Learning the Large-Scale Structure of the MAX-SAT Landscape Using Populations

Qasem, Mohamed; Prügel-Bennett, Adam

doi:10.1109/tevc.2009.2033579

Cited by 20 publications

(24 citation statements)

References 25 publications

(27 reference statements)

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“…More details can be found in [1]. We were unable to compare our algorithm with most other algorithms that appear in the literature since the other studied were performed on much smaller instances (typically around 100 variables).…”

Section: Resultsmentioning

confidence: 99%

“…However, there are few examples of EAs on real world problems where the algorithm unambiguously exploits this global knowledge of the landscape. Recently we proposed an algorithm for solving large MAX-SAT problems based on clustering good solutions which we argued does precisely this [1]. We review that work here and extend the idea to a second classic NP-Hard problem, Vertex Cover.…”

Section: Introductionmentioning

confidence: 92%

See 1 more Smart Citation

Improving Performance in Combinatorial Optimisation Using Averaging and Clustering

Qasem

Prügel-Bennett

2009

Evolutionary Computation in Combinatorial Optimization

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Abstract. In a recent paper an algorithm for solving MAX-SAT was proposed which worked by clustering good solutions and restarting the search from the closest feasible solutions. This was shown to be an extremely effective search strategy, substantially out-performing traditional optimisation techniques. In this paper we extend those ideas to a second classic NP-Hard problem, namely Vertex Cover. Again the algorithm appears to provide an advantage over more established search algorithms, although it shows different characteristics to MAX-SAT. We argue this is due to the different large-scale landscape structure of the two problems.

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Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 92%

Improving Performance in Combinatorial Optimisation Using Averaging and Clustering

Qasem

Prügel-Bennett

2009

Evolutionary Computation in Combinatorial Optimization

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“…al [15]. In both of these cases, local search must first be run multiple times with a uniform random initialization to construct a set of local optima.…”

Section: Estimating Backbone Variablesmentioning

confidence: 99%

“…The frequency of assignments for each bit found in the set of local optima are then used to initialize subsequent runs of local search. It is hypothesized that these frequencies can provide a good estimation of the backbone, a subset of variables that are consistently assigned either true or false across all global optima [26,15].…”

Section: Estimating Backbone Variablesmentioning

confidence: 99%

Hyperplane initialized local search for MAXSAT

Hains

Whitley

Howe

et al. 2013

Proceedings of the 15th Annual Conference on Genetic and Evolutionary Computation

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By converting the MAXSAT problem to Walsh polynomials, we can efficiently and exactly compute the hyperplane averages of fixed order k. We use this fact to construct initial solutions based on variable configurations that maximize the sampling of hyperplanes with good average evaluations. The Walsh coefficients can also be used to implement a constant time neighborhood update which is integral to a fast next descent local search for MAXSAT (and for all bounded pseudo-Boolean optimization problems.) We evaluate the effect of initializing local search with hyperplane averages on both the first local optima found by the search and the final solutions found after a fixed number of bit flips. Hyperplane initialization not only provides better evaluations, but also finds local optima closer to the globally optimal solution in fewer bit flips than search initialized with random solutions. A next descent search initialized with hyperplane averages is able to outperform several state-of-the art stochastic local search algorithms on both random and industrial instances of MAXSAT.

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“…That is, the high-fitness regions of the search space has to lie directly in the centre of a larger region containing good quality solutions. This very particular landscape might appear slightly artificial and unlikely to occur in real world problems, however, in a recent paper this strategy was found to be very effective on one of the classic combinatorial optimisation problems, namely MAX-3-SAT [24].…”

Section: A Strong Focusingmentioning

confidence: 99%

Benefits of a Population: Five Mechanisms That Advantage Population-Based Algorithms

Prügel-Bennett

2010

IEEE Trans. Evol. Computat.

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Abstract-This paper identifies five distinct mechanisms by which a population-based algorithm might have an advantage over a solo-search algorithm in classical optimisation. These mechanisms are illustrated through a number of toy problems. Simulations are presented comparing different search algorithms on these problems. The plausibility of these mechanisms occurring in classical optimisation problems is discussed.The first mechanism we consider relies on putting together building blocks from different solutions. This is extended to include problems containing critical variables. The second mechanism is the result of focusing of the search caused by crossover. Also discussed in this context is strong focusing produced by averaging many solutions. The next mechanism to be examined is the ability of a population to act as a low-pass filter of the landscape, ignoring local distractions. The fourth mechanism is a population's ability to search different parts of the fitness landscape, thus hedging against bad luck in the initial position or the decisions it makes. The final mechanism is the opportunity of learning useful parameter values to balance exploration against exploitation.

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Learning the Large-Scale Structure of the MAX-SAT Landscape Using Populations

Cited by 20 publications

References 25 publications

Improving Performance in Combinatorial Optimisation Using Averaging and Clustering

Improving Performance in Combinatorial Optimisation Using Averaging and Clustering

Hyperplane initialized local search for MAXSAT

Benefits of a Population: Five Mechanisms That Advantage Population-Based Algorithms

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