A Unified Framework for Modeling and Solving Combinatorial Optimization Problems: A Tutorial

Kochenberger, Gary A.; Glover, Fred

doi:10.1007/0-387-29550-x_4

Cited by 16 publications

(9 citation statements)

References 37 publications

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“…Dropping the additive constant, the equivalent unconstrained version of our constrained problem becomes UBQP : max xQx, x binary (7) From a computational standpoint, a suitable choice of the penalty scalar P can always be chosen so that the optimal solution to UBQP is the optimal solution to the original constrained problem. This approach has proven to be successful for a wide variety of problem classes as reported in Kochenberger et al (2004) and Kochenberger and Glover (2005).…”

Section: New Formulationmentioning

confidence: 99%

Clustering of Microarray data via Clique Partitioning

et al. 2005

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Abstract. Microarrays are repositories of gene expression data that hold tremendous potential for new understanding, leading to advances in functional genomics and molecular biology. Cluster analysis (CA) is an early step in the exploration of such data that is useful for purposes of data reduction, exposing hidden patterns, and the generation of hypotheses regarding the relationship between genes and phenotypes. In this paper we present a new model for the clique partitioning problem and illustrate how it can be used to perform cluster analysis in this setting.

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Section: New Formulationmentioning

confidence: 99%

Clustering of Microarray data via Clique Partitioning

et al. 2005

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“…A commercial optimizer. We first transform the Max-Cut problem into a QUBO (Quadratic Unconstrained Binary Optimization) task (Kochenberger and Glover 2006). Strictly, for a graph, G(V, W ), with vertices V connected by edges W , this task is to minimize the Hamiltonian…”

Section: Supplemental Materialsmentioning

confidence: 99%

Exploratory Combinatorial Optimization with Reinforcement Learning

Barrett

Clements²,

Foerster

et al. 2019

Preprint

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Many real-world problems can be reduced to combinatorial optimization on a graph, where the subset or ordering of vertices that maximize some objective function must be found. With such tasks often NP-hard and analytically intractable, reinforcement learning (RL) has shown promise as a framework with which efficient heuristic methods to tackle these problems can be learned. Previous works construct the solution subset incrementally, adding one element at a time, however, the irreversible nature of this approach prevents the agent from revising its earlier decisions, which may be necessary given the complexity of the optimization task. We instead propose that the agent should seek to continuously improve the solution by learning to explore at test time. Our approach of exploratory combinatorial optimization (ECO-DQN) is, in principle, applicable to any combinatorial problem that can be defined on a graph. Experimentally, we show our method to produce state-of-the-art RL performance on the Maximum Cut problem. Moreover, because ECO-DQN can start from any arbitrary configuration, it can be combined with other search methods to further improve performance, which we demonstrate using a simple random search.

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“…As pointed out in Kochenberger and Glover (2006) Details of such applications are elaborated more fully in Kochenberger et al (2014).…”

Section: Section 1: Introductionmentioning

confidence: 99%

Quantum Bridge Analytics I: a tutorial on formulating and using QUBO models

Glover

Kochenberger²,

Du³

2019

4OR-Q J Oper Res

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The Quadratic Unconstrained Binary Optimization (QUBO) model has gained prominence in recent years with the discovery that it unifies a rich variety of combinatorial optimization problems. By its association with the Ising problem in physics, the QUBO model has emerged as an underpinning of the quantum computing area known as quantum annealing and Fujitsu's digital annealing, and has become a subject of study in neuromorphic computing. Through these connections, QUBO models lie at the heart of experimentation carried out with quantum computers developed by D-Wave Systems and neuromorphic computers developed by IBM. The consequences of these new computational technologies and their links to QUBO models are being explored in initiatives by organizations such as Google, Amazon and Lockheed Martin in the commercial realm and Los Alamos National Laboratory, Oak Ridge National Laboratory, Lawrence Livermore National Laboratory and NASA's Ames Research Center in the public sector. Computational experience is being amassed by both the classical and the quantum computing communities that highlights not only the potential of the QUBO model but also its effectiveness as an alternative to traditional modeling and solution methodologies.

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A Unified Framework for Modeling and Solving Combinatorial Optimization Problems: A Tutorial

Cited by 16 publications

References 37 publications

Clustering of Microarray data via Clique Partitioning

Clustering of Microarray data via Clique Partitioning

Exploratory Combinatorial Optimization with Reinforcement Learning

Quantum Bridge Analytics I: a tutorial on formulating and using QUBO models

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