Neighborhood search techniques for solving uncapacitated multilevel lot-sizing problems Yiyong Xiao a , Ikou Kaku b , Qiuhong Zhao c,n , Renqian Zhang c a School of Reliability and System Engineering, Beihang University, Beijing 100191, China b Department of Management Science and Engineering, Akita Prefectural University, Yulihonjo, Akita 015-0055 Japan c School of Economics and Management, Beihang University, Beijing 100191, China article info Available online 12 June 2011 Keywords: Multilevel lot-sizing (MLLS) problem Meta-heuristic algorithm Neighborhood search techniques Index Comparative simulations abstract In this paper, several neighborhood search techniques for solving uncapacitated multilevel lot-sizing problems are investigated. We introduce three indexes: distance, changing range, and changing level that have great influence on the searching efficacy of neighborhood search techniques. These insights can help develop more efficient heuristic algorithms. As a result, we have developed an iterated neighborhood search (INS) algorithm that is very simple but that demonstrates good performance when tested against 176 benchmark instances under different scales (small, medium, and large), with 25 instances having been updated with new best known solutions in the computing experiments. & 2011 Elsevier Ltd. All rights reserved. 1. Introduction The multilevel lot-sizing (MLLS) problem concerns how to determine the lot size for producing or procuring an item at each level so as to minimize total setup cost and inventory holding cost. The MLLS problem plays an important role in the efficient operation of modern manufacturing and assembly processes. Optimal algorithms exist for MLLS problems, including dynamic programming formulations [1,2], an assembly-structure-based method [3], and branch and bound algorithms [4,5]. However, only small instances can be solved in a reasonable time because the problem is NP-hard [6]. Quite a few heuristic approaches have been developed to solve the MLLS problem and its variants. Early works consisted first of the sequential application of single-level lot-sizing models to each component of the product structure [7,8], and later of the approximate application of multilevel lot- sizing models [9–11]. Along with the increasing structural complexity of modern products and decreasing marginal profits for manufacturing firms due to the rise in customer demand and fierce competition, it has become more and more difficult to provide satisfactory solutions for the MLLS problem. Recently, several meta-heuristic algorithms have been developed to solve large-sized MLLS problems with complex product structures. It has been reported that the evolu- tionary algorithms are capable of providing highly cost-efficient solutions within reasonable computing load. Dellaert and Jeunet [12] and Dellaert et al. [13] first presented a hybrid genetic algorithm (HGA) to solve large-sized MLLS problems with a general product structure. They introduced a competitive strategy for mixing the use of five operators by which the incumbent chromosomes were evolved from one generation to the next. Homberger [14] presented a parallel genetic algorithm (PGA) and an empirical policy for deme migration (rate, interval, and selection) for the MLLS problem. He utilized the power of parallelized calculations to decentralize the huge computational load among multiple processors (30 processors were used in his computational experiments). Besides genetic algorithms, other meta-heuristic algorithms, including simulated annealing (SA) algorithms [15,16], particle swarm optimization (PSO) algorithm by Han et al. [17], MAX–MIN ant colony optimization (ACO) system by Pitakaso et al. [18], soft optimization approach (SOA) based on segmentation by Kaku et al. [19,20], and reduced variable neighborhood search (RVNS) algorithm by Xiao et al. [21] have been developed for solving the uncapacitated MLLS (UMLLS) problem. Despite the diversity in the searching mechan- isms inspired by different models of biological species or physical phenomena, a common underlying feature that may be observed among these algorithms is that their schemes all fall into the category of neighborhood search algorithms (or generate-and-test algorithm) in that new candidate solutions are always produced from the current status of incumbent solutions (GA, SA, and RVND) or affected by previous search experiences (PSO and ACO). Then a question may be raised: Are there some general rules behind those neighborhood-search-based algorithms that are crucial for their searching effectiveness and efficiency? Or can we find out these rules via systematical analysis rather than through imitating biological species or natural phenomena? In this study we introduce some general rules into neighbor- hood search techniques for solving the uncapacitated MLLS problem, and we provide insights for improving the search effect Contents lists available at ScienceDirect journal homepage: www.elsevier.com/locate/caor Computers & Operations Research 0305-0548/$ - see front matter & 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.cor.2011.06.004 n Corresponding author. Tel.: þ86 10 82316181; fax: þ86 10 82328037. E-mail address: qhzhao@buaa.edu.cn (Q. Zhao). Computers & Operations Research 39 (2012) 647–658