A simple and effective algorithm for the MaxMin diversity problem |
| |
Authors: | Daniel Cosmin Porumbel Jin-Kao Hao Fred Glover |
| |
Institution: | 1.UArtois, LGI2A,Univ. Lille-Nord de France,Béthune,France;2.LERIA,Université d’Angers,Angers Cedex 01,France;3.OptTek Systems, Inc.,Boulder,USA |
| |
Abstract: | The challenge of maximizing the diversity of a collection of points arises in a variety of settings, including the setting
of search methods for hard optimization problems. One version of this problem, called the Maximum Diversity Problem (MDP),
produces a quadratic binary optimization problem subject to a cardinality constraint, and has been the subject of numerous
studies. This study is focused on the Maximum Minimum Diversity Problem (MMDP) but we also introduce a new formulation using
MDP as a secondary objective. We propose a fast local search based on separate add and drop operations and on simple tabu
mechanisms. Compared to previous local search approaches, the complexity of searching for the best move at each iteration
is reduced from quadratic to linear; only certain streamlining calculations might (rarely) require quadratic time per iteration.
Furthermore, the strong tabu rules of the drop strategy ensure a powerful diversification capacity. Despite its simplicity,
the approach proves superior to most of the more advanced methods from the literature, yielding optimally-proved solutions
for many problems in a matter of seconds and even attaining a new lower bound. |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|