An Improved Bi-level Multi-objective Evolutionary Algorithm for the Production-Distribution Planning System

Bi-level Optimization Problem (BOP) presents a special class of challenging problems that contains two optimization tasks. This nested structure has been adopted extensively during recent years to solve many real-world applications. Besides, a number of solution methodologies are proposed in the literature to handle both single andmulti-objective BOPs. Among the well-cited algorithms solving the multi-objective case, we find the Bi-Level Evolutionary Multi-objective Optimization algorithm (BLEMO). This method uses the elitist Non-dominated Sorting Genetic Algorithm (NSGA-II) with the bi-level framework to solve Multi-objective Bi-level Optimization Problems (MBOPs). BLEMO has proved its efficiency and effectiveness in solving such kind of NP-hard problem over the last decade. To this end, we aim in this paper to investigate the performance of this method on a new proposed multi-objective variant of the Bilevel Multi Depot Vehicle Routing Problem (Bi-MDVRP) which is a well-known problem in combinatorial optimization. The proposed BLEMO adaptation is further improved combining jointly three techniques in order to accelerate the convergence rate of the whole algorithm. Experimental results on well-established benchmarks reveal a good performance of the proposed algorithm against the baseline version.