Simulated annealing for the unconstrained quadratic pseudo-Boolean function

Abstract In this paper, we develop a simulated annealing (SA) based heuristic for the unconstrained quadratic pseudo-Boolean function. An algorithm that solves the problem in O ( n 2 ) at each temperature of the cooling schedule is given. The performance of SA based heuristic is compared with existing bounding algorithms for this problem. Computational results and comparisons on several hundred test problems demonstrate the efficiency of our heuristic in terms of solution quality and computational time. A new set of hard test problems with their best solution is provided to facilitate future comparison.

[1]  Endre Boros,et al.  Chvátal Cuts and ODD Cycle Inequalities in Quadratic 0 - 1 Optimization , 1992, SIAM J. Discret. Math..

[2]  Alain Billionnet,et al.  Minimization of a quadratic pseudo-Boolean function , 1994 .

[3]  Pierre Hansen,et al.  Roof duality, complementation and persistency in quadratic 0–1 optimization , 1984, Math. Program..

[4]  Y. Crama,et al.  Upper-bounds for quadratic 0-1 maximization , 1990 .

[5]  Robert E. Tarjan,et al.  A Linear-Time Algorithm for Testing the Truth of Certain Quantified Boolean Formulas , 1979, Inf. Process. Lett..

[6]  Christos Koulamas,et al.  A survey of simulated annealing applications to operations research problems , 1994 .

[7]  Alain Billionnet,et al.  Unconstrained 0-1 optimization and Lagrangean relaxation , 1990, Discret. Appl. Math..

[8]  Francisco Barahona,et al.  A solvable case of quadratic 0-1 programming , 1986, Discret. Appl. Math..

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

[10]  P. L. Ivanescu.  Some Network Flow Problems Solved with Pseudo-Boolean Programming , 1965 .

[11]  P. V. Laarhoven,et al.  A quantitative analysis of the simulated annealing algorithm: A case study for the traveling salesman problem , 1988 .

[12]  David S. Johnson,et al.  Computers and Intractability: A Guide to the Theory of NP-Completeness , 1978 .

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

[14]  H. D. Ratliff,et al.  Minimum cuts and related problems , 1975, Networks.

[15]  Michael Jünger,et al.  Experiments in quadratic 0–1 programming , 1989, Math. Program..

[16]  C. D. Gelatt,et al.  Optimization by Simulated Annealing , 1983, Science.

[17]  Pierre Hansen,et al.  The basic algorithm for pseudo-Boolean programming revisited , 1988, Discret. Appl. Math..

[18]  Srimat T. Chakradhar,et al.  A solvable class of quadratic 0-1 programming , 1992, Discret. Appl. Math..

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

[20]  N. Metropolis,et al.  Equation of State Calculations by Fast Computing Machines , 1953, Resonance.