Estimation of Distribution Algorithm for the Max-Cut Problem

Sousa, Samuel de; Haxhimusa, Yll; Kropatsch, Walter G.

doi:10.1007/978-3-642-38221-5_26

Cited by 17 publications

(7 citation statements)

References 20 publications

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“…By examining the performance of each individual reduction rule, we can see that this is solely due to Reduction Rule 1 w=c . These findings could improve the work by de Sousa et al [13], which also affects the work by Dunning et al [14]. In conclusion, our novel reduction rules give us a simple but powerful tool for speeding up existing Table 2: Impact of kernelization on the computation of a maximum cut by LocalSolver (LS) and Biq Mac (BM).…”

Section: Exactly Computing a Maximum Cutmentioning

confidence: 64%

“…Such a partition is called a maximum cut. Computing a maximum cut of a graph is a well-known problem in the area of computer science; it is one of Karp's 21 NP-complete problems [26] While signed and weighted variants are often considered throughout the literature [4,5,6,9,13,23,24], the simpler (unweighted) case still presents a significant challenge for researchers, and solving it quickly is of paramount importance to all variants. Max Cut variants have many applications, including social network modeling [23], statistical physics [4], portfolio risk analysis [24], VLSI design [6,9], network design [5], and image segmentation [13].…”

Section: Introductionmentioning

confidence: 99%

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Engineering Kernelization for Maximum Cut

Ferizovic¹,

Hespe²,

Lamm³

et al. 2020

2020 Proceedings of the Twenty-Second Workshop on Algorithm Engineering and Experiments (ALENEX)

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Kernelization is a general theoretical framework for preprocessing instances of NP-hard problems into (generally smaller) instances with bounded size, via the repeated application of data reduction rules. For the fundamental Max Cut problem, kernelization algorithms are theoretically highly efficient for various parameterizations. However, the efficacy of these reduction rules in practice-to aid solving highly challenging benchmark instances to optimality-remains entirely unexplored.We engineer a new suite of efficient data reduction rules that subsume most of the previously published rules, and demonstrate their significant impact on benchmark data sets, including synthetic instances, and data sets from the VLSI and image segmentation application domains. Our experiments reveal that current state-of-the-art solvers can be sped up by up to multiple orders of magnitude when combined with our data reduction rules. On social and biological networks in particular, kernelization enables us to solve four instances that were previously unsolved in a ten-hour time limit with state-of-the-art solvers; three of these instances are now solved in less than two seconds.

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Section: Exactly Computing a Maximum Cutmentioning

confidence: 64%

Section: Introductionmentioning

confidence: 99%

Engineering Kernelization for Maximum Cut

Ferizovic¹,

Hespe²,

Lamm³

et al. 2020

2020 Proceedings of the Twenty-Second Workshop on Algorithm Engineering and Experiments (ALENEX)

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“…In recent years, EDA has been successfully applied to a large number of discrete optimization problems by using its estimation feature. Such as permutation flowshop [26], job shop [27], hybrid flow-shop [28], nurse scheduling [29], semiconductor final test [30], resource-constrained project [31], multiobjective resource-constrained project [32], permutation-based combinatorial optimization [33], large scale global optimization [34] and max-cut problem [35].…”

Section: Introductionmentioning

confidence: 99%

Using estimation of distribution algorithm to coordinate decentralized learning automata for meta-task scheduling

Zhang

2014

2014 IEEE Congress on Evolutionary Computation (CEC)

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Learning automaton (LA) is a reinforcement learning model that aims to determine the optimal action out of a set of actions. It is characterized by updating a selection probability vector through a sequence of repetitive feedback cycles interacting with an environment. Decentralized learning automata (DLAs) consists of many learning automata (LAs) that learn at the same time. Each LA independently selects an action based on its own selection probability vector. In order to provide an appropriate central coordination mechanism in DLAs, this paper proposes a novel decentralized coordination learning automaton (DCLA) using a new selection probability vector which is combined with the probability vectors derived from both LA and estimation of distribution algorithm (EDA). LA contributes to the own learning experience of each LA while EDA estimates the distribution of the whole swarm's promising individuals. Thus, decentralized LAs can be coordinated by EDA using the swarm's comprehensive knowledge. The proposed automaton is applied to solve the real problem of meta-task scheduling in heterogeneous computing system. Extensive experiments demonstrate a superiority of DCLA over other counterpart algorithms. The results show that the proposed DCLA provides an effective and efficient way to coordinate LAs for solving complicated problems.

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“…Many heuristics have been designed for these problems -in a systematic review completed as part of this work (see Appendix C), we found that 95 papers have performed empirical testing on such heuristics, 31 of which were published since 2010. These problems are also of interest due to their broad practical applicability: Max-Cut applications include VLSI design, network design, statistical physics, and image segmentation (Barahona et al 1988, Barahona 1996, de Sousa et al 2013, and QUBO applications include capital budgeting and financial analysis, computer aided design, traffic message management problems, machine scheduling, and molecular conformation (Merz and Freisleben 2002).…”

Section: Introductionmentioning

confidence: 99%

What Works Best When? A Systematic Evaluation of Heuristics for Max-Cut and QUBO

Dunning

Gupta

Silberholz

2018

INFORMS Journal on Computing

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Though empirical testing is broadly used to evaluate heuristics, there are shortcomings with how it is often applied in practice. In a systematic review of Max-Cut and Quadratic Unconstrained Binary Optimization (QUBO) heuristics papers, we found only 4% publish source code, only 14% compare heuristics with identical termination criteria, and most experiments are performed with an artificial, homogeneous set of problem instances. To address these limitations, we implement and release as open-source a code-base of 10 Max-Cut and 27 QUBO heuristics. We perform heuristic evaluation using cloud computing on a library of 3,296 instances. This large-scale evaluation provides insight into the types of problem instances for which each heuristic performs well or poorly. Because no single heuristic outperforms all others across all problem instances, we use machine learning to predict which heuristic will work best on a previously unseen problem instance, a key question facing practitioners.

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Estimation of Distribution Algorithm for the Max-Cut Problem

Cited by 17 publications

References 20 publications

Engineering Kernelization for Maximum Cut

Engineering Kernelization for Maximum Cut

Using estimation of distribution algorithm to coordinate decentralized learning automata for meta-task scheduling

What Works Best When? A Systematic Evaluation of Heuristics for Max-Cut and QUBO

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