Variable neighborhood search for quadratic multiple constraint variable sized bin-packing problem

The bin-packing problem is well known in the field of combinatorial optimization. In this paper, we propose a quadratic multiple constraint variable sized bin-packing problem (QMC-VSBPP), which is a generalization of the variable sized bin-packing problem (VSBPP). In QMC-VSBPP, each bin type has multiple capacities, each item has multiple weights, and the items in different bins have joint costs. The objective of QMC-VSBPP is to minimize the sum of costs of used bins and the joint costs of items in different bins. QMC-VSBPP is a new combinatorial optimization problem. Herein, a variable neighborhood search (VNS) heuristic is proposed to solve QMC-VSBPP. The proposed VNS uses a special hierarchical clustering algorithm to generate the initial solution, in which three neighborhood operators are presented to expand solution space, and a local search algorithm based on a combination of two local operators is presented to find a local optimal solution. To evaluate the performance of the proposed VNS for QMC-VSBPP, a genetic algorithm and a variable neighborhood search for VSBPP were adapted for the state-of-the-art QMC-VSBPP, and the commercial solver CPLEX was also applied to QMC-VSBPP. Results of computational experiments on 96 test instances show that the proposed VNS could yield better solutions than those of the adapted genetic algorithm (GA), the adapted VNS, and CPLEX.