A family of composite discrete bivariate distributions with uniform marginals for simulating realistic and challenging optimization-problem instances

    Authors

    C. H. Reilly;N. Sapkota

    Comments

    Authors: contact us about adding a copy of your work at STARS@ucf.edu

    Abbreviated Journal Title

    Eur. J. Oper. Res.

    Keywords

    Entropy; Heuristics; Simulation; Correlation; Knapsack Problem; 0-1 KNAPSACK-PROBLEM; SINGLE-MACHINE; ALGORITHMS; COEFFICIENTS; PERFORMANCE; MINIMIZE; BOUNDS; Management; Operations Research & Management Science

    Abstract

    We consider a family of composite bivariate distributions, or probability mass functions (pmfs), with uniform marginals for simulating optimization-problem instances. For every possible population correlation, except the extreme values, there are an infinite number of valid joint distributions in this family. We quantify the entropy for all member distributions, including the special cases under independence and both extreme correlations. Greater variety is expected across optimization-problem instances simulated based on a high-entropy pmf. We present a closed-form solution to the problem of finding the joint pmf that maximizes entropy for a specified population correlation, and we show that this entropy-maximizing pmf belongs to our family of pmfs. We introduce the entropy range as a secondary indicator of the variety of instances that may be generated for a particular correlation. Finally, we discuss how to systematically control entropy and correlation to simulate a set of synthetic problem instances that includes challenging examples and examples with realistic characteristics. (C) 2014 Elsevier B.V. All rights reserved.

    Journal Title

    European Journal of Operational Research

    Volume

    241

    Issue/Number

    3

    Publication Date

    1-1-2015

    Document Type

    Article

    Language

    English

    First Page

    642

    Last Page

    652

    WOS Identifier

    WOS:000347605100006

    ISSN

    0377-2217

    Share

    COinS