A Hybridised Evolutionary Algorithm for Multi-Criterion Minimum Spanning Tree Problems

Davis-Moradkhan, Madeleine; Browne, Will N.

doi:10.1109/his.2008.86

Cited by 4 publications

(5 citation statements)

References 22 publications

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“…In the case of three criteria, comparisons with the deterministic algorithm EPDA [1] and KEA on instances with 20, 30, 40 and 50 nodes showed a superior performance for KEA-W. The results, averaged over ten independent runs, obtained with 50 nodes and random costs are shown in Figure 2 and in Tables 1 and 2.…”

Section: Resultsmentioning

confidence: 91%

“…Further comparative results, for instances of up to 100 nodes in the bi-criterion case, showed the superiority of KEA-W over KEA, in terms of non-dominated middle section of the PF, as shown in Figure 1. For benchmark tests against NSGA2 see [1].…”

Section: Resultsmentioning

confidence: 99%

“…Moreover, the four indicators defined in [1]: CPU, TTC (Total number of trees calculated), FO (Front occupation) and %FO (ratio of FO to TTC showing efficiency in discovering a large FO with few calculations) are also used to refine the comparison. For the S-measure, the nadir (anti-ideal) point of the PF is used as reference.…”

Section: Resultsmentioning

confidence: 99%

“…The extension to the knowledge-based evolutionary algorithm (KEA), termed KEA-W, has many features in common with KEA [1]. It is comprised of four phases: Phase 1: Calculation of the p extreme points using Kruskal's algorithm [2].…”

Section: Description Of Kea-wmentioning

confidence: 99%

See 3 more Smart Citations

Extending evolutionary algorithms to discover tri-criterion and non-supported solutions for the minimum spanning tree problem

Davis-Moradkhan

Browne

Grindrod

2009

Proceedings of the 11th Annual Conference on Genetic and Evolutionary Computation

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The study of multi-criterion minimum spanning trees is important as many optimization problems in networks, such as communication, transport and utilities can be represented by this model. Conventional evolutionary approaches struggle to discover near-optimal solutions due to the combinatorial search space, and the difficulty in discovering the non-supported solutions. Recently, a knowledge-based evolutionary approach, KEA, has been developed that overcomes some of the problems of the earlier algorithms as it is not restricted to the bi-criterion case, finds nonsupported solutions and scales well to larger problems; however, the mid-point of its Pareto front is often dominated by alternative algorithms where they are applicable. Novel extensions to KEA, increasing the knowledge of the mid-point, termed KEA-W are examined, eliminating the mid-point deficiencies at the cost of computational time.

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Section: Resultsmentioning

confidence: 91%

Section: Resultsmentioning

confidence: 99%

Section: Resultsmentioning

confidence: 99%

Section: Description Of Kea-wmentioning

confidence: 99%

See 2 more Smart Citations

Extending evolutionary algorithms to discover tri-criterion and non-supported solutions for the minimum spanning tree problem

Davis-Moradkhan

Browne

Grindrod

2009

Proceedings of the 11th Annual Conference on Genetic and Evolutionary Computation

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“…Matroid optimization problems, especially the minimum spanning tree problem, are well investigated even for multi-objective optimization (cf. Ehrgott (1996) for matroids and Ehrgott and Klamroth (1997), Hamacher and Ruhe (1994), Chen et al (2007), Arroyo et al (2008), Davis-Moradkhan and Browne (2008) among others for spanning trees). In this paper, we consider multiobjective optimization problems where, in addition to one sum objective function, one or more ordinal objective functions are to be considered.…”

Section: Introductionmentioning

confidence: 99%

Multi-objective Matroid Optimization with Ordinal Weights

Klamroth¹,

Stiglmayr²

2021

Preprint

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Bi-objective optimization problems on matroids are in general intractable and their corresponding decision problems are in general NP-hard. However, if one of the objective functions is restricted to binary cost coefficients the problem becomes efficiently solvable by an exhaustive swap algorithm. Binary cost coefficients often represent two categories and are thus a special case of ordinal coefficients that are in general non-additive.In this paper we consider ordinal objective functions with more than two categories in the context of matroid optimization. We introduce several problem variants that can be distinguished w.r.t. their respective optimization goals, analyze their interrelations, and derive a polynomial time solution method that is based on the repeated solution of matroid intersection problems. Numerical tests on minimum spanning tree problems and on partition matroids confirm the efficiency of the approach.

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Evolutionary Algorithms for the Multi Criterion Minimum Spanning Tree Problem

Davis-Moradkhan

Browne

2010

Computational Intelligence in Expensive Optimization Problems

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A Hybridised Evolutionary Algorithm for Multi-Criterion Minimum Spanning Tree Problems

Cited by 4 publications

References 22 publications

Extending evolutionary algorithms to discover tri-criterion and non-supported solutions for the minimum spanning tree problem

Extending evolutionary algorithms to discover tri-criterion and non-supported solutions for the minimum spanning tree problem

Multi-objective Matroid Optimization with Ordinal Weights

Evolutionary Algorithms for the Multi Criterion Minimum Spanning Tree Problem

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