Abstract. Today, a variety of heuristic approaches are available to the operations research practitioner. One methodology that has a strong intuitive appeal, a prominent empirical track record, and is trivial to efficiently implement on parallel processors is GRASP (Greedy Randomized Adaptive Search Procedures). GRASP is an iterative randomized sampling technique in which each iteration provides a solution to the problem at hand. The incumbent solution over all GRASP iterations is kept as the final result. There are two phases within each GRASP iteration: the first intelligently constructs an initial solution via an adaptive randomized greedy function; the second applies a local search procedure to the constructed solution in hope of finding an improvement. In this paper, we define the various components comprising a GRASP and demonstrate, step by step, how to develop such heuristics for combinatorial optimization problems. Intuitive justifications for the observed empirical behavior of the methodology are discussed. The paper concludes with a brief literature review of GRASP implementations and mentions two industrial applications.

. Quadratic Assignment Problems model many applications in diverse areas such as operations research, parallel and distributed computing, and combinatorial data analysis. In this paper we survey some of the most important techniques, applications, and methods regarding the quadratic assignment problem. We focus our attention on recent developments. 1. Introduction Given a set N = f1; 2; : : : ; ng and n \Theta n matrices F = (f ij ) and D = (d kl ), the quadratic assignment problem (QAP) can be stated as follows: min p2\Pi N n X i=1 n X j=1 f ij d p(i)p(j) + n X i=1 c ip(i) ; where \Pi N is the set of all permutations of N . One of the major applications of the QAP is in location theory where the matrix F = (f ij ) is the flow matrix, i.e. f ij is the flow of materials from facility i to facility j, and D = (d kl ) is the distance matrix, i.e. d kl represents the distance from location k to location l [62, 67, 137]. The cost of simultaneously assigning facility i to locat...

Parallel programs may be represented as a set of interrelated sequential tasks. When multiprocessors are used to execute such programs, the parallel portion of the application can be speeded up by an appropriate allocation of processors to the tasks of the application. Given a parallel application defined by a task precedence graph, the goal of task scheduling (or processor assignment) is thus the minimization of the makespan of the application. In a heterogeneous multiprocessor system, task scheduling consists in determining which tasks will be assigned to each processor, as well as the execution order of the tasks assigned to each processor. In this work, we apply the tabu search metaheuristic to the solution of the task scheduling problem on a heterogeneous multiprocessor environment under precedence constraints. The topology of the Mean Value Analysis solution package for product form queueing networks is used as the framework for performance evaluation. We show that tabu search ob...

We consider the following map labelling problem: given distinct points p 1 , p 2 , . . . , p n in the plane, and given #, find a maximum cardinality set of pairwise disjoint axis-parallel # # squares Q 1 , Q 2 , . . . , Q r . This problem reduces to that of finding a maximum cardinality independent set in an associated graph called the conflict graph. We describe several heuristics for the maximum cardinality independent set problem, some of which use an LP solution as input. Also, we describe a branch-and-cut algorithm to solve it to optimality. The standard independent set formulation has an inequality for each edge in the conflict graph which ensures that only one of its endpoints can belong to an independent set. To obtain good starting points for our LP-based heuristics and good upper bounds on the optimal value for our branch-and-cut algorithm we replace this set of inequalities by the set of inequalities describing all maximal cliques in the conflict graph. For this streng...

We present a combined use of Genetic Algorithms (GAs) and column generation to approximately solve graph-coloring problems. The proposed method is divided in two phases. The constructive phase builds the initial pool of columns using a Constructive Genetic Algorithm (CGA). Each column forms an independent set. The second phase solves by column generation the set covering formulation. The columns are generated solving weighted independent set problems. Some computational experience is given.

Edge projection is a specialization of Lovász and Plummer's clique projection when restricted to edges. A concept of augmenting sequences of edge-projections is defined w.r.t. a stable set S. It is then proved the equivalence between the optimality of S and the existence of an augmenting sequence w.r.t. S. This result is then exploited to develop a new tabu-search heuristic for the Maximum Stable Set Problem (weighted and unweighted). The resulting code proved to be competitive with the best codes presented in the literature.

this article, G = (V; E) is an arbitrary undirected and weighted graph unless otherwise specified, where V = f1; 2; : : : ; ng is the vertex set of G and E ` V \Theta V is its edge set. For each vertex i 2 V , a positive weight w i is associated with i, collected in the weight vector w 2 IR

Abstract. This paper introduces tight upper bounds for the daily photograph scheduling problem of earth observation satellites. These bounds, which were unavailable until now, allow us to assess the quality of the heuristic solutions obtained previously. These bounds are obtained with a partition-based approach following the “divide and pas conquer ” principle. Dynamic programming and tabu search are conjointly used in this approach. We present also simplex-based linear programming relaxation and a relaxed knapsack approach for the problem.

This paper investigates the capabilities of the Ant Colony Optimization (ACO) meta-heuristic for solving the maximum clique problem, the goal of which is to find a largest set of pairwise adjacent vertices in a graph. We propose two ACO algorithms for this problem. Basically, these algorithms successively generate maximal cliques through the repeated addition of vertices into partial cliques, and both of them use “pheromone trails ” as a greedy heuristic to choose, at each step, the next vertex to enter the clique. However, these two algorithms differ in the way pheromone trails are laid and exploited, i.e., on edges or on vertices of the graph. We illustrate and compare the behavior of the two proposed ACO algorithms on a representative benchmark instance and we study the impact of pheromone on the solution process. We consider two measures —the re-sampling and the dispersion ratio — for providing an insight into the two algorithms performances. We also study the benefit of integrating a local search procedure within the proposed ACO algorithms, and we show that this improves the solution process. Finally, we compare ACO performances with three representative heuristic approaches, showing that it obtains competitive results.

this paper, we present a variant of local search, namely the Life Span Method (LSM), for generic combinatorial optimization problems. The LSM can be seen as a variation of tabu search introduced by Glover [18, 19]. We outline applications of the LSM to several combinatorial optimization problems such as the maximum stable set problem, the traveling salesman problem, the quadratic assignment problem, the graph partitioning problem, the graph coloring problem, and the job-shop scheduling problem.