Pooling problem: Alternate formulations and solution methods

Copyright @ 2004 INFORMSThe pooling problem, which is fundamental to the petroleum industry, describes a situation in which products possessing different attribute qualities are mixed in a series of pools in such a way that the attribute qualities of the blended products of the end pools must satisfy given requirements. It is well known that the pooling problem can be modeled through bilinear and nonconvex quadratic programming. In this paper, we investigate how best to apply a new branch-and-cut quadratic programming algorithm to solve the pooling problem. To this effect, we consider two standard models: One is based primarily on flow variables, and the other relies on the proportion. of flows entering pools. A hybrid of these two models is proposed for general pooling problems. Comparison of the computational properties of flow and proportion models is made on several problem instances taken from the literature. Moreover, a simple alternating procedure and a variable neighborhood search heuristic are developed to solve large instances and compared with the well-known method of successive linear programming. Solution of difficult test problems from the literature is substantially accelerated, and larger ones are solved exactly or approximately.This project was funded by Ultramar Canada and Luc Massé. The work of C. Audet was supported by NSERC (Natural Sciences and Engineering Research Council) fellowship PDF-207432-1998 and by CRPC (Center for Research on Parallel Computation). The work of J. Brimberg was supported by NSERC grant #OGP205041. The work of P. Hansen was supported by FCAR(Fonds pour la Formation des Chercheurs et l’Aide à la Recherche) grant #95ER1048, and NSERC grant #GP0105574

Solving the planar p-median problem by variable neighborhood and concentric searches

Two new approaches for the solution of the p-median problem in the plane are proposed. One is a Variable Neighborhood Search (VNS) and the other one is a concentric search. Both approaches are enhanced by a front-end procedure for finding good starting solutions and a decomposition heuristic acting as a post optimization procedure. Computational results confirm the effectiveness of the proposed algorithms

An oil pipeline design problem

Copyright @ 2003 INFORMSWe consider a given set of offshore platforms and onshore wells producing known (or estimated) amounts of oil to be connected to a port. Connections may take place directly between platforms, well sites, and the port, or may go through connection points at given locations. The configuration of the network and sizes of pipes used must be chosen to minimize construction costs. This problem is expressed as a mixed-integer program, and solved both heuristically by Tabu Search and Variable Neighborhood Search methods and exactly by a branch-and-bound method. Two new types of valid inequalities are introduced. Tests are made with data from the South Gabon oil field and randomly generated problems.The work of the first author was supported by NSERC grant #OGP205041. The work of the second author was supported by FCAR (Fonds pour la Formation des Chercheurs et l’Aide à la Recherche) grant #95-ER-1048, and NSERC grant #GP0105574

Optimal solutions for the continuous p-centre problem and related α-neighbour and conditional problems: A relaxation-based algorithm

This paper aims to solve large continuous p-centre problems optimally by re-examining a recent relaxation-based algorithm. The algorithm is strengthened by adding four mathematically supported enhancements to improve its efficiency. This revised relaxation algorithm yields a massive reduction in computational time enabling for the first time larger data-sets to be solved optimally (e.g., up to 1323 nodes). The enhanced algorithm is also shown to be flexible as it can be easily adapted to optimally solve related practical location problems that are frequently faced by senior management when making strategic decisions. These include the α-neighbour p-centre problem and the conditional p-centre problem. A scenario analysis using variable α is also performed to provide further managerial insights

Using injection points in reformulation local search for solving continuous location problems

Reformulation local search (RLS) has been recently proposed as a new approach for solving continuous location problems. The main idea, although not new, is to exploit the relation between the continuous model and its discrete counterpart. The RLS switches between the continuous model and a discrete relaxation in order to expand the search. In each iteration new points obtained in the continuous phase are added to the discrete formulation. Thus, the two formulations become equivalent in a limiting sense. In this paper we introduce the idea of adding 'injection points' in the discrete phase of RLS in order to escape a current local solution. Preliminary results are obtained on benchmark data sets for the multi-source Weber problem that support further investigation of the RLS framework

New heuristic algorithms for solving the planar p-median problem

In this paper we propose effective heuristics for the solution of the planar p-median problem. We develop a new distribution based variable neighborhood search and a new genetic algorithm, and also test a hybrid algorithm that combines these two approaches. The best results were obtained by the hybrid approach. The best known solution was found in 466 out of 470 runs, and the average solution was only 0.000016% above the best known solution on 47 well explored test instances of 654 and 1060 demand points and up to 150 facilities

A new local search for . . .

This paper presents a new local search approach for solving continuous location problems. The main idea is to exploit the relation between the continuous model and its discrete counterpart. A local search is first conducted in the continuous space until a local optimum is reached. It then switches to a discrete space that represents a discretisation of the continuous model to find an improved solution from there. The process continues switching between the two problem formulations until no further improvement can be found in either. Thus, we may view the procedure as a new adaption of formulatio