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Finding Diverse Solutions of High Quality to Binary Integer Programs

Andrew C. Trapp(atrapp***at***wpi.edu)
Renata A. Konrad(rkonrad***at***wpi.edu)

Abstract: Typical output from an optimization solver is a single optimal solution. At the same time, a set of high-quality and diverse solutions could be beneficial in a variety of contexts, for example problems involving imperfect information, or those for which the structure of high-quality solution vectors can reveal meaningful insights. In view of this, we discuss a new method to obtain multiple high-quality yet diverse solutions to pure binary (0–1) integer programs, employing fractional programming techniques to manage these typically competing goals. Specifically, we develop a general approach that makes use of Dinkelbach's algorithm to sequentially generate solutions that evaluate well with respect to both i) individual performance and, as a whole, ii) mutual variety. Experiments on a number of test instances yield encouraging computational results.

Keywords: binary (0–1) integer programming; fractional programming; Dinkelbach’s algorithm; decision making; multiple solutions; solution diversity; solution quality

Category 1: Nonlinear Optimization (Other )

Category 2: Integer Programming (0-1 Programming )

Category 3: Other Topics (Multi-Criteria Optimization )

Citation: Technical Report October, 2013 School of Business Worcester Polytechnic Institute 100 Institute Rd., Worcester, MA 01609, USA

Download: [PDF]

Entry Submitted: 10/31/2013
Entry Accepted: 10/31/2013
Entry Last Modified: 10/31/2013

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