A selection of useful theoretical tools for the design and analysis of optimization heuristics

Gutin, Gregory; Karapetyan, Daniel

doi:10.1007/s12293-008-0001-8

Cited by 17 publications

(18 citation statements)

References 39 publications

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“…Moreover, an estimation of the mean optimal solution is provided in Grundel et al (2004) but this estimation is not accurate enough for our experiments. In Gutin and Karapetyan (2009) we prove that it is very likely that every big enough Random instance has at least one an-assignment, where x-assignment means an assignment of weight x.…”

Section: Instances With Independent Weightsmentioning

confidence: 95%

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Local search heuristics for the multidimensional assignment problem

Gutin

Karapetyan

2010

J Heuristics

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The Multidimensional Assignment Problem (MAP) (abbreviated s-AP in the case of s dimensions) is an extension of the well-known assignment problem. The most studied case of MAP is 3-AP, though the problems with larger values of s also have a large number of applications. We consider several known neighborhoods, generalize them and propose some new ones. The heuristics are evaluated both theoretically and experimentally and dominating algorithms are selected. We also demonstrate that a combination of two neighborhoods may yield a heuristics which is superior to both of its components.

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Section: Instances With Independent Weightsmentioning

confidence: 95%

“…We would like to have an upper bound on the probability Pr(α = 0). Such an upper bound is given in the following theorem whose proof (see Gutin and Karapetyan 2009) is based on the Extended Jansen Inequality (see Theorem 8.1.2 of Alon and Spencer 2000).…”

Section: Instances With Independent Weightsmentioning

confidence: 99%

Local search heuristics for the multidimensional assignment problem

Gutin

Karapetyan

2010

J Heuristics

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“…There are flexible tools, such as iOpt [54], EasyLocall++ [26] and some other theoretical tools [32], which allow the user to discover metaheuristics manually more easily. However, the development effort and cost for new heuristics remains considerable and often results are not directly re-usable for other problems.…”

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confidence: 99%

Evolving timetabling heuristics using a grammar-based genetic programming hyper-heuristic framework

2009

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This paper introduces a Grammar-based Genetic Programming Hyper-Heuristic framework (GPHH) for evolving constructive heuristics for timetabling. In this application GP is used as an online learning method which evolves heuristics while solving the problem. In other words, the system keeps on evolving heuristics for a problem instance until a good solution is found. The framework is tested on some of the most widely used benchmarks in the field of exam timetabling and compared with the best state-of-the-art approaches. Results show that the framework is very competitive with other constructive techniques, and did outperform other hyper-heuristic frameworks on many occasions.

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“…In spite of this, MNNGA demonstrates good performance within limited iterations without having stuck into local minima. A recent work highlights the importance of proper selection of theoretical tools for the analysis of optimization heuristics [7]. We are planning to carry out such studies on MFCP for the search of better heuristics.…”

Section: Discussionmentioning

confidence: 99%

Solving maximum fuzzy clique problem with neural networks and its applications

Bhattacharyya

Bandyopadhyay

2009

Memetic Comp.

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The maximum clique problem is an important problem in graph theory. Many real-life problems are still being mapped into this problem for their effective solutions. A natural extension of this problem that has emerged very recently in many real-life networks, is its fuzzification. The problem of finding the maximum fuzzy clique has been formalized on fuzzy graphs and subsequently addressed in this paper. It has been shown here that the problem reduces to an unconstrained quadratic 0-1 programming problem. Using a maximum neural network, along with mutation capability of genetic adaptive systems, the reduced problem has been solved. Empirical studies have been done by applying the method on stock flow graphs to identify the collusion set, which contains a group of traders performing unfair trading among themselves. Additionally, it has been applied on a gene co-expression network to find out significant gene modules and on some benchmark graphs.

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A selection of useful theoretical tools for the design and analysis of optimization heuristics

Cited by 17 publications

References 39 publications

Local search heuristics for the multidimensional assignment problem

Local search heuristics for the multidimensional assignment problem

Evolving timetabling heuristics using a grammar-based genetic programming hyper-heuristic framework

Solving maximum fuzzy clique problem with neural networks and its applications

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