In the recently published book on the Traveling Salesman Problem, half of Chapter 6 is devoted to domination analysis (DA) of heuristics for the Traveling Salesman Problem. Another chapter (in preparation) is a detailed overview of the whole area of DA. Both chapters are of considerable length. The purpose of this paper is to give … Read more
Interior-point methods (IPMs), originally conceived in the context of linear programming have found a variety of applications in integer programming, and combinatorial optimization. This survey presents an up to date account of IPMs in solving NP-hard combinatorial optimization problems to optimality, and also in developing approximation algorithms for some of them. The surveyed approaches include … Read more
This problem deals with the uncapacitated multiple allocation hub location problem. The dual problem of a four-indexed formulation is considered and a heuristic method, based on a dual-ascent technique, is designed. This heuristic, which is reinforced with several specifical subroutines and does not require any external linear problem solver, is the core tool embedded in … Read more
This paper deals with a capacitated hub location problem arising in the design of telecommunications networks. The problem is different from the classical hub location problem in two ways: the cost of using an edge is not linear but stepwise and the capacity of an hub restricts the amount of traffic transiting through the hub … Read more
A classical theorem by Block and Levin says that certain variants of the relaxation method for solving systems of linear inequalities produce bounded sequences of intermediate solutions even when running on inconsistent input data. Using a new approach, we prove a more general version of this result and answer an old open problem of quantifying … Read more
A parallel computational method SDPARA-C is presented for SDPs (semidefinite programs). It combines two methods SDPARA and SDPA-C proposed by the authors who developed a software package SDPA. SDPARA is a parallel implementation of SDPA and it features parallel computation of the elements of the Schur complement equation system and a parallel Cholesky factorization of … Read more
It is well known that a sparse Jacobian matrix can be determined with fewer function evaluations or automatic differentiation \emph{passes} than the number of independent variables of the underlying function. In this paper we show that by grouping together rows into blocks one can reduce this number further. We propose a graph coloring technique for … Read more
We provide two new, simple proofs of Afriat’s celebrated theorem stating that a finite set of price-quantity observations is consistent with utility maximization if, and only if, the observations satisfy a variation of the Strong Axiom of Revealed Preference known as the Generalized Axiom of Revealed Preference. CitationTechnical Report No. 1381, School of Operations Research … Read more
A Greedy Randomized Adaptive Search Procedure (GRASP) is a metaheuristic for combinatorial optimization. It usually consists of a construction procedure based on a greedy randomized algorithm and local search. Path-relinking is an intensification strategy that explores trajectories that connect high quality solutions. We analyze two parallel strategies for GRASP with path-relinking and propose a criterion … Read more
We present a multi-exchange local search algorithm for approximating the capacitated facility location problem (CFLP), where a new local improvement operation is introduced that possibly exchanges multiple facilities simultaneously. We give a tight analysis for our algorithm and show that the performance guarantee of the algorithm is between $3+2\sqrt{2}-\epsilon$ and $3+2\sqrt{2}+\epsilon$ for any given constant … Read more