A Pareto evolutionary algorithm based on incremental learning for a kind of multi-objective multidimensional knapsack problem

Abstract

Multidimensional knapsack problem (MKP) is a classic combinatorial optimization problem arising from many practical applications. To be closer to real-life applications, this paper focuses on a special kind of multi-objective MKP (MOMKP), where the optimization objectives are to maximize the total profit and minimize the maximum consumption of multidimensional resources. To solve it, a Pareto evolutionary algorithm based on Incremental Learning (PEAIL) is proposed, whose components mainly consist of two parts, i.e., the online Incremental Learning and the nondominated sorting. PEAIL is unique in that it can extract the historical information of the search behavior and then feed them back to the main evolutionary framework. Firstly, problem-dependent heuristics, including genetic operators and a repair mechanism for infeasible solutions, are proposed and discussed. Secondly, an online Incremental Learning approach is put forward to learn the probability model of excellent solutions during the iteration process. Thereby, we can predict promising individuals from this probability model, which are used for further strengthening PEAIL’s search ability. Thirdly, a simple yet effective competition-based improvement mechanism is proposed to refine the offspring of PEAIL. Finally, results of experiments on 45 benchmark instances and a real-life case study demonstrate the effectiveness and practical values of the proposed PEAIL.