Un algorithme glouton randomisé pour le problème de placement sur bande en deux dimensions

Date du colloque : 2012National audienc

Sports League Scheduling: Enumerative Search for Prob026 from CSPLib

This paper presents an enumerative approach for a sports league scheduling problem. This simple method can solve some instances involving a number T of teams up to 70 while the best known constraint programing algorithm is limited to T≤40. The proposed approach relies on interesting properties which are used to constraint the search process

A Dedicated Genetic Algorithm for Two-Dimensional Non-Guillotine Strip Packing

This paper introduces DGA, a new dedicated genetic algorithm for a two-dimensional (2D) non-guillotine strip packing problem (2D-SPP). DGA integrates two key features: a hierarchical fitness function and a problem-specific crossover operator (WAX for "wasted area based crossover"). The fitness function takes into account not only the final height of the strip (to be minimized), but also the wasted areas. The goal of the meaningful (and "visual”) WAX crossover operator is to preserve the good property of parent packing configurations. To assess the proposed DGA, experimental results are shown on a set of well-known zero-waste benchmark instances and compared with previously reported genetic algorithms as well as the best performing meta-heuristic algorithms

A Reinforced Tabu Search Approach for 2D Strip Packing:

This paper discusses a particular “packing” problem, namely the two dimensional strip packing problem, where a finite set of objects have to be located in a strip of fixed width and infinite height. The variant studied considers regular items, rectangular to be precise, that must be packed without overlap, not allowing rotations. The objective is to minimize the height of the resulting packing. In this regard, the authors present a local search algorithm based on the well-known tabu search metaheuristic. Two important components of the presented tabu search strategy are reinforced in attempting to include problem knowledge. The fitness function incorporates a measure related to the empty spaces, while the diversification relies on a set of historically “frozen” objects. The resulting reinforced tabu search approach is evaluated on a set of well-known hard benchmark instances and compared with state-of-the-art algorithms

Using solution properties within an enumerative search to solve a sports league scheduling problem

This paper presents an enumerative approach for a particular sports league scheduling problem known as “Prob026” in CSPLib. Despite its exponential-time complexity, this simple method can solve all instances involving a number T of teams up to 50 in a reasonable amount of time while the best known tabu search and constraint programming algorithms are limited to T ⩽ 40 and the direct construction methods available only solve instances where ( T - 1 ) mod 3 ≠ 0 or T / 2 is odd. Furthermore, solutions were also found for some T values up to 70. The proposed approach relies on discovering, by observation, interesting properties from solutions of small problem instances and then using these properties in the final algorithm to constraint the search process