Minmax regret combinatorial optimization problems: an Algorithmic Perspective

Candia-Vejar, A (reprint author), Univ Talca, Modeling & Ind Management Dept, Curico, Chile.Uncertainty in optimization is not a new ingredient. Diverse models considering uncertainty have been developed over the last 40 years. In our paper we essentially discuss a particular uncertainty model associated with combinatorial optimization problems, developed in the 90's and broadly studied in the past years. This approach named minmax regret (in particular our emphasis is on the robust deviation criteria) is different from the classical approach for handling uncertainty, stochastic approach, where uncertainty is modeled by assumed probability distributions over the space of all possible scenarios and the objective is to find a solution with good probabilistic performance. In the minmax regret (MMR) approach, the set of all possible scenarios is described deterministically, and the search is for a solution that performs reasonably well for all scenarios, i.e., that has the best worst-case performance. In this paper we discuss the computational complexity of some classic combinatorial optimization problems using MMR. approach, analyze the design of several algorithms for these problems, suggest the study of some specific research problems in this attractive area, and also discuss some applications using this model

Worst-case performance of Wong's Steiner tree heuristic

Candia-Vejar, A. Department of Systems Engineering, Universidad de Talca, Merced 437, Curicó, Chile.A study of the worst-case performance of Wong's heuristic for the Steiner problem in directed networks (SPDN) is presented in this paper. SPDN is a classic combinatorial optimization problem having the status of a very difficult problem (-hard problem) and it is known as an optimization model for a broad class of problems in networks. Several exact and heuristic approaches have been designed for SPDN in the last twenty five years. Some papers analyze theoretical and experimental behavior of heuristics for SPDN, specially for undirected networks, but none of these has studied the worst-case performance of Wong's heuristic. In this paper, we find a lower bound for that performance and show that this bound is consistent with comparable results in the literature on SPDN and its undirected version

The optimization of success probability for software projects using genetic algorithms

Addresses: 1. Univ Talca, Fac Ingn, Dept Comp Sci, Curico, Chile 2. Univ Talca, Fac Ingn, Modeling & Operat Management Dept, Curico, Chile 3. Univ Talca, Acad field Teaching Algorithms & Programming, Curico, ChileThe software development process is usually affected by many risk factors that may cause the loss of control and failure, thus which need to be identified and mitigated by project managers. Software development companies are currently improving their process by adopting internationally accepted practices, with the aim of avoiding risks and demonstrating the quality of their work. This paper aims to develop a method to identify which risk factors are more influential in determining project outcome. This method must also propose a cost effective investment of project resources to improve the probability of project success. To achieve these aims, we use the probability of success relative to cost to calculate the efficiency of the probable project outcome. The definition of efficiency used in this paper was proposed by researchers in the field of education. We then use this efficiency as the fitness function in an optimization technique based on genetic algorithms. This method maximizes the success probability output of a prediction model relative to cost. The optimization method was tested with several software risk prediction models that have been developed based on the literature and using data from a survey which collected information from in-house and outsourced software development projects in the Chilean software industry. These models predict the probability of success of a project based on the activities undertaken by the project manager and development team. The results show that the proposed method is very useful to identify those activities needing greater allocation of resources, and which of these will have a higher impact on the projects success probability. Therefore using the measure of efficiency has allowed a modular approach to identify those activities in software development on which to focus the project's limited resources to improve its probability of success. The genetic algorithm and the measure of efficiency presented in this paper permit model independence, in both prediction of success and cost evaluation. (C) 2010 Elsevier Inc. All rights reserved. Accession Number: WOS:00028917930000

On exact solutions for the Minmax Regret Spanning Tree problem

Univ Talca, Programa Magister Gest Operac, Curico, Chile; Perez-Galarce, F (Perez-Galarce, Francisco); Alvarez-Miranda, E (Alvarez-Miranda, Eduardo); Candia-Vejar, A (Candia-Vejar, Alfredo)The Minmax Regret Spanning Tree problem is studied in this paper. This is a generalization of the well-known Minimum Spanning Tree problem, which considers uncertainty in the cost function. Particularly, it is assumed that the cost parameter associated with each edge is an interval whose lower and upper limits are known, and the Minmax Regret is the optimization criterion. The Minmax Regret Spanning Tree problem is an NP-Hard optimization problem for which exact and heuristic approaches have been proposed. Several exact algorithms are proposed and computationally compared with the most effective approaches of the literature. It is shown that a proposed branch-and-cut approach outperforms the previous approaches when considering several classes of instances from the literature. (C) 2014 Elsevier Ltd. All rights reserved

Deterministic risk control for cost-effective network connections

Alvarez-Miranda, E (Alvarez-Miranda, Eduardo);Candia-Vejar, A (Candia-Vejar, Alfredo).Univ Talca, Ind Management Dept, Talca, ChileThis paper considers the minimum connection problem in networks with uncertain data. In such a network it is assumed that one can establish a link e by paying a cost c(e) in a given interval [c(e)(-), c(e)(+)] while taking a risk (c(e)(+) - c(e))/(c(e)(+) - c(e)(-)) of link failure. We develop polynomial time algorithms for minimum cost network connection with paths or spanning trees under risk-sum constraints. (C) 2009 Elsevier B.V. All rights reserved