Transfer of learning with the co-evolutionary decomposition-based algorithm-II: a realization on the bi-level production-distribution planning system

Abstract

Bi-Level Optimization Problem (BLOP) is a class of challenging problems with two levels of optimization tasks. The main goal is to optimize the upper level problem, which has another optimization problem as a constraint. In this way, the evaluation of each upper level solution requires finding an optimal solution to the corresponding lower level problem, which is computationally so expensive. For this reason, most proposed bi-level resolution methods have been restricted to solve the simplest case (linear continuous BLOPs). This fact has attracted the evolutionary computation community to solve such complex problems. Besides, to enhance the search performance of Evolutionary Algorithms (EAs), reusing knowledge captured from past optimization experiences along the search process has been proposed in the literature, and was demonstrated much promise. Motivated by this observation, we propose in this paper, a memetic version of our proposed Co-evolutionary Decomposition-based Algorithm-II (CODBA-II), that we named M-CODBA-II, to solve combinatorial BLOPs. The main motivation of this paper is to incorporate transfer learning within our recently proposed CODBA-II scheme to make the search process more effective and more efficient. Our proposed hybrid algorithm is investigated on two bi-level production-distribution problems in supply chain management formulated to: (1) Bi-CVRP and (2) Bi-MDVRP. The experimental results reveal a potential advantage of memes incorporation in CODBA-II. Most notably, the results emphasize that transfer learning allows not only accelerating the convergence but also finding better solutions.