The research paper “Biobjective Branch-and-Cut Algorithms Based on LP Relaxation and Bound Sets” have been published in Informs Journal on Computing Abstract: Most real-world optimization problems are of a multi-objective nature, involving objectives which are conflicting and incomparable. Solving a multi-objective optimization problem requires a method which can generate the set of rational compromises between the objectives. In this paper, we propose two distinct bound set based branch-and-cut algorithms for bi-objective combinatorial optimization problems, based on implicitly and explicitly stated lower bound sets, respectively. The algorithm based on explicitly given lower bound sets computes for each branching node a lower bound set and compares it to an upper bound set. The implicit bound set based algorithm, on the other hand, fathoms branching nodes by generating a single point on the lower bound set for each local nadir point. We outline several approaches for fathoming branching nodes and we propose an […]
R package gMOIP has been updated to version 1.3.0 and now can plot 3D models too. The package can make 2D and 3D plots of the polytope of a linear programming (LP), integer linear programming (ILP) model, or mixed integer linear programming (MILP) model with 2 or 3 variables, including integer points, ranges and iso profit curve. Moreover you can also make a plot of the bi-objective criterion space and the non-dominated (Pareto) set for bi-objective LP/ILP/MILP programming models. Figures can be prepared for LaTeX and can automatically be transformed to TikZ using package tikzDevice.
From November 4-7, 2018 we have been participating the annual INFORMS conference, Phoenix, AZ, US. Talks have been interesting and for the first time CORAL joined the job fair to promote open Assistant and Associate Professor positions. The interest was overwhelming and some good candidates were found.
The research paper “An improved cut-and-solve algorithm for the single-source capacitated facility location problem” have been published in EURO Journal on Computational Optimization. Abstract: In this paper, we present an improved cut-and-solve algorithm for the single-source capacitated facility location problem. The algorithm consists of three phases. The first phase strengthens the integer program by a cutting plane algorithm to obtain a tight lower bound. The second phase uses a two-level local branching heuristic to find an upper bound, and if optimality has not yet been established, the third phase uses the cut-and-solve framework to close the optimality gap. Extensive computational results are reported, showing that the proposed algorithm runs 10–80 times faster on average compared to state-of-the-art problem-specific algorithms.
The past weeks we have created Multi-Objective Optimization Repository (MOrepo) which is a response to the needs of researchers from the MCDM society to access multi-objective (MO) optimization instances. The repository contains instances, results, generators etc. for different MO problems and is continuously updated. The repository can be used as a test set for testing new algorithms, validating existing results and for reproducibility. All researchers within MO optimization are welcome to contribute. For more information see https://github.com/MCDMSociety/MOrepo.
The last days I have been playing a bit with LocalSolver and tried to model various vehicle routing problems (VRP). LocalSolver is a heuristic solver based on a heuristic search approach combining different optimization techniques. It includes a math modeling language (LSP) and there is a package so that it can be used from R. You need to download and install LocalSolver (I used v7.0) and get an academic license from their webpage.
I recent released a small package gMOIP which can make 2D plots of linear and integer programming models (LP/IP). With the package you can make plots of the feasible region (or solution space) of an LP, visualize the integer points inside the region and the iso profit curve. Moreover, can also make a plot of a bi-objective criterion space and the non-dominated (Pareto) set. Figures are prepared for LaTeX and can automatically be transformed to TikZ using tikzDevice.
The research paper “A bi-objective approach to discrete cost-bottleneck location problems” have been published in Annals of Operations Research. Abstract: This paper considers a family of bi-objective discrete facility location problems with a cost objective and a bottleneck objective. A special case is, for instance, a bi-objective version of the (vertex) p-centdian problem. We show that bi-objective facility location problems of this type can be solved efficiently by means of an epsilon-constraint method that solves at most (n-1)m minisum problems, where n is the number of customer points and m the number of potential facility sites. Additionally, we compare the approach to a lexicographic epsilon-constrained method that only returns efficient solutions and to a two-phase method relying on the perpendicular search method. We report extensive computational results obtained from several classes of facility location problems. The proposed algorithm compares very favorably to both the lexicographic epsilon-constrained method and to the two […]
Sune one of my PhD students has just finished his defense of his thesis titled “Discrete Location Problems – Theory, Algorithms, and Extensions to Multiple Objectives“. I would like to congratulate Sune with his PhD title and for a good presentation at the defense. I have included the thesis summary below. Summary This PhD–dissertation proposes a number of solution procedures for discrete facility location problems. In the literature of operations research, location problems are mathematical models describing optimization problems where one or more facilities need to be placed in relation to a given set of customers or demand points. An example is the location of hospitals which needs to be performed in such a way as to take into account capacity limits and the sizes of nearby towns and cities.
Reza one of my PhD students has just finished his defense of his thesis titled “Optimization Methods in a Stochastic Production Environment“. I would like to congratulate Reza with his PhD title and for a good presentation at the defense. I have included the thesis summary below. Summary This dissertation with an interdisciplinary approach applies techniques from Operations Research and Statistics in order to develop models that support decisions regarding feeding and marketing of growing/finishing pigs. Stochastic dynamic programming is used as the main optimization tool to model decisions, and state space models are used as the primary statistical technique to describe the stochastic nature of the system. Based on data streams from online farm sensors and market prices, the state space model transforms data into information which is embedded into the decision models using Bayesian updating.