Memetic Search for the Generalized Quadratic Multiple Knapsack Problem

The generalized quadratic multiple knapsack problem (GQMKP) extends the classical quadratic multiple knapsack problem with setups and knapsack preference of the items. The GQMKP can accommodate a number of real-life applications and is computationally difficult. In this paper, we demonstrate the interest of the memetic search approach for approximating the GQMKP by presenting a highly effective memetic algorithm (denoted by MAGQMK). The algorithm combines a backbone-based crossover operator (to generate offspring solutions) and a multineighborhood simulated annealing procedure (to find high quality local optima). To prevent premature convergence of the search, MAGQMK employs a quality-and-distance (QD) pool updating strategy. Extensive experiments on two sets of 96 benchmarks show a remarkable performance of the proposed approach. In particular, it discovers improved best solutions in 53 and matches the best known solutions for 39 other cases. A case study on a pseudo real-life problem demonstrates the efficacy of the proposed approach in practical situations. Additional analyses show the important contribution of the novel general-exchange neighborhood, the backbone-based crossover operator as well as the QD pool updating rule to the performance of the proposed algorithm

Path relinking for the fixed spectrum frequency assignment problem

The fixed spectrum frequency assignment problem (FS-FAP) is a highly relevant application in modern wireless systems. This paper presents the first path relinking (PR) approach for solving FS-FAP. We devise four relinking operators to generate intermediate solutions (or paths) and a tabu search procedure for local optimization. We also adopt a diversity-and-quality technique to maintain population diversity. To show the effectiveness of the proposed approach, we present computational results on the set of 42 benchmark instances commonly used in the literature and compare them with the current best results obtained by any other existing methods. By showing improved best results (new upper bounds) for 19 instances, we demonstrate the effectiveness of the proposed PR approach. We investigate the impact of the relinking operators and the population updating strategy. The ideas of the proposed could be applicable to other frequency assignment problems and search problems

Effective Learning-Based Hybrid Search for Bandwidth Coloring

The bandwidth coloring problem (BCP) and the bandwidth multicoloring problem (BMCP) are two important generalizations of the classical vertex coloring problem. This paper presents learning-based hybrid search (LHS) for BCP and BMCP. LHS combines a construction phase to progressively build feasible (partial) colorings and a local search phase to reestablish feasibility when an illegal partial solution is encountered. The construction phase relies on a learning-based guiding function to determine the next vertex for color assignment while the local search phase uses a tabu search repair procedure to resolve coloring conflicts. Experiments on a set of 33 well-known benchmarks for BCP and a set of 33 benchmarks for BMCP demonstrate that the proposed LHS approach can match the best known solution for most benchmarks. In particular, LHS finds an improved best solution for 14 instances

Advances in metaheuristics for gene selection and classification of microarray data

Gene selection aims at identifying a (small) subset of informative genes from the initial data in order to obtain high predictive accuracy for classification. Gene selection can be considered as a combinatorial search problem and thus be conveniently handled with optimization methods. In this article, we summarize some recent developments of using metaheuristic-based methods within an embedded approach for gene selection. In particular, we put forward the importance and usefulness of integrating problem-specific knowledge into the search operators of such a method. To illustrate the point, we explain how ranking coefficients of a linear classifier such as support vector machine (SVM) can be profitably used to reinforce the search efficiency of Local Search and Evolutionary Search metaheuristic algorithms for gene selection and classification

List-graph colouring for multiple depot vehicle scheduling

This article addresses a multiple depot vehicle scheduling problem (MDVSP) arising in public transportation. The general problem consists in assigning vehicles to trips while minimising the number of scheduled vehicles and the operational costs. The MDVSP considered here takes into account heterogeneous types of vehicles with complex relations among them. This special feature matches well situations encountered in practice, but makes the problem particularly difficult. We introduce a new formulation based on list-graph colouring, from which an iterative tabu search is developed for vehicle minimisation. The approach is assessed on seven real-world benchmarks and yields highly satisfactory results in terms of solution quality and computation time

Adaptive neighborhood search for nurse rostering

This paper presents an adaptive neighborhood search method (ANS) for solving the nurse rostering problem proposed for the First International Nurse Rostering Competition (INRC-2010). ANS uses jointly two distinct neighborhood moves and adaptively switches among three intensification and diversification search strategies according to the search history. Computational results assessed on the three sets of 60 competition instances show that ANS improves the best known results for 12 instances while matching the best bounds for 39 other instances. An analysis of some key elements of ANS sheds light on the understanding of the behavior of the proposed algorithm

Efficient evaluations for solving large 0-1 unconstrained quadratic optimisation problems

We provide a method for efficiently evaluating moves that complement values of 0-1 variables in search methods for binary unconstrained quadratic optimisation problems. Our method exploits a compact matrix representation and offers further improvements in speed by exploiting sparse matrices that arise in large-scale applications. The resulting approach, which works with integer or real data, can be applied to improve the efficiency of a variety of different search processes, especially in the case of commonly encountered applications that involve large and sparse matrices. It also enables larger problems to be solved than could previously be handled within a given amount of available memory. Our evaluation method has been embedded in a tabu search algorithm in a sequel to this paper, yielding a method that efficiently matches or improves currently best-known results for instances from widely used benchmark sets having up to 7,000 variables