The p-facility Huff location problem aims at locating facilities on a competitive environment so as to maximize the market share. While it has been deeply studied in the field of continuous location, in this paper we study the p-facility Huff location problem on networks formulated as a Mixed Integer Nonlinear Programming problem that can be … Read more
Covering problems are well studied in the Operations Research literature under the assumption that both the set of users and the set of potential facilities are finite. In this paper we address the following variant, which leads to a Mixed Integer Nonlinear Program (MINLP): locations of p facilities are sought along the edges of a … Read more
This work deals with a Huff-like Stackelberg problem, where the leader facility wants to decide its location so that its profit is maximal after the competitor (the follower) also built its facility. It is assumed that the follower makes a rational decision, maximizing their profit. The inelastic demand is aggregated into the vertices of a … Read more
We show the importance of selecting good branching variables by exhibiting a family of instances for which an optimal solution is both trivial to find and provably optimal by a fixed-size branch-and-bound tree, but for which state-of-the-art Mixed Integer Programming solvers need an increasing amount of resources. The instances encode the edge-coloring problem on a … Read more
We propose a new method for solving univariate global optimization problems by combining a lower bound function of ®BB method (see [1]) with the lower bound function of the method developed in [4]. The new lower bound function is better than the two lower bound functions. We add the convex/concave test and pruning step which … Read more
We present a fast branch-and-bound algorithm for solving convex quadratic integer programs with few linear constraints. In each node, we solve the dual problem of the continuous relaxation using an infeasible active set method proposed by Kunisch and Rendl to get a lower bound; this active set algorithm is well suited for reoptimization. Our algorithm … Read more
PEBBL is a C++ class library implementing the underlying operations needed to support a wide variety of branch-and-bound algorithms in a message-passing parallel computing environment. Deriving application-speci c classes from PEBBL, one may create parallel branch-and-bound applications through a process focused on the unique aspects of the application, while relying on PEBBL for generic aspects of … Read more
Performance variability of modern mixed-integer programming solvers and possible ways of exploiting this phenomenon present an interesting opportunity in the development of algorithms to solve mixed-integer linear programs (MILPs). We propose a framework using multiple branch-and-bound trees to solve MILPs while allowing them to share information in a parallel execution. We present computational results on … Read more
We discuss some difficulties in determining valid upper bounds in spatial branch-and-bound methods for global minimization in the presence of nonconvex constraints. In fact, two examples illustrate that standard techniques for the construction of upper bounds may fail in this setting. Instead, we propose to perturb infeasible iterates along Mangasarian-Fromovitz directions to feasible points whose … Read more
We propose a branch-and-bound (BB) algorithm for biobjective mixed-integer linear programs (BOMILPs). Our approach makes no assumption on the type of problem and we prove that it returns all Pareto points of a BOMILP. We discuss two techniques upon which the BB is based: fathoming rules to eliminate those subproblems that are guaranteed not to … Read more