Dominance guarantees for above-average solutions

Twitto, Yochai

doi:10.1016/j.disopt.2007.11.009

Cited by 6 publications

(4 citation statements)

References 19 publications

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“…Gutin and Yeo [16], Sarvanov [31], and Angel et al [5] studied heuristics for the quadratic assignment problem with performance guarantee in terms of average value of solutions. Similar analysis for the three-dimensional assignment problem was considered by Sarvanov [31], for the Maximum clique problem by Bendall and Margot [6], and for the satisfiability problem by Twitto [36]. Berend et al [7] considered dominance analysis by including infeasible solutions.…”

Section: Introductionmentioning

confidence: 82%

“…Worst case analysis of approximation algorithms (heuristics) are carried out normally through the measure of performance ratio [37]. Other important measures include differential ratio [8], dominance ratio [11,17], dominance number [40,11], comparison to average value of solutions [5,36,31,30,28] etc. Our focus in this paper is on domination analysis and average value based analysis of approximation algorithms for BBQP.…”

Section: Introductionmentioning

confidence: 99%

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Average value of solutions for the bipartite boolean quadratic programs and rounding algorithms

Punnen

Sripratak

Karapetyan

2015

Theoretical Computer Science

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We consider domination analysis of approximation algorithms for the bipartite boolean quadratic programming problem (BBQP) with m + n variables. A closed form formula is developed to compute the average objective function value A of all solutions in O(mn) time. However, computing the median objective function value of the solutions is shown to be NPhard. Also, we show that any solution with objective function value no worse than A dominates at least 2 m+n−2 solutions and this bound is the best possible. Further, we show that such a solution can be identified in O(mn) time and hence the dominance ratio of this algorithm is at least 1 4 . We then show that for any fixed rational number α > 1, no polynomial time approximation algorithm exists for BBQP with dominance ratio larger than 1 − 2 (1−α) α (m+n) , unless P=NP. We then analyze some powerful local search algorithms and show that they can get trapped at a local maximum with objective function value less than A . One of our approximation algorithms has an interesting rounding property which provides a data dependent lower bound on the optimal objective function value. A new integer programming formulation of BBQP is also given and computational results with our rounding algorithms are reported.

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Section: Introductionmentioning

confidence: 82%

Section: Introductionmentioning

confidence: 99%

Average value of solutions for the bipartite boolean quadratic programs and rounding algorithms

Punnen

Sripratak

Karapetyan

2015

Theoretical Computer Science

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“…Domination analysis has been successfully pursued by many researchers to provide performance guarantee of heuristics for various combinatorial optimization problems [2,4,11,[16][17][18][19][20][21][22]25,26,29,30,32,33,[35][36][37][43][44][45]. Domination analysis is also linked to exponential neighborhoods [12] and very large-scale neighborhood search [1,27].…”

Section: Domination Analysismentioning

confidence: 99%

The Bilinear Assignment Problem: Complexity and polynomially solvable special cases

Ćustić¹,

Sokol²,

Punnen³

et al. 2016

Preprint

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In this paper we study the bilinear assignment problem (BAP) with size parameters m and n, m ≤ n. BAP is a generalization of the well known quadratic assignment problem and the three dimensional assignment problem and hence NP-hard. We show that BAP cannot be approximated within a constant factor unless P=NP even if the associated quadratic cost matrixWhen the rank of Q is fixed, BAP is observed to admit FPTAS and when this rank is one, it is solvable in polynomial time under some additional restrictions. We then provide a necessary and sufficient condition for BAP to be equivalent to two linear assignment problems. A closed form expression to compute the average of the objective function values of all solutions is presented, whereas the median of the solution values cannot be identified in polynomial time, unless P=NP. We then provide polynomial time heuristic algorithms that find a solution with objective function value no worse than that of (m − 1)!(n − 1)! solutions. However, computing a solution whose objective function value is no worse than that of m!n! − ⌈ m β ⌉!⌈ n β ⌉! solutions is NP-hard for any fixed rational number β > 1.

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“…Let us now analyze some heuristics for BQAP1 and BQAP2 from the domination analysis [2,6,12,26,28] point of view. First, we consider two local search heuristics that performed very well in experimental analysis [21].…”

Section: Domination Analysis Of Heuristicsmentioning

confidence: 99%

Average value of solutions of the bipartite quadratic assignment problem and linkages to domination analysis

usti

Punnen

2017

Operations Research Letters

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In this paper we study the complexity and domination analysis in the context of the bipartite quadratic assignment problem. Two variants of the problem, denoted by BQAP1 and BQAP2, are investigated. A formula for calculating the average objective function value A of all solutions is presented whereas computing the median objective function value is shown to be NP-hard. We show that any heuristic algorithm that produces a solution with objective function value at most A has the domination ratio at least

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Dominance guarantees for above-average solutions

Cited by 6 publications

References 19 publications

Average value of solutions for the bipartite boolean quadratic programs and rounding algorithms

Average value of solutions for the bipartite boolean quadratic programs and rounding algorithms

The Bilinear Assignment Problem: Complexity and polynomially solvable special cases

Average value of solutions of the bipartite quadratic assignment problem and linkages to domination analysis

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