Strengthening evolution-based differential evolution with prediction strategy for multimodal optimization and its application in multi-robot task allocation

Many real-world problems can be considered multimodal optimization problems (MMOPs), which require locating as many global optima as possible and refining the accuracy of the found optima as high as possible. However, there are some issues with existing algorithms for solving MMOPs. For instance, most of the existing methods adopt the greedy selection strategy to select offspring, which may lead some individuals to fall into local optima and the repetitive evaluations for these local optima will exhaust many fitness evaluations (FEs). Moreover, many MMOPs tend to be expensive to evaluate, and the rational allocation of evaluation resources to better deal with MMOPs is a critical challenge within a limited number of FEs. How to allocate FEs reasonably in a whole evolution and how to avoid individuals becoming trapped in local optima are two key problems in solving MMOPs. Therefore, this paper proposes a strengthening evolution-based differential evolution with prediction strategy (SEDE-PS) for solving MMOPs and verifies its performance in a multirobot task allocation (MRTA) problem, which has the following three contributions. First, a neighbour-based evolution prediction (NEP) strategy is proposed to predict the position of individuals in the next generation by using the historical information of individuals as much as possible. Second, a prediction-based mutation (PM) strategy is introduced to accelerate convergence by combining it with the NEP strategy. Third, a strengthening evolution (SE) strategy is proposed to select inferior individuals to evolve them unconditionally several times and make them approach global optima or jump out of local optima. We compare the SEDE-PS with state-of-the-art multimodal optimization algorithms on the widely used CEC’2013 benchmark. The experimental results show that SEDE-PS performs better than, or is competitive with these compared algorithms. Moreover, SEDE-PS is applied to a real-world MRTA problem to further verify the effectiveness of SEDE-PS.