NILS: a Neutrality-based Iterated Local Search and its application to Flowshop Scheduling

This paper presents a new methodology that exploits specific characteristics from the fitness landscape. In particular, we are interested in the property of neutrality, that deals with the fact that the same fitness value is assigned to numerous solutions from the search space. Many combinatorial optimization problems share this property, that is generally very inhibiting for local search algorithms. A neutrality-based iterated local search, that allows neutral walks to move on the plateaus, is proposed and experimented on a permutation flowshop scheduling problem with the aim of minimizing the makespan. Our experiments show that the proposed approach is able to find improving solutions compared with a classical iterated local search. Moreover, the tradeoff between the exploitation of neutrality and the exploration of new parts of the search space is deeply analyzed

Algorithms for the minimum sum coloring problem: a review

The Minimum Sum Coloring Problem (MSCP) is a variant of the well-known vertex coloring problem which has a number of AI related applications. Due to its theoretical and practical relevance, MSCP attracts increasing attention. The only existing review on the problem dates back to 2004 and mainly covers the history of MSCP and theoretical developments on specific graphs. In recent years, the field has witnessed significant progresses on approximation algorithms and practical solution algorithms. The purpose of this review is to provide a comprehensive inspection of the most recent and representative MSCP algorithms. To be informative, we identify the general framework followed by practical solution algorithms and the key ingredients that make them successful. By classifying the main search strategies and putting forward the critical elements of the reviewed methods, we wish to encourage future development of more powerful methods and motivate new applications

Metaheuristics for the Order Batching Problem in Manual Order Picking Systems

In manual order picking systems, order pickers walk or drive through a distribution warehouse in order to collect items which are requested by (internal or external) customers. In order to perform these operations effciently, it is usually required that customer orders are combined into (more substantial) picking orders of limited size. The Order Batching Problem considered in this paper deals with the question of how a given set of customer orders should be combined such that the total length of all tours is minimized which are necessary to collect all items. The authors introduce two metaheuristic approaches for the solution of this problem; the rst one is based on Iterated Local Search, the second one on Ant Colony Optimization. In a series of extensive numerical experiments, the newly developed approaches are benchmarked against classic solution methods. It is demonstrated that the proposed methods are not only superior to existing methods, but provide solutions which may allow for operating distribution warehouses signicantly more effcient.Warehouse Management, Order Picking, Order Batching, Iterated Local Search, Ant Colony Optimization

On Neighborhood Tree Search

We consider the neighborhood tree induced by alternating the use of different neighborhood structures within a local search descent. We investigate the issue of designing a search strategy operating at the neighborhood tree level by exploring different paths of the tree in a heuristic way. We show that allowing the search to 'backtrack' to a previously visited solution and resuming the iterative variable neighborhood descent by 'pruning' the already explored neighborhood branches leads to the design of effective and efficient search heuristics. We describe this idea by discussing its basic design components within a generic algorithmic scheme and we propose some simple and intuitive strategies to guide the search when traversing the neighborhood tree. We conduct a thorough experimental analysis of this approach by considering two different problem domains, namely, the Total Weighted Tardiness Problem (SMTWTP), and the more sophisticated Location Routing Problem (LRP). We show that independently of the considered domain, the approach is highly competitive. In particular, we show that using different branching and backtracking strategies when exploring the neighborhood tree allows us to achieve different trade-offs in terms of solution quality and computing cost.Comment: Genetic and Evolutionary Computation Conference (GECCO'12) (2012

Combinatorial optimization and metaheuristics

Today, combinatorial optimization is one of the youngest and most active areas of discrete mathematics. It is a branch of optimization in applied mathematics and computer science, related to operational research, algorithm theory and computational complexity theory. It sits at the intersection of several fields, including artificial intelligence, mathematics and software engineering. Its increasing interest arises for the fact that a large number of scientific and industrial problems can be formulated as abstract combinatorial optimization problems, through graphs and/or (integer) linear programs. Some of these problems have polynomial-time (“efficient”) algorithms, while most of them are NP-hard, i.e. it is not proved that they can be solved in polynomial-time. Mainly, it means that it is not possible to guarantee that an exact solution to the problem can be found and one has to settle for an approximate solution with known performance guarantees. Indeed, the goal of approximate methods is to find “quickly” (reasonable run-times), with “high” probability, provable “good” solutions (low error from the real optimal solution). In the last 20 years, a new kind of algorithm commonly called metaheuristics have emerged in this class, which basically try to combine heuristics in high level frameworks aimed at efficiently and effectively exploring the search space. This report briefly outlines the components, concepts, advantages and disadvantages of different metaheuristic approaches from a conceptual point of view, in order to analyze their similarities and differences. The two very significant forces of intensification and diversification, that mainly determine the behavior of a metaheuristic, will be pointed out. The report concludes by exploring the importance of hybridization and integration methods