2015 journal article

p-Median and p-dispersion problems: A bi-criteria analysis

*COMPUTERS & OPERATIONS RESEARCH*, *61*, 46–55.

author keywords: Location theory; Max-min diversity; p-Median partitioning; Integer programming; Lagrangian heuristic

TL;DR:
This work studies this problem as a multi-objective optimization problem and proposes an iterative algorithm to obtain its non-dominated frontier and proposes a Lagrangian heuristic algorithm for solving larger instances of this problem.
(via Semantic Scholar)

Source: Web Of Science

Added: August 6, 2018

Given a collection of n locations and a symmetric measure of distance (difference) between each pair of locations, we seek to identify (select) a subset of p locations so as to achieve two distinct objectives. The first objective is to use the selected locations as centers (medians) of p groups that would partition the entire collection and minimize the total distance between the locations and their respective group medians. The second objective is to maximize the minimum distance (diversity) among the selected locations themselves. We study this problem as a multi-objective optimization problem and propose an iterative algorithm to obtain its non-dominated frontier. At each iteration we construct and solve a 0–1 integer programming problem. Through a computational experiment we show that this algorithm is computationally effective for small to medium size instances of the problem. We also propose a Lagrangian heuristic algorithm for solving larger instances of this problem.