Finding Evenly Spaced Pareto Fronts for Three-Objective Optimization Problems

Trautmann, Heike; Rudolph, Günter; Domínguez-Medina, Christian; Schütze, Oliver

doi:10.1007/978-3-642-31519-0_6

Cited by 17 publications

(6 citation statements)

References 14 publications

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“…Therefore, it is important that the POF approximation should be arranged in order to be a sufficiently good representation of the POF. In practice, it is often desirable that the POF approximation is well-diversified over the whole range of the POF so as to maximize the information of the POF presented to the DMs [20].…”

Section: A Diversity Indicatorsmentioning

confidence: 99%

On the use of hypervolume for diversity measurement of Pareto front approximations

Jiang

Yang

2016

2016 IEEE Symposium Series on Computational Intelligence (SSCI)

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In multiobjective optimization, a good quality indicator is of great importance to the performance assessment of algorithms. This paper investigates the effectiveness of the widelyused hypervolume indicator, which is the only one found so far to strictly comply with the Pareto dominance. While hypervolume is of undisputed success to assess the quality of an approximation, it is sensitive to misleading cases, particularly for diversity assessment. To address this issue, this paper presents a modified hypervolume indicator based on linear projection for diversity evaluation. In addition to experimental studies to demonstrate the effectiveness of the proposed indicator, the indicator is introduced into the environmental selecction of an indicator-based multiobjective optimization evolutionary algorithm. Experiments show that the proposed indicator yields more evenly-distributed approximations than the original hypervolume indicator.

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Section: A Diversity Indicatorsmentioning

confidence: 99%

On the use of hypervolume for diversity measurement of Pareto front approximations

Jiang

Yang

2016

2016 IEEE Symposium Series on Computational Intelligence (SSCI)

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“…Next, the mean and standard deviations of the first Pareto front individual fitness values are used for analyzing the performance of the optimizers. In addition, the Pareto front spread metric (∆) [29], generational distance (GD) [30], and the Pareto front spacing is used to evaluate the performance of the optimizers.…”

Section: Performance Evaluationmentioning

confidence: 99%

Elite Multi-Criteria Decision Making—Pareto Front Optimization in Multi-Objective Optimization

Kesireddy,

Medrano

2024

Algorithms

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Optimization is a process of minimizing or maximizing a given objective function under specified constraints. In multi-objective optimization (MOO), multiple conflicting functions are optimized within defined criteria. Numerous MOO techniques have been developed utilizing various meta-heuristic methods such as Evolutionary Algorithms (EAs), Genetic Algorithms (GAs), and other biologically inspired processes. In a cooperative environment, a Pareto front is generated, and an MOO technique is applied to solve for the solution set. On other hand, Multi-Criteria Decision Making (MCDM) is often used to select a single best solution from a set of provided solution candidates. The Multi-Criteria Decision Making–Pareto Front (M-PF) optimizer combines both of these techniques to find a quality set of heuristic solutions. This paper provides an improved version of the M-PF optimizer, which is called the elite Multi-Criteria Decision Making–Pareto Front (eMPF) optimizer. The eMPF method uses an evolutionary algorithm for the meta-heuristic process and then generates a Pareto front and applies MCDM to the Pareto front to rank the solutions in the set. The main objective of the new optimizer is to exploit the Pareto front while also exploring the solution area. The performance of the developed method is tested against M-PF, Non-Dominated Sorting Genetic Algorithm-II (NSGA-II), and Non-Dominated Sorting Genetic Algorithm-III (NSGA-III). The test results demonstrate the performance of the new eMPF optimizer over M-PF, NSGA-II, and NSGA-III. eMPF was not only able to exploit the search domain but also was able to find better heuristic solutions for most of the test functions used.

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“…Δ p -EMOA performs better than NSGA-II [22], while consuming a lower number of function evaluations. An extension of this approach to three-objective problems is reported in [23]. In this case, the algorithm requires some previous mathematical steps which include reducing the dimensionality of the non-dominated solutions and calculating their convex hull.…”

Section: Related Workmentioning

confidence: 99%

MOMBI: A new metaheuristic for many-objective optimization based on the R2 indicator

Gómez

Coello

2013

2013 IEEE Congress on Evolutionary Computation

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The incorporation of performance indicators as the selection mechanism of a multi-objective evolutionary algorithm (MOEA) is a topic that has attracted increasing interest in the last few years. This has been mainly motivated by the fact that Pareto-based selection schemes do not perform properly when solving problems with four or more objectives. The indicator that has been most commonly used for being incorporated in the selection mechanism of a MOEA has been the hypervolume. Here, however, we explore the use of the R2 indicator, which presents some advantages with respect to the hypervolume, the main one being its low computational cost. In this paper, we propose a new MOEA called Many-Objective Metaheuristic Based on the R2 Indicator (MOMBI), which ranks individuals using a utility function. The proposed approach is compared with respect to MOEA/D (based on scalarization) and SMS-EMOA (based on hypervolume) using several benchmark problems. Our preliminary experimental results indicate that MOMBI obtains results of similar quality to those produced by SMS-EMOA, but at a much lower computational cost. Additionally, MOMBI outperforms MOEA/D in most of the test instances adopted, particularly when dealing with high-dimensional problems having complicated Pareto fronts. Thus, we believe that our proposed approach is a viable alternative for solving many-objective optimization problems. 1 The Hypervolume (also known as the S metric or the Lebesgue Measure) of a set of solutions measures the size of the portion of objective space that is dominated by those solutions collectively [6].

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Finding Evenly Spaced Pareto Fronts for Three-Objective Optimization Problems

Cited by 17 publications

References 14 publications

On the use of hypervolume for diversity measurement of Pareto front approximations

On the use of hypervolume for diversity measurement of Pareto front approximations

Elite Multi-Criteria Decision Making—Pareto Front Optimization in Multi-Objective Optimization

MOMBI: A new metaheuristic for many-objective optimization based on the R2 indicator

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