# Yearly Archives: 2019

2 posts

## New publications

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 […]

## Package update – Plotting multi-objective linear/integer programming models in R

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.