A study on exponential-size neighborhoods for the bin packing problem with conflicts

We propose an iterated local search based on several classes of local and large neighborhoods for the bin packing problem with conflicts. This problem, which combines the characteristics of both bin packing and vertex coloring, arises in various application contexts such as logistics and transportation, timetabling, and resource allocation for cloud computing. We introduce $O(1)$ evaluation procedures for classical local-search moves, polynomial variants of ejection chains and assignment neighborhoods, an adaptive set covering-based neighborhood, and finally a controlled use of 0-cost moves to further diversify the search. The overall method produces solutions of good quality on the classical benchmark instances and scales very well with an increase of problem size. Extensive computational experiments are conducted to measure the respective contribution of each proposed neighborhood. In particular, the 0-cost moves and the large neighborhood based on set covering contribute very significantly to the search. Several research perspectives are open in relation to possible hybridizations with other state-of-the-art mathematical programming heuristics for this problem.Comment: 26 pages, 8 figure

Satellite downlink scheduling problem: A case study

The synthetic aperture radar (SAR) technology enables satellites to efficiently acquire high quality images of the Earth surface. This generates significant communication traffic from the satellite to the ground stations, and, thus, image downlinking often becomes the bottleneck in the efficiency of the whole system. In this paper we address the downlink scheduling problem for Canada's Earth observing SAR satellite, RADARSAT-2. Being an applied problem, downlink scheduling is characterised with a number of constraints that make it difficult not only to optimise the schedule but even to produce a feasible solution. We propose a fast schedule generation procedure that abstracts the problem specific constraints and provides a simple interface to optimisation algorithms. By comparing empirically several standard meta-heuristics applied to the problem, we select the most suitable one and show that it is clearly superior to the approach currently in use.Comment: 23 page

A time predefined variable depth search for nurse rostering

This paper presents a variable depth search for the nurse rostering problem. The algorithm works by chaining together single neighbourhood swaps into more effective compound moves. It achieves this by using heuristics to decide whether to continue extending a chain and which candidates to examine as the next potential link in the chain. Because end users vary in how long they are willing to wait for solutions, a particular goal of this research was to create an algorithm that accepts a user specified computational time limit and uses it effectively. When compared against previously published approaches the results show that the algorithm is very competitive

Design of Heuristic Algorithms for Hard Optimization

This open access book demonstrates all the steps required to design heuristic algorithms for difficult optimization. The classic problem of the travelling salesman is used as a common thread to illustrate all the techniques discussed. This problem is ideal for introducing readers to the subject because it is very intuitive and its solutions can be graphically represented. The book features a wealth of illustrations that allow the concepts to be understood at a glance. The book approaches the main metaheuristics from a new angle, deconstructing them into a few key concepts presented in separate chapters: construction, improvement, decomposition, randomization and learning methods. Each metaheuristic can then be presented in simplified form as a combination of these concepts. This approach avoids giving the impression that metaheuristics is a non-formal discipline, a kind of cloud sculpture. Moreover, it provides concrete applications of the travelling salesman problem, which illustrate in just a few lines of code how to design a new heuristic and remove all ambiguities left by a general framework. Two chapters reviewing the basics of combinatorial optimization and complexity theory make the book self-contained. As such, even readers with a very limited background in the field will be able to follow all the content

POPMUSIC for the Travelling Salesman Problem

POPMUSIC— Partial OPtimization Metaheuristic Under Special Intensification Conditions — is a template for tackling large problem instances. This metaheuristic has been shown to be very efficient for various hard combinatorial problems such as p-median, sum of squares clustering, vehicle routing, map labelling and location routing. A key point for treating large Travelling Salesman Problem (TSP) instances is to consider only a subset of edges connecting the cities. The main goal of this article is to present how to build a list of good candidate edges with a complexity lower than quadratic in the context of TSP instances given by a general function. The candidate edges are found with a technique exploiting tour merging and the POPMUSIC metaheuristic. When these candidate edges are provided to a good local search engine, high quality solutions can be found quite efficiently. The method is tested on TSP instances of up to several million cities with different structures (Euclidean uniform, clustered, 2D to 5D, grids, toroidal distances). Numerical results show that solutions of excellent quality can be obtained with an empirical complexity lower than quadratic without exploiting the geometrical properties of the instances