Very Large-Scale Neighborhood Search for the K-Constraint Multiple Knapsack Problem

Abstract

The K -Constraint Multiple Knapsack Problem (K-MKP) is a generalization of the multiple knapsack problem, which is one of the representative combinatorial optimization problems known to be NP-hard. In K-MKP, each item has K types of weights and each knapsack has K types of capacity. In this paper, we propose several very large-scale neighborhood search (VLSN) algorithms to solve K-MKP. One of the VLSN algorithms incorporates a novel approach that consists of randomly perturbing the current solution in order to efficiently produce a set of simultaneous non-profitable moves. These moves would allow several items to be transferred from their current knapsacks and assigned to new knapsacks, which makes room for new items to be inserted through multi-exchange movements and allows for improved solutions. Computational results presented show that the method is effective, and provides better solutions compared to exact algorithms run for the same amount of time.

A hypergraph multi-exchange heuristic for the single-source capacitated facility location problem

“…VLNS algorithms based on the idea of searching for special paths or cycles in an improvement graph have been widely studied and successfully applied to several hard combinatorial optimization problems. These include: vehicle routing problems (Thompson and Psaraftis, 1993); airline fleet assignment problems (Talluri, 1996); capacitated minimum spanning tree problems (Ahuja et al, 2001); machine scheduling problems (Frangioni et al, 2004); capacitated facility location problems, such as SSCFLP and the p-center problem (Ahuja et al, 2004;Scaparra et al, 2004); k -constraint multiple knapsack problems (Ahuja and Cunha, 2005); covering assignment and single source transportation problems (Öncan et al, 2008); location routing problems (Ambrosino et al, 2009); location problems with flexible demand (Rainwater et al, 2012); and hierarchical facility location problems (Addis et al, 2013).…”

On Merging Cover Inequalities for Multiple Knapsack Problems

“…An integer program (IP) is a common type of optimization problem, defined as maximize T c x subject to Solutions to KP and MK problems support a wide variety of real-world applications, including examples in Ahuja and Cunha [1], Chang and Lee [2], Dawande et al [3], Dizdar et al [4], Kellerer and Strusevich [5], Martello and Toth [6], Shachnai and Tamir [7], and Szeto and Lo [8]. This paper focuses on MK problems.…”