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37th Conference of the North-American-Fuzzy-Information-Processing-Society (NAFIPS)

作者： Villanueva, Fabiola Roxana de Oliveira, Valeriano Antunes Sao Paulo State Univ UNESP Inst Biosci Letters & Exact Sci Dept Appl Math Sao Jose Do Rio Preto SP Brazil

ISBN: (纸本)9783319953120;9783319953113

This work considers an optimization problem where the objective function possesses interval uncertainty in the coefficients. In this sense, first, an order relation will be defined for the interval space and, from this, it will be defined a solution concept for the interval problem in question. Subsequently, it will be shown that an interval problem is equivalent to a bi-objective problem. Finally, it will be established the necessary conditions of Fritz John and Karush-Kuhn-Tucker types for the interval-valued optimization problem.

关键词： multi-objective optimization problems Karush-Kuhn-Tucker LU order relation LU solutions Classical necessary condition of Fritz John Interval optimization problems Necessary optimality conditions for the LU-solution

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A Study on Two-Step Search based on PSO to Improve Convergence and Diversity for Many-objective optimization problems

A Study on Two-Step Search based on PSO to Improve Convergen...

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IEEE Congress on Evolutionary Computation

作者： Hirano, Hiroyuki Yoshikawa, Tomohiro Nagoya Univ Grad Sch Engn Nagoya Aichi 4648601 Japan

ISBN: (纸本)9781479904549;9781479904532

Particle Swarm optimization (PSO) is one of the most effective search methods in optimization problems. multi-objective optimization problems (MOPs) has been focused on and PSO researches applied to MOPs have been reported. On the other hand, the problem that the search performance using conventional methods for MOPs becomes low is reported in Many-objective optimization problems (MaOPs) which have four or more objective functions. The authors have proposed two-step search method based on PSO for MaOPs. In the first step, it divides the population into some groups, and each group performs the single objective search for each objective function and the center of them. In the second step, the search is performed to acquire the diversity of Pareto solutions by PSO search with the goal, global-best, based on the solutions acquired in the first step. This paper defines the real coded multi-objective knapsack problem and studies the performance of the proposed method applied to this problem. The experimental results shows that the search of the first step for high convergence and that of the second step for large diversity aimed in the proposed method works well. It also shows that the proposed method is superior to other conventional methods especially in terms of the convergence in MaOPs.

关键词： Many-objective optimization problems Two-Step Search real coded multi-objective knapsack problem Particle Swarm optimization multi-objective optimization problems global-best

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Opposition-based multi-objective whale optimization algorithm with multi-leader guiding

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SOFT COMPUTING 2021年第24期25卷 15131-15161页

作者： Li, Yang Li, Wei-gang Zhao, Yun-tao Liu, Ao Minist Educ Engn Res Ctr Met Automat & Measurement Technol Wuhan 430081 Peoples R China Wuhan Univ Sci & Technol Sch Evergrande Management Wuhan 430081 Peoples R China

During recent decades, evolutionary algorithms have been widely studied in optimization problems. The multi-objective whale optimization algorithm based on multi-leader guiding is proposed in this paper, which attempts to offer a proper framework to apply whale optimization algorithm and other swarm intelligence algorithms to solving multi-objective optimization problems. The proposed algorithm adopts several improvements to enhance optimization performance. First, search agents are classified into leadership set and ordinary set by grid mechanism, and multiple leadership solutions guide the population to search the sparse spaces to achieve more homogeneous exploration in per iteration. Second, the differential evolution and whale optimization algorithm are employed to generate the offspring for the leadership and ordinary solutions, respectively. In addition, a novel opposition-based learning strategy is developed to improve the distribution of the initial population. The performance of the proposed algorithm is verified in contrast to 10 classic or state-of-the-arts algorithms on 20 bi-objective and tri-objective unconstrained problems, and experimental results demonstrate the competitive advantages in optimization quality and convergence speed. Moreover, it is tested on load distribution of hot rolling, and the result proves its good performance in real-world applications. Thus, all of the aforementioned experiments have indicated that the proposed algorithm is comparatively effective and efficient.

关键词： multi-objective optimization problems Whale optimization algorithm multi-leader guiding Opposition-based learning strategy

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An improved multi-objective evolutionary algorithm for simultaneously detecting separated and overlapping communities

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NATURAL COMPUTING 2016年第4期15卷 635-651页

作者： Liu, Chenlong Liu, Jing Jiang, Zhongzhou Xidian Univ Key Lab Intelligent Percept & Image Understanding Minist Educ Xian 710071 Peoples R China

In our previous work, a multi-objective evolutionary algorithm (MEA_CDPs) was proposed for detecting separated and overlapping communities simultaneously. However, MEA_CDPs has a couple of defects, like individuals cannot be transformed to community structure by the decoder when the quality of community structure is lower certain thresholds, many vertices with weak overlapping nature are identified as overlapping nodes, and the objective functions can not control the ratio of separated nodes to overlapping nodes. Therefore, in this paper, to overcome these defects, we improve MEA_CDPs by designing more efficient objective functions. We also extend MEA_CDPs' capability in detecting hierarchical community structures. The improved algorithm is named as iMEA_CDPs. In the experiments, a set of computer-generated networks are first used to test the effect of parameters in iMEA_CDPs, and then four real-world networks are used to validate the performance of iMEA_CDPs. The experimental results show that iMEA_CDPs outperforms MEA_CDPs. Moreover, compared with MEA_CDPs, iMEA_CDPs can detect various kinds of overlapping and hierarchical community structures.

关键词： Evolutionary algorithms multi-objective optimization problems Community detection problems Overlapping communities Separated communities

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A polar-based guided multi-objective evolutionary algorithm to search for optimal solutions interested by decision-makers in a logistics network design problem

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JOURNAL OF INTELLIGENT MANUFACTURING 2014年第4期25卷 699-726页

作者： Cheshmehgaz, Hossein Rajabalipour Islam, Md. Nazrul Desa, Mohammad Ishak UTM Skudai Johor Malaysia

In practical multi-objective optimization problems, respective decision-makers might be interested in some optimal solutions that have objective values closer to their specified values. Guided multi-objective evolutionary algorithms (guided MOEAs) have been significantly used to guide their evolutionary search direction toward these optimal solutions using by decision makers. However, most guided MOEAs need to be iteratively and interactively evaluated and then guided by decision-makers through re-formulating or re-weighting objectives, and it might negatively affect the algorithms performance. In this paper, a novel guided MOEA that uses a dynamic polar-based region around a particular point in objective space is proposed. Based on the region, new selection operations are designed such that the algorithm can guide the evolutionary search toward optimal solutions that are close to the particular point in objective space without the iterative and interactive efforts. The proposed guided MOEA is tested on the multi-criteria decision-making problem of flexible logistics network design with different desired points. Experimental results show that the proposed guided MOEA outperforms two most effective guided and non-guided MOEAs, R-NSGA-II and NSGA-II.

关键词： multi-objective optimization problems Guided multi-objective evolutionary algorithms Polar coordinate system Flexible logistics network design problem

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Optimal design and operation of a wastewater purification system

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MATHEMATICS AND COMPUTERS IN SIMULATION 2008年第3期79卷 668-682页

作者： Alvarez-Vazquez, Lino J. Balsa-Canto, Eva Martinez, Aurea Univ Vigo ETSI Telecomunicac Dept Matemat Aplicada 2 Vigo 36310 Spain CSIC Inst Invest Marinas Vigo Spain

Due to the importance of coastal areas, is of the highest interest to implement purification systems that with minimum cost are able to assure water quality standards in agreement with the regional legislations. This work addresses the optimal design (outfall locations) and optimal operation (level of oxygen discharges) of a wastewater treatment system. This problem can be mathematically formulated as a two-objective mixed design and optimal control problem with constraints on the states and the design and control variables. The two-objective problem is formulated as a single-objective problem through the use of the weighted sum method. The existence of the optimal solution is then demonstrated for an arbitrary set of weights and a first order optimality condition is obtained to characterize that solution. The numerical solution for a realistic case study posed in the ria of Vigo is also accomplished by using the combination of the control vector parametrization approach with a global non-linear programming (NLP) solver. Remark that, as the problem under consideration is two-objective, there is not an unique solution but a set of equivalent solutions, the Pareto solutions, requiring the involvement of a decision maker to select one solution from the set. (C) 2008 IMACS. Published by Elsevier B.V. All rights reserved.

关键词： Wastewater treatment Pointwise control Control vector parameterization multi-objective optimization problems Global optimization methods

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An improved multi-objective bacterial colony chemotaxis algorithm based on Pareto dominance

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SOFT COMPUTING 2022年第1期26卷 69-87页

作者： Lu, Zhigang Qi, Shengjing Zhang, Jiangfeng Cai, Yao Guo, Xiaoqiang Luo, Shifan Yanshan Univ Key Lab Power Elect Energy Conservat & Motor Driv Qinhuangdao Hebei Peoples R China Clemson Univ Dept Automot Engn Clemson SC USA Northeastern Univ Coll Engn Boston MA 02115 USA

This paper puts forward an improved multi-objective bacterial colony chemotaxis (MOBCC) algorithm based on Pareto dominance. A time-varying step size tactic is adopted to increase the global and local searching abilities of the improved MOBCC algorithm. An external archive is created to keep previously found Pareto optimal solutions. A non-dominated sorting method integrating crowding distance assignment is applied to enhance the time efficiency of the improved MOBCC algorithm. A hybrid method combining bacterial individual mutation, oriented mutation of bacterial colony and local search of external archive is applied to enhance the convergence of the algorithm and maintain the diversity of solution set. The framework of MOEAs based on Pareto dominance is integrated into the improved MOBCC algorithm properly through replacements of the bacterial individuals in the bacterial colony, archive operation, and updating of the bacterial colony. The improved MOBCC algorithm is compared with three common multi-objective optimization algorithms SPEA2, NSGA-II and MOEA/D on fifteen test problems and evolution of optimization, and the experimental results confirm the validity of the improved MOBCC algorithm. Furthermore, the effects of the improved MOBCC algorithm's parameters on the performance of the improved MOBCC algorithm are analyzed.

关键词： multi-objective optimization problems Bacterial colony chemotaxis Pareto dominance Time-varying step size Hybrid method

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Scheduling multi-objective open shop scheduling using a hybrid immune algorithm

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INTERNATIONAL JOURNAL OF ADVANCED MANUFACTURING TECHNOLOGY 2013年第5-8期66卷 895-905页

作者： Naderi, B. Mousakhani, M. Khalili, M. Islamic Azad Univ Qazvin Branch Young Researchers Club Qazvin Iran Islamic Azad Univ Sci & Res Branch Fac Management & Econ Dept Business Management Tehran Iran Islamic Azad Univ Karaj Branch Dept Ind Engn Karaj Iran

Despite their importance, hardly ever have multi-objective open shop problems been the topic of researches. This paper studies the mentioned problem and proposes some novel multi-objective solution methods centered on the idea behind artificial immune and simulated annealing algorithms incorporating with powerful and fast local search engines. First, the algorithms are tuned and then carefully evaluated for their performance by means of multi-objective performance measures and statistical tools. An available ant colony optimization is also brought into the experiment. Among the proposed algorithms, the results show that the variant of enhanced artificial immune algorithm outperforms the others.

关键词： Open shop scheduling multi-objective optimization problems Metaheuristics Artificial immune algorithm Simulated annealing Performance quality measure

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An effective model of multiple multi-objective evolutionary algorithms with the assistance of regional multi-objective evolutionary algorithms: VIPMOEAs

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APPLIED SOFT COMPUTING 2013年第5期13卷 2863-2895页

作者： Cheshmehgaz, Hossein Rajabalipour Desa, Mohamad Ishak Wibowo, Antoni UTM Fac Comp Sci & Informat Syst Skudai 81310 JB Malaysia

Division of the evolutionary search among multiple multi-objective evolutionary algorithms (MOEAs) is a recent advantage in MOEAs design, particularly in effective parallel and distributed MOEAs. However, most these algorithms rely on such a central (re) division that affects the algorithms' efficiency. This paper first proposes a local MOEA that searches on a particular region of objective space with its novel evolutionary selections. It effectively searches for Pareto Fronts (PFs) inside the given polar-based region, while nearby the region is also explored, intelligently. The algorithm is deliberately designed to adjust its search direction to outside the region - but nearby - in the case of a region with no Pareto Front. With this contribution, a novel island model is proposed to run multiple forms of the local MOEA to improve a conventional MOEA (e. g. NSGA-II or MOEA/D) running along - in another island. To dividing the search, a new division technique is designed to give particular regions of objective space to the local MOEAs, frequently and effectively. Meanwhile, the islands benefit from a sophisticated immigration strategy without any central (re) collection, (re) division and (re) distribution acts. Results of three experiments have confirmed that the proposed island model mostly outperforms to the clustering MOEAs with similar division technique and similar island models on DTLZs. The model is also used and evaluated on a real-world combinational problem, flexible logistic network design problem. The model definitely outperforms to a similar island model with conventional MOEA (NSGA-II) used in each island. (C) 2012 Elsevier B. V. All rights reserved.

关键词： multi-objective optimization problems multi-objective evolutionary algorithms multiple MOEAs Island model Pareto Fronts

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A survey on multi-objective evolutionary algorithms for many-objective problems

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COMPUTATIONAL optimization AND APPLICATIONS 2014年第3期58卷 707-756页

作者： von Luecken, Christian Baran, Benjamin Brizuela, Carlos Univ Nacl Asuncion Fac Politecn San Lorenzo Paraguay Univ Nacl Asuncion San Lorenzo Paraguay CISESE Ensenada 22860 Baja California Mexico

multi-objective evolutionary algorithms (MOEAs) are well-suited for solving several complex multi-objective problems with two or three objectives. However, as the number of conflicting objectives increases, the performance of most MOEAs is severely deteriorated. How to improve MOEAs' performance when solving many-objective problems, i.e. problems with four or more conflicting objectives, is an important issue since a large number of this type of problems exists in science and engineering;thus, several researchers have proposed different alternatives. This paper presents a review of the use of MOEAs in many-objective problems describing the evolution of the field, the methods that were developed, as well as the main findings and open questions that need to be answered in order to continue shaping the field.

关键词： multi-objective optimization problems Many-objective optimization multi-objective evolutionary algorithms

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