A unified modeling and solution framework for combinatorial optimization problems

Kochenberger, Gary A.; Glover, Fred; Alidaee, Bahram; Rego, César

doi:10.1007/s00291-003-0153-3

Cited by 101 publications

(71 citation statements)

References 30 publications

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“…QUBO has been extensively studied [12] and is used to model and solve numerous categories of optimization problems including important instances of network flows, scheduling, max-cut, max-clique, vertex cover and other graph and management science problems, integrating them into a unified modeling framework [11]. Many NP-complete problems such as graph and number partitioning, covering and set packing, satisfiability, matching, spanning tree as well as others can be converted into the Ising form as shown in [14].…”

Section: Literaturementioning

confidence: 99%

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Quadratic unconstrained binary optimization problem preprocessing: Theory and empirical analysis

Lewis

Glover

2017

Networks

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Abstract. The Quadratic Unconstrained Binary Optimization problem (QUBO) has become a unifying model for representing a wide range of combinatorial optimization problems, and for linking a variety of disciplines that face these problems. A new class of quantum annealing computer that maps QUBO onto a physical qubit network structure with specific size and edge density restrictions is generating a growing interest in ways to transform the underlying QUBO structure into an equivalent graph having fewer nodes and edges. In this paper we present rules for reducing the size of the QUBO matrix by identifying variables whose value at optimality can be predetermined. We verify that the reductions improve both solution quality and time to solution and, in the case of metaheuristic methods where optimal solutions cannot be guaranteed, the quality of solutions obtained within reasonable time limits.We discuss the general QUBO structural characteristics that can take advantage of these reduction techniques and perform careful experimental design and analysis to identify and quantify the specific characteristics most affecting reduction. The rules make it possible to dramatically improve solution times on a new set of problems using both the exact Cplex solver and a tabu search metaheuristic.

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Section: Literaturementioning

confidence: 99%

“…In order to strongly couple a collection of nodes we make use of penalty functions described in [11]. Specifically, if we wish to strongly couple nodes i and j in G*, then we use the penalty function M(x i -2 x i x j + x j ) in the objective function, where M is a large negative number in a maximization.…”

Section: Graph Expansion Via Strongly Coupled Nodesmentioning

confidence: 99%

Quadratic unconstrained binary optimization problem preprocessing: Theory and empirical analysis

Lewis

Glover

2017

Networks

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“…Moreover, many combinatorial optimization problems pertaining to graphs such as determining maximum cliques, maximum cuts, maximum vertex packing, minimum coverings, maximum independent sets, maximum independent weighted sets are known to be capable of being formulated by the UBQP problem as documented in papers of Pardalos and Rodgers (1990), Pardalos and Xue (1994). A review of additional applications and formulations can be found in Kochenberger et al (2004Kochenberger et al ( , 2005, Alidaee et al (2008), Lewis et al (2008).…”

Section: Introductionmentioning

confidence: 99%

Diversification-driven tabu search for unconstrained binary quadratic problems

Glover

Hao

2010

4OR-Q J Oper Res

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This paper describes a Diversification-Driven Tabu Search (D 2 TS) algorithm for solving unconstrained binary quadratic problems. D 2 TS is distinguished by the introduction of a perturbation-based diversification strategy guided by long-term memory. The performance of the proposed algorithm is assessed on the largest instances from the ORLIB library (up to 2500 variables) as well as still larger instances from the literature (up to 7000 variables). The computational results show that D 2 TS is highly competitive in terms of both solution quality and computational efficiency relative to some of the best performing heuristics in the literature.

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“…The formulation UBQP is notable for its ability to represent a wide range of important problems [2]. The literature reports a number of evolutionary and memetic algorithms with two-parent crossover operators for solving the UBQP problem ( [3,4,5,6]).…”

Section: Introductionmentioning

confidence: 99%

A Study of Multi-parent Crossover Operators in a Memetic Algorithm

Wang

Hao

2010

Parallel Problem Solving From Nature, PPSN XI

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Abstract. Using unconstrained binary quadratic programming problem as a case study, we investigate the role of multi-parent crossover operators within the memetic algorithm framework. We evaluate the performance of four multi-parent crossover operators (called MSX, Diagonal, U-Scan and OB-Scan) and provide evidences and insights as to why one particular multi-parent crossover operator leads to better computational results than another one. For this purpose, we employ several indicators like population entropy and average solution distance in the population.

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A unified modeling and solution framework for combinatorial optimization problems

Cited by 101 publications

References 30 publications

Quadratic unconstrained binary optimization problem preprocessing: Theory and empirical analysis

Quadratic unconstrained binary optimization problem preprocessing: Theory and empirical analysis

Diversification-driven tabu search for unconstrained binary quadratic problems

A Study of Multi-parent Crossover Operators in a Memetic Algorithm

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