Clustering-driven evolutionary algorithms: an application of path relinking to the quadratic unconstrained binary optimization problem

Samorani, Michele; Wang, Yang; Lv, Zhipeng; Glover, Fred

doi:10.1007/s10732-018-9403-z

Cited by 23 publications

(14 citation statements)

References 23 publications

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“…Pudenz and Lidar (2013) An application of QUBO to unsupervised machine learning in provides an approach that can be employed either together with quantum computing or independently. In a complementary development, clustering is used to facilitate the solution of QUBO models in Samorani et al (2018), thereby providing a foundation for studying additional uses of clustering in this context.…”

Section: Y = 2588mentioning

confidence: 99%

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

Glover

Kochenberger²,

Du³

2019

4OR-Q J Oper Res

Self Cite

201

139

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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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Section: Y = 2588mentioning

confidence: 99%

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

Glover

Kochenberger²,

Du³

2019

4OR-Q J Oper Res

Self Cite

201

139

View full text Add to dashboard Cite

show abstract

“…There remains a possibility that earlier stopping points will still yield overall results that are as good, where solutions gradually improve to a desired level even if they are not as good at some intermediate point. It may additionally be observed that X * may be constructed by reference to clustering, using clustering ideas as proposed by Glover and Laguna [16] and Samorani et al [17]. For constructing X * , the focal distance algorithm can keep track of the best solutions x * (including in a variant that initially applies the single solution x * approach) and then using clustering to group solutions that are closer together to form new X * sets.…”

Section: Main Routinementioning

confidence: 99%

Focal distance tabu search

Glover

2021

Sci. China Inf. Sci.

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Focal distance tabu search modifies a standard tabu search algorithm for binary optimization by augmenting a periodic diversification step that drives the search away from a current best (or elite) solution until the objective function deteriorates beyond a specified threshold or until attaining a lower bound on the distance from the originating solution. The new augmented algorithm combines the threshold and lower bound approaches by introducing an initial focal distance for the lower bound which is updated when the diversification step is completed. However, rather than terminating the diversification step at the customary completion point, focal distance tabu search (TS) retains the focal distance bound through additional search phases designed to improve the objective function, drawing on a strategy proposed with strategic oscillation. The algorithm realizes this strategy by partitioning the variables into two sets which are managed together with an abbreviated tabu search process. An advanced version of the approach drives the search away from a collection of solutions rather than a single originating solution, introducing the concept of a signature solution to guide the search. The method can be employed to augment a variety of other metaheuristic algorithms such as those using threshold procedures, late acceptance hill climbing, iterated local search, breakout local search, GRASP, and path relinking.

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“…Algorithms 5, 9 and 11 can be used to address this issue, embedded in MOO approaches, similarly to [49]. Archiving diversified solutions of Pareto sets has application for the diversification of genetic algorithms, to select diversified solutions for cross-over and mutation phases [61,62], but also for swarm particle optimization heuristics [63]. In these applications, clustering has to run quickly.…”

Section: Applications To Bi-objective Meta-heuristicsmentioning

confidence: 99%

Unified Polynomial Dynamic Programming Algorithms for P-Center Variants in a 2D Pareto Front

2021

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With many efficient solutions for a multi-objective optimization problem, this paper aims to cluster the Pareto Front in a given number of clusters K and to detect isolated points. K-center problems and variants are investigated with a unified formulation considering the discrete and continuous versions, partial K-center problems, and their min-sum-K-radii variants. In dimension three (or upper), this induces NP-hard complexities. In the planar case, common optimality property is proven: non-nested optimal solutions exist. This induces a common dynamic programming algorithm running in polynomial time. Specific improvements hold for some variants, such as K-center problems and min-sum K-radii on a line. When applied to N points and allowing to uncover M<N points, K-center and min-sum-K-radii variants are, respectively, solvable in O(K(M+1)NlogN) and O(K(M+1)N2) time. Such complexity of results allows an efficient straightforward implementation. Parallel implementations can also be designed for a practical speed-up. Their application inside multi-objective heuristics is discussed to archive partial Pareto fronts, with a special interest in partial clustering variants.

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Clustering-driven evolutionary algorithms: an application of path relinking to the quadratic unconstrained binary optimization problem

Cited by 23 publications

References 23 publications

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

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

Focal distance tabu search

Unified Polynomial Dynamic Programming Algorithms for P-Center Variants in a 2D Pareto Front

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