An adaptive large neighborhood search metaheuristic for the Generalized Bin Packing problem with incompatible categories

Abstract

This paper addresses the Generalized Bin Packing Problem with Incompatible Categories (GBPPIC), a challenging optimization problem related to last-mile distribution in large cities. We aim to determine the best assignment of deliveries of distinct products to a homogeneous fleet of capacitated vehicles to minimize the number of required vehicles (bins), considering the concept of incompatible categories (i.e., types of items that cannot be transported together). Unlike the Bin Packing Problem with Compatible Categories (BPCC), deliveries to be assigned to the vehicles can be of two types: to regular or sporadic customers; the former must be serviced while the latter does not necessarily need to be serviced but may bring additional revenue that does not offset the cost of an additional vehicle. Due to the difficulty in solving to optimality large instances found in practice, an Adaptive Large Neighborhood Search (ALNS) metaheuristic is proposed. It is applied to new benchmark instances derived from the BPCC, and the results are compared to exact solutions. The computational experiments indicate that our ALNS algorithm can effectively solve the GBPPIC in very short running times, even for larger instances that require significantly longer times for the exact approach. The ALNS also outperforms a previous VNS heuristic for the BPCC.