An Effective Genetic Algorithm with Uniform Crossover for Bi-objective Unconstrained Binary Quadratic Programming Problem

The unconstrained binary quadratic programming problem is one of the most studied NP-hard problem with its various practical applications. In this paper, we propose an effective multi-objective genetic algorithm with uniform crossover for solving bi-objective unconstrained binary quadratic programming problem. In this algorithm, we integrate the uniform crossover within the hypervolume-based multi-objective optimization framework for further improvements. The computational studies on 10 benchmark instances reveal that the proposed algorithm is very effective in comparison with the original multi-objective optimization algorithms.

[1]  P. Hammer,et al.  Quadratic knapsack problems , 1980 .

[2]  Jin-Kao Hao,et al.  A Study of Multi-parent Crossover Operators in a Memetic Algorithm , 2010, PPSN.

[3]  G. Kochenberger,et al.  0-1 Quadratic programming approach for optimum solutions of two scheduling problems , 1994 .

[4]  Bahram Alidaee,et al.  A scatter search approach to unconstrained quadratic binary programs , 1999 .

[5]  Xiao-Bing Hu,et al.  An efficient Genetic Algorithm with uniform crossover for the multi-objective Airport Gate Assignment Problem , 2007 .

[6]  Fred W. Glover,et al.  The unconstrained binary quadratic programming problem: a survey , 2014, Journal of Combinatorial Optimization.

[7]  Edmund K. Burke,et al.  The efficiency of indicator-based local search for multi-objective combinatorial optimisation problems , 2011, Journal of Heuristics.

[8]  Sébastien Vérel,et al.  Experiments on Local Search for Bi-objective Unconstrained Binary Quadratic Programming , 2015, EMO.

[9]  Jakob Krarup,et al.  Computer-aided layout design , 1978 .

[10]  P. Merz,et al.  Memetic algorithms for the unconstrained binary quadratic programming problem. , 2004, Bio Systems.

[11]  F. Glover,et al.  Adaptive Memory Tabu Search for Binary Quadratic Programs , 1998 .

[12]  Lothar Thiele,et al.  Multiobjective evolutionary algorithms: a comparative case study and the strength Pareto approach , 1999, IEEE Trans. Evol. Comput..

[13]  Talal M. Alkhamis,et al.  Simulated annealing for the unconstrained quadratic pseudo-Boolean function , 1998, Eur. J. Oper. Res..

[14]  Jin-Kao Hao,et al.  Memetic search for the quadratic assignment problem , 2015, Expert Syst. Appl..

[15]  Sébastien Vérel,et al.  A hybrid metaheuristic for multiobjective unconstrained binary quadratic programming , 2014, Appl. Soft Comput..

[16]  R. McBride,et al.  An Implicit Enumeration Algorithm for Quadratic Integer Programming , 1980 .

[17]  Gary B. Lamont,et al.  Evolutionary Algorithms for Solving Multi-Objective Problems (Genetic and Evolutionary Computation) , 2006 .

[18]  Fred W. Glover,et al.  A Study of Memetic Search with Multi-parent Combination for UBQP , 2010, EvoCOP.

[19]  Jin-Kao Hao,et al.  Hypervolume-based multi-objective local search , 2011, Neural Computing and Applications.