multiple conflicting objectives is termed as a multiobjective optimization problem with interval parameters (IMOP). Few studies have addressed IMOPs compared to deterministic multiobjective optimization at present. In addition, the uncertainty involved in the problems raises higher demands on the diversity and efficiency of an algorithm. Therefore, an adaptive reference vector-based interval multiobjective evolutionary algorithm in the framework of MOEA/D (IMOEA/D) was proposed in this article. First, an IMOP is decomposed into a number of subproblems with interval parameters by setting an interval-valued reference point and constructing interval-valued scalar functions. Following that, an ensemble scheme for evaluating interval individuals is developed via the rank sum ratio method. Finally, reference vectors are adaptively adjusted based on the interval crowding distance to enhance the distribution of a population. The proposed IMOEA/D was tested on 20 bench-mark IMOPs as well as a scheduling problem of underwater wireless sensor networks, and compared with four state-of-the-art interval MOEAs. The empirical results demonstrate its superior performance and strong competitiveness.