Interval-based ranking in noisy evolutionary multi-objective optimization

Karshenas, Hossein; Bielza, Concha; Larrañaga, Pedro

doi:10.1007/s10589-014-9717-1

Cited by 11 publications

(7 citation statements)

References 46 publications

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“…Researches of interval dominance relation have become a trend in recent years, such as interval credibility [39], [40], interval probability dominant strategy [41], α-degree Pareto dominance [42], possibility degree [43]. In [44], a large amount of related interval programming methods have been reviewed, and an ensemble framework was designed for choosing a suitable approach and producing optimal solutions.…”

Section: A Review Of Interval Multi-objective Optimizationmentioning

confidence: 99%

An Angle-Based Bi-Objective Optimization Algorithm for Redundancy Allocation in Presence of Interval Uncertainty

Yang

et al. 2023

IEEE Trans. Automat. Sci. Eng.

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Uncertainty is a practical issue in system design optimization because some characteristics of components, such as reliability and cost, cannot be determined precisely in many situations. Considering the imprecise characteristics of components, few works have focused on the multi-objective optimization for the redundancy allocation due to the challenges of comparing multi intervals. To tackle the issue, a novel angle-based bi-objective redundancy allocation algorithm is proposed in this study, introducing three original contributions: 1) An angle-based interval crowding distance (ICA) is especially designed for effective performance and reduced computational time; 2) Two techniques are applied to tackle the problem: An elite selection for mutation is presented for generating better offsprings; A penalty-guided constraint handling technique is introduced for converting the problem into an unconstrained one. 3) Since a set of optimal solutions is obtained by the proposed method and no preference on uncertainties is provided, this paper proposes a novel knee interval method to help DMs make a decision. To be specific, the proposed ICA can describe the distribution of the whole population intuitively and effectively, considering not only the angle between two compared individuals but also the angle range of the interval values. The computational results from two typical experiments demonstrate that the proposed algorithm is more efficient than other state-of-the-art algorithms, generating Pareto sets with less repeating individuals, stronger convergence, wider distribution, less imprecision, and reduced computational time.Note to Practitioners-This article is motivated by two practical problems in multi-objective redundancy allocation in presence of interval uncertainty: First, this paper tries to solve the multiobjective redundancy allocation problem with the imprecise characteristics of components, which is rarely considered in the field of reliability optimization design. Second, the calculation of the crowding distance needs extra time cost and is less efficient. To tackle this issue, an interval crowding angle is especially designed, considering not only the angle between two compared individuals, but also the angle range of the interval values. The proposed method can be embedded in most multi-objective

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Section: A Review Of Interval Multi-objective Optimizationmentioning

confidence: 99%

An Angle-Based Bi-Objective Optimization Algorithm for Redundancy Allocation in Presence of Interval Uncertainty

Yang

et al. 2023

IEEE Trans. Automat. Sci. Eng.

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“…However, different studies investigating hybrid methods applying interval analysis techniques to deal with uncertainties and evolutionary algorithms to guide the search of a solution have been proposed. For instance, hybrid approaches based on multi-objective evolutionary algorithms, either based on the conversion of an interval multi-objective evolutionary algorithm to a deterministic single-or multi-objective optimization problem [29][30][31], or based on the interval dominance relation [32,33]. Furthermore, hybrid approaches on multiple types of evolutionary algorithms have also been presented.…”

Section: Related Workmentioning

confidence: 99%

“…where K is a constant for weighting constraint (33). Secondly, we consider an internal approximation of the estimates, i.e., we seek solutions that are contained in the experimental measures, thus fulfilling the following condition…”

Section: Modeling River Velocitymentioning

confidence: 99%

Combining Grammatical Evolution with Modal Interval Analysis: An Application to Solve Problems with Uncertainty

et al. 2021

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Complex systems are usually affected by various sources of uncertainty, and it is essential to account for mechanisms that ensure the proper management of such disturbances. This paper introduces a novel approach to solve symbolic regression problems, which combines the potential of Grammatical Evolution to obtain solutions by describing the search space with context-free grammars, and the ability of Modal Interval Analysis (MIA) to handle quantified uncertainty. The presented methodology uses an MIA solver to evaluate the fitness function, which represents a novel method to manage uncertainty by means of interval-based prediction models. This paper first introduces the theory that establishes the basis of the proposed methodology, and follows with a description of the system architecture and implementation details. Then, we present an illustrative application example which consists of determining the outer and inner approximations of the mean velocity of the water current of a river stretch. Finally, the interpretation of the obtained results and the limitations of the proposed methodology are discussed.

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“…Goh and Tan calculated the probability with which a solution dominates another, and compared solutions based on the probability [38]. Karshenas et al presented an α-degree Pareto dominance to discriminate solutions to an interval MOP [39]. In addition, Dou et al presented the scheme of the interval hesitation dominance to distinguish solutions [40].…”

Section: Interval Multi-objective Evolutionary Optimizationmentioning

confidence: 99%

A Similarity-Based Cooperative Co-Evolutionary Algorithm for Dynamic Interval Multiobjective Optimization Problems

Gong

Zhang

et al. 2020

IEEE Trans. Evol. Computat.

142

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Dynamic interval multi-objective optimization problems (DI-MOPs) are very common in real-world applications. However, there are few evolutionary algorithms that are suitable for tackling DI-MOPs up to date. A framework of dynamic interval multi-objective cooperative co-evolutionary optimization based on the interval similarity is presented in this paper to handle DI-MOPs. In the framework, a strategy for decomposing decision variables is first proposed, through which all the decision variables are divided into two groups according to the interval similarity between each decision variable and interval parameters. Following that, two sub-populations are utilized to cooperatively optimize decision variables in the two groups. Furthermore, two response strategies, i.e., a strategy based on the change intensity and a random mutation strategy, are employed to rapidly track the changing Pareto front of the optimization problem. The proposed algorithm is applied to eight benchmark optimization instances as well as a multi-period portfolio selection problem and compared with five state-of-the-art evolutionary algorithms. The experimental results reveal that the proposed algorithm is very competitive on most optimization instances.

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Interval-based ranking in noisy evolutionary multi-objective optimization

Cited by 11 publications

References 46 publications

An Angle-Based Bi-Objective Optimization Algorithm for Redundancy Allocation in Presence of Interval Uncertainty

An Angle-Based Bi-Objective Optimization Algorithm for Redundancy Allocation in Presence of Interval Uncertainty

Combining Grammatical Evolution with Modal Interval Analysis: An Application to Solve Problems with Uncertainty

A Similarity-Based Cooperative Co-Evolutionary Algorithm for Dynamic Interval Multiobjective Optimization Problems

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