Algorithm Selection for Combinatorial Search Problems: A Survey

Kotthoff, Lars

doi:10.1609/aimag.v35i3.2460

Cited by 178 publications

(164 citation statements)

References 108 publications

(353 reference statements)

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“…Which metric is a reasonable to measure the performance of A on x? Figure 3.1: Refined model for the Algorithm Selection Problem (taken from [118]). …”

Section: Chaptermentioning

confidence: 99%

“…The boundary between Algorithm Selection and Algorithm Portfolios is fuzzy and these two related problems could be considered as synonyms. According to [118] definition, Algorithm…”

Section: Chaptermentioning

confidence: 99%

“…According to [118], a first discrimination can be made depending on the domain knowledge re-quired to use the features. Indeed, some features may be so specific as to require a deep knowledge of the application domain in which they are embedded.…”

Section: Featuresmentioning

confidence: 99%

“…As pointed out in [118], there are many different ways to properly select one or more constituent solver(s). Note that, even if the prediction accuracy is of course welcome, in the CP context this requirement can be relaxed pragmatically.…”

Section: Selectorsmentioning

confidence: 99%

“…According to [118] definition, Algorithm Portfolios [103] can be seen as particular instances of the more general AS problem in which the algorithm selection is performed case-by-case instead that in advance. In this case, a portfolio of algorithms corresponds to the algorithm space A.…”

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confidence: 99%

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Portfolio approaches in constraint programming

Amadini

2015

Constraints

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Recent research has shown that the performance of a single, arbitrarily efficient algorithm can be significantly outperformed by using a portfolio of -possibly onaverage slower-algorithms. Within the Constraint Programming (CP) context, a portfolio solver can be seen as a particular constraint solver that exploits the synergy between the constituent solvers of its portfolio for predicting which is (or which are) the best solver(s) to run for solving a new, unseen instance.In this thesis we examine the benefits of portfolio solvers in CP. Despite portfolio approaches have been extensively studied for Boolean Satisfiability (SAT) problems, in the more general CP field these techniques have been only marginally studied and used. We conducted this work through the investigation, the analysis and the construction of several portfolio approaches for solving both satisfaction and optimization problems. We focused in particular on sequential approaches, i.e., single-threaded portfolio solvers always running on the same core.We started from a first empirical evaluation on portfolio approaches for solving Constraint Satisfaction Problems (CSPs), and then we improved on it by introducing new data, solvers, features, algorithms, and tools. Afterwards, we addressed the more general Constraint Optimization Problems (COPs) by implementing and testing a number of models for dealing with COP portfolio solvers. Finally, we have come full circle by developing sunny-cp: a sequential CP portfolio solver that turned out to be competitive also in the MiniZinc Challenge, the reference competition for CP solvers.iii iv

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“…Which metric is a reasonable to measure the performance of A on x? Figure 3.1: Refined model for the Algorithm Selection Problem (taken from [118]). …”

Section: Chaptermentioning

confidence: 99%

“…The boundary between Algorithm Selection and Algorithm Portfolios is fuzzy and these two related problems could be considered as synonyms. According to [118] definition, Algorithm…”

Section: Chaptermentioning

confidence: 99%

Section: Featuresmentioning

confidence: 99%

Section: Selectorsmentioning

confidence: 99%

mentioning

confidence: 99%

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Portfolio approaches in constraint programming

Amadini

2015

Constraints

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Solver Tuning and Model Configuration

Barry

Abgottspon

Schumann

2018

Lecture Notes in Computer Science

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An Investigation into Prediction + Optimisation for the Knapsack Problem

Demirović

Stuckey

Bailey

et al. 2019

Lecture Notes in Computer Science

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We study a prediction+optimisation formulation of the knapsack problem. The goal is to predict the profits of knapsack items based on historical data, and afterwards use these predictions to solve the knapsack. The key is that the item profits are not known beforehand and thus must be estimated, but the quality of the solution is evaluated with respect to the true profits. We formalise the problem, the goal of minimising expected regret and the learning problem, and investigate different machine learning approaches that are suitable for the optimisation problem. Recent methods for linear programs have incorporated the linear relaxation directly into the loss function. In contrast, we consider less intrusive techniques of changing the loss function, such as standard and multi-output regression, and learning-to-rank methods. We empirically compare the approaches on real-life energy price data and synthetic benchmarks, and investigate the merits of the different approaches.Combinatorial optimisation is crucial in today's society and used throughout many industries. In this paper, we work with the fundamental knapsack problem, which has been studied for over a century and is well understood [17,9]. It is studied in fields such as combinatorics, computer science, complexity theory, cryptography, and applied mathematics. It has numerous applications, including resource allocation problems where the aim is to select as many resources as possible under given financial constraints. The knapsack problem is NP-hard, though highly efficient solution methods exist for reasonably sized instances [9].In traditional optimisation, it is assumed that all parameters, e.g. the profits and weights in a knapsack, are precisely known beforehand. In practice, these are often crude estimates based on domain expertise or historic data. As we enter the age of big data, large amounts of data is available and thus parameters can be estimated with greater precision. For example, ongoing promotion and current weather might influence the demand. The question that arises is whether such contextual data, together with historical data, can be used to improve decision making, i.e. solve the underlying optimisation problem more effectively.Such problems are encountered in load shifting [10], where the aim is to create an energy-aware day-head schedule based on predicted hourly energy prices.

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Algorithm Selection for Combinatorial Search Problems: A Survey

Cited by 178 publications

References 108 publications

Portfolio approaches in constraint programming

Portfolio approaches in constraint programming

Solver Tuning and Model Configuration

An Investigation into Prediction + Optimisation for the Knapsack Problem

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