GRASP is a multi-start metaheuristic for combinatorial problems, in which each iteration consists basically of two phases: construction and local search. The construction phase builds a feasible solution, whose neighborhood is investigated until a local minimum is found during the local search phase. The best overall solution is kept as the result. In this chapter, … Read more
Interior point methods, the traditional methods for the $SDP$, are fairly limited in the sizes of problems they can handle. This paper deals with an $LP$ approach to overcome some of these shortcomings. We begin with a semi-infinite linear programming formulation of the $SDP$ and discuss the issue of its discretization in some detail. We … Read more
We introduce an anti-matroid as a family $\cal F$ of subsets of a ground set $E$ for which there exists an assignment of weights to the elements of $E$ such that the greedy algorithm to compute a maximal set (with respect to inclusion) in $\cal F$ of minimum weight finds, instead, the unique maximal set … Read more
Lagrangian relaxation is a tool to find upper bounds on a given (arbitrary) maximization problem. Sometimes, the bound is exact and an optimal solution is found. Our aim in this paper is to review this technique, the theory behind it, its numerical aspects, its relation with other techniques such as column generation. Citationin: Computational Combinatorial … Read more
A GRASP (greedy randomized adaptive search procedure) is a multi-start metaheuristic for combinatorial optimization. We study the probability distributions of solution time to a sub-optimal target value in five GRASPs that have appeared in the literature and for which source code is available. The distributions are estimated by running 12,000 independent runs of the heuristic. … Read more