A Set of Test Cases for Performance Measures in Multiobjective Optimization

Lizárraga, Giovanni; Botello, Salvador

doi:10.1007/978-3-540-88636-5_41

Cited by 5 publications

(5 citation statements)

References 4 publications

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“…In the literature, some researchers proposed or reviewed the PIs for evaluating multi-objective optimizers from different perspectives [60][61][62][63][64]. Usually, the quality of a non-dominated set can be assessed from three aspects: the size of the non-dominated set, the accuracy of the solutions in the set, i. e., the closeness of the solutions to the theoretical PF and distribution and spread of the solutions.…”

Section: Accuracy Pismentioning

confidence: 99%

“…Generally speaking, it is difficult to judge the performance of the multi-objective optimization algorithm because there is no universally accepted definition of optimum in the multi-objective optimization cases as in the single optimization [60]. Also, the evaluations according to different PIs may disagree with the common sense of when a multi-objective algorithm is performing better than another [63].…”

Section: Accuracy Pismentioning

confidence: 99%

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A two phase approach for the bi-objective non-convex combined heat and power production planning problem

Rong

Figueira

Lahdelma

2015

European Journal of Operational Research

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In this paper, we deal with the bi-objective non-convex combined heat and power (CHP) planning problem. A medium and long term planning problem decomposes into thousands of single period (hourly) subproblems and dynamic constraints can usually be ignored in this context. The hourly subproblem can be formulated as a mixed integer linear programming (MILP) model. First, an efficient two phase approach for constructing the Pareto Frontier (PF) of the hourly subproblem is presented. Then a merging algorithm is developed to approximate the PF for the multi-period planning problem. Numerical results with real CHP plants demonstrate the effectiveness and efficiency of the solution approach using the Cplex based ε-constraint method as benchmark.

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Section: Accuracy Pismentioning

confidence: 99%

Section: Accuracy Pismentioning

confidence: 99%

A two phase approach for the bi-objective non-convex combined heat and power production planning problem

Rong

Figueira

Lahdelma

2015

European Journal of Operational Research

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“…Moreover, some quality measures require additional problem knowledge in the evaluation of solution sets, for example, the reference point in the hypervolume metric and the ideal point in the Tchebycheff-based IPF. This may affect the evaluation results, especially when comparing several solution sets with different spatial locations [25]. Finally, parameter setting is an important issue in those parameter-dependent quality measures.…”

Section: Introductionmentioning

confidence: 99%

Dominance Move: A Measure of Comparing Solution Sets in Multiobjective Optimization

Li¹,

Yao²

2017

Preprint

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One of the most common approaches for multiobjective optimization is to generate a solution set that well approximates the whole Pareto-optimal frontier to facilitate the later decision-making process. However, how to evaluate and compare the quality of different solution sets remains challenging. Existing measures typically require additional problem knowledge and information, such as a reference point or a substituted set of the Pareto-optimal frontier. In this paper, we propose a quality measure, called dominance move (DoM), to compare solution sets generated by multiobjective optimizers. Given two solution sets, DoM measures the minimum sum of move distances for one set to weakly Pareto dominate the other set. DoM can be seen as a natural reflection of the difference between two solutions, capturing all aspects of solution sets' quality, being compliant with Pareto dominance, and does not need any additional problem knowledge and parameters. We present an exact method to calculate the DoM in the biobjective case. We show the necessary condition of constructing the optimal partition for a solution set's minimum move, and accordingly propose an efficient algorithm to recursively calculate the DoM. Finally, DoM is evaluated on several groups of artificial and real test cases as well as by a comparison with two well-established quality measures.

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“…Furthermore, the hypervolume indicator may be biased toward solutions having certain properties. Lizarraga et al (2008) compare several measures, including the hypervolume indicator and the socalled epsilon indicator. They find that the hypervolume indicator performs well in general but has handicaps in certain problems.…”

Section: Introductionmentioning

confidence: 99%

Quantitative Comparison of Approximate Solution Sets for Multicriteria Optimization Problems with Weighted Tchebycheff Preference Function

Bozkurt

Fowler

Gel

et al. 2010

Operations Research

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We consider the problem of evaluating the quality of solution sets generated by heuristics for multiple-objective combinatorial optimization problems. We extend previous research on the integrated preference functional (IPF), which assigns a scalar value to a given discrete set of nondominated points so that the weighted Tchebycheff function can be used as the underlying implicit value function. This extension is useful because modeling the decision maker's value function with the weighted Tchebycheff function reflects the impact of unsupported points when evaluating sets of nondominated points. We present an exact calculation method for the IPF measure in this case for an arbitrary number of criteria. We show that every nondominated point has its optimal weight interval for the weighted Tchebycheff function. Accordingly, all nondominated points, and not only the supported points in a set, contribute to the value of the IPF measure when using the weighted Tchebycheff function. Two-and three-criteria numerical examples illustrate the desirable properties of the weighted Tchebycheff function, providing a richer measure than the original IPF based on a convex combination of objectives.

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A Set of Test Cases for Performance Measures in Multiobjective Optimization

Cited by 5 publications

References 4 publications

A two phase approach for the bi-objective non-convex combined heat and power production planning problem

A two phase approach for the bi-objective non-convex combined heat and power production planning problem

Dominance Move: A Measure of Comparing Solution Sets in Multiobjective Optimization

Quantitative Comparison of Approximate Solution Sets for Multicriteria Optimization Problems with Weighted Tchebycheff Preference Function

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