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A coevolutionary technique based on multi-swarm particle swarm optimization for dynamic multi-objective optimization

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2017年第3期261卷 1028-1051页

作者： Liu, Ruochen Li, Jianxia Fan, Jing Mu, Caihong Jiao, Licheng Xidian Univ Int Collaborat Joint Lab Intelligent Percept & Co Minist EducInt Res Ctr Intelligent Percept & Com Key Lab Intelligent Percept & Image Understanding Xian 710071 Shaanxi Peoples R China

In real-world applications, there are many fields involving dynamic multi-objective optimization problems (DMOPs), in which objectives are in conflict with each other and change over time or environments. In this paper, a modified coevolutionary multi-swarm particle swarm optimizer is proposed to solve DMOPs in the rapidly changing environments (denoted as CMPSODMO). A frame of multi-swarm based particle swarm optimization is adopted to optimize the problem in dynamic environments. In CMPSODMO, the number of swarms (PSO) is determined by the number of the objective functions, and all of these swarms utilize an information sharing strategy to evolve cooperatively. Moreover, a new velocity update equation and an effective boundary constraint technique are developed during evolution of each swarm. Then, a similarity detection operator is used to detect whether a change has occurred, followed by a memory based dynamic mechanism to response to the change. The proposed CMPSODMO has been extensively compared with five state-of-the-art algorithms over a test suit of benchmark problems. Experimental results indicate that the proposed algorithm is promising for dealing with the DMOPs in the rapidly changing environments. (C) 2017 Elsevier B.V. All rights reserved.

关键词： multiple objective programming Dynamic multi-objective optimization Coevolution Multi-swarm Particle swarm optimization Similarity detective

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Discrete representation of the non-dominated set for multi-objective optimization problems using kernels

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2017年第3期260卷 814-827页

作者： Bazgan, Cristina Jamain, Florian Vanderpooten, Daniel Univ Paris 09 PSL Res Univ CNRS LAMSADE F-75016 Paris France Inst Univ France Paris France

In this paper, we are interested in producing discrete and tractable representations of the set of non dominated points for multi-objective optimization problems, both in the continuous and discrete cases. These representations must satisfy some conditions of coverage, i.e. providing a good approximation of the non-dominated set, spacing, i.e. without redundancies, and cardinality, i.e. with the smallest possible number of points. This leads us to introduce the new concept of (epsilon, epsilon')-kernels, or epsilon-kernels when epsilon' = epsilon is possible, which correspond to epsilon=Pareto sets satisfying an additional. condition, of epsilon'-stability. Among these, the kernels of small, or possibly optimal, cardinality are claimed to be good representations of the non-dominated set. We first establish some general properties on epsilon-kernels. Then, for the bi-objective case, we propose some generic algorithms computing in polynomial time either an epsilon-kernel of small size or, for a fixed size k, an epsilon-kernel with a nearly optimal approximation ratio 1 + epsilon. For more than two objectives, we show that epsilon-kernels do not necessarily exist but that (epsilon, epsilon' )-kernels with epsilon' <= root 1 + epsilon-1 always exist. Nevertheless, we show that the size of a smallest (epsilon, epsilon')-kernel can be very far from the size of a smallest epsilon-Pareto set. (C) 2016 Published by Elsevier B.V.

关键词： multiple objective programming Pareto set Non-dominated points Discrete representation Exact and approximation algorithms kernel

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Agent assisted interactive algorithm for computationally demanding multiobjective optimization problems

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COMPUTERS & CHEMICAL ENGINEERING 2015年 77卷 105-115页

作者： Ojalehto, Vesa Podkopaev, Dmitry Miettinen, Kaisa Univ Jyvaskyla Dept Math Informat Technol FI-40014 Jyvaskyla Finland Polish Acad Sci Syst Res Inst PL-01447 Warsaw Poland

We generalize the applicability of interactive methods for solving computationally demanding, that is, time-consuming, multiobjective optimization problems. For this purpose we propose a new agent assisted interactive algorithm. It employs a computationally inexpensive surrogate problem and four different agents that intelligently update the surrogate based on the preferences specified by a decision maker. In this way, we decrease the waiting times imposed on the decision maker during the interactive solution process and at the same time decrease the amount of preference information expected from the decision maker. The agent assisted algorithm is not specific to any interactive method or surrogate problem. As an example we implement our algorithm for the interactive NIMBUS method and the PAINT method for constructing the surrogate. This implementation was applied to support a real decision maker in solving a two-stage separation problem. (C) 2015 Elsevier Ltd. All rights reserved.

关键词： multiple objective programming Interactive methods Agent-based optimization Surrogate problem NIMBUS PAINT

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Sensitivity analysis on the priority of the objective functions in lexicographic multiple objective linear programs

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2010年第3期207卷 1162-1168页

作者： Khorram, E. Zarepisheh, M. Ghaznavi-ghosoni, B. A. Amir Kabir Univ Technol Fac Math & Comp Sci Tehran 15914 Iran

This paper deals with a class of multiple objective linear programs (MOLP) called lexicographic multiple objective linear programs (LMOLP). In this paper, by providing an efficient algorithm which employs the preceding computations as well, it is shown how we can solve the LMOLP problem if the priority of the objective functions is changed. In fact, the proposed algorithm is a kind of sensitivity analysis on the priority of the objective functions in the LMOLP problems. (C) 2010 Elsevier B.V. All rights reserved.

关键词： multiple objective programming Vector optimization Preemptive priority Lexicographic ordering Sensitivity analysis

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Dominance for multi-objective robust optimization concepts

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2019年第2期273卷 430-440页

作者： Botte, Marco Schoebel, Anita Georg August Univ Gottingen Lotzestr 16-18 D-37083 Gottingen Germany

In robust optimization, the parameters of an optimization problem are not deterministic but uncertain. Their values depend on the scenarios which may occur. Single-objective robust optimization has been studied extensively. Since 2012, researchers have been looking at robustness concepts for multi-objective optimization problems as well. In another line of research, single-objective uncertain optimization problems are transformed to deterministic multi-objective problems by treating every scenario as an objective function. In this paper we combine these two points of view. We treat every scenario as an objective function also in uncertain multi-objective optimization, and we define a corresponding concept of dominance which we call multi scenario efficiency. We sketch this idea for finite uncertainty sets and extend it to the general case of infinite uncertainty sets. We then investigate the relation between this dominance and the concepts of highly, locally highly, flimsily, and different versions of minmax robust efficiency. For all these concepts we prove that every strictly robust efficient solution is multi-scenario efficient. On the other hand, under a compactness condition, the set of multi-scenario efficient solutions contains a robust efficient solution for all these concepts which generalizes the Pareto robustly optimal (PRO) solutions from single-objective optimization to Pareto robust efficient (PRE) solutions in the multi-objective case. We furthermore present two results on reducing an infinite uncertainty set to a finite one which are a basis for computing multi scenario efficient solutions. (C) 2018 Elsevier B.V. All rights reserved.

关键词： multiple objective programming Robustness and sensitivity analysis Pareto robust efficiency

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Asymptotic convergence of a simulated annealing algorithm for multiobjective optimization problems

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MATHEMATICAL METHODS OF OPERATIONS RESEARCH 2006年第2期64卷 353-362页

作者： Villalobos-Arias, Mario Coello, Carlos A. Coello Hernandez-Lerma, Onesimo CINVESTAV IPN Depto Ingn Elect Secc Computac Mexico City DF Mexico CINVESTAV IPN Dept Matemat Mexico City DF Mexico

In this paper we consider a simulated annealing algorithm for multiobjective optimization problems. With a suitable choice of the acceptance probabilities, the algorithm is shown to converge asymptotically, that is, t... 详细信息

关键词： simulated annealing multiple objective programming multiobjective optimization vector optimization convergence

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Diversified portfolios with different entropy measures

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APPLIED MATHEMATICS AND COMPUTATION 2014年 241卷 47-63页

作者： Yu, Jing-Rung Lee, Wen-Yi Chiou, Wan-Jiun Paul Natl Chi Nan Univ Dept Informat Management Puli Nantou 545 Taiwan Natl Chiao Tung Univ Dept Technol Management Hsinchu 30010 Taiwan Cent Michigan Univ Dept Finance & Law Pleasant MI 48859 USA

One of the major issues for Markowitz mean-variance model is the errors in estimations cause "corner solutions" and low diversity in the portfolio. In this paper, we compare the mean-variance efficiency, realized portfolio values, and diversity of the models incorporating different entropy measures by applying multiple criteria method. Differing from previous studies, we evaluate twenty-three portfolio over-time rebalancing strategies with considering short-sales and various transaction costs in asset diversification. Using the data of the most liquid stocks in Taiwan's market, our finding shows that the models with Yager's entropy yield higher performance because they respond to the change in market by reallocating assets more effectively than those with Shannon's entropy and with the minimax disparity model. Furthermore, including entropy in models enhances diversity of the portfolios and makes asset allocation more feasible than the models without incorporating entropy. (C) 2014 Elsevier Inc. All rights reserved.

关键词： multiple criteria analysis multiple objective programming Entropy Portfolio selection Short selling Transaction cost

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Approximating the Pareto optimal set using a reduced set of objective functions

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2010年第3期207卷 1519-1534页

作者： Lindroth, Peter Patriksson, Michael Stromberg, Ann-Brith Univ Gothenburg SE-41296 Gothenburg Sweden Chalmers Univ Technol SE-41296 Gothenburg Sweden

Real-world applications of multi-objective optimization often involve numerous objective functions. But while such problems are in general computationally intractable, it is seldom necessary to determine the Pareto optimal set exactly. A significantly smaller computational burden thus motivates the loss of precision lithe size of the loss can be estimated. We describe a method for finding an optimal reduction of the set of objectives yielding a smaller problem whose Pareto optimal set w.r.t. a discrete subset of the decision space is as close as possible to that of the original set of objectives. Utilizing a new characterization of Pareto optimality and presuming a Finite decision space, we derive a program whose solution represents an optimal reduction. We also propose an approximate, computationally less demanding formulation which utilizes correlations between the objectives and separates into two parts. Numerical results from an industrial instance concerning the configuration of heavy-duty trucks are also reported. demonstrating the usefulness of the method developed. The results show that multi-objective optimization problems can be significantly simplified with an induced error which can be measured. (C) 2010 Elsevier B.V. All rights reserved.

关键词： multiple objective programming Many-objective optimization Pareto optimality objective space reduction Engineering optimization

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Optimal water and land resource allocation in pastoral areas based on a water-land forage-livestock balance: a case study of Otog Front Banner, Inner Mongolia, China

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ENVIRONMENTAL SCIENCE AND POLLUTION RESEARCH 2020年第10期27卷 10328-10341页

作者： Lu, Haiyuan Li, Heping Wang, Jun Zheng, Hexiang Cao, Xuesong Tong, Changfu China Inst Water Resources & Hydropower Res State Key Lab Simulat & Regulat Water Cycle River Beijing 10038 Peoples R China Minist Water Resources Peoples Republ China Inst Water Resources Pastoral Area Hohhot 010020 Peoples R China

Natural grasslands provide important land resources in pastoral areas, and greatly contribute to ecological functioning. Overgrazing and other unreasonable exploitations have led to the degradation and desertification of natural grasslands, exacerbating the forage-livestock imbalance. In areas suffering from water shortage, this imbalance gradually evolves into a water-land forage-livestock imbalance. In this study, a water-land forage-livestock balance-based model was developed to optimise the allocation of water, land, and forage resources in pastoral areas, while addressing economic and ecological benefits in a coupled manner. The model was applied in a case study of Otog Front Banner to simulate the comprehensive economic and ecological benefits to the development of water, land, and forage resources in different coupled allocations of artificial and natural grasslands. The results showed that as the duration of supplementary and barn feeding increased, local development was first constrained by the availability of natural grasslands and then by the availability of water resources. The optimal resource allocation in Otog Front Banner predicted for 2030 included a water consumption of 266,000,000 m(3), an irrigation area of 43,000 ha, a natural grassland utilisation area of 684,700 ha, and a livestock farming scale of 1,188,500 sheep units.

关键词： Water and land resources Forage resources Optimal allocation Water-land forage-livestock balance multiple objective programming Pastoral area

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A goal programming approach to solve the multiple criteria DEA model

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2017年第1期260卷 134-139页

作者： dos Santos Rubem, Ana Paula Soares de Mello, Joao Carlos C. B. Meza, Lidia Angulo Ctr Naval Syst Anal Decis Aid Dept Praca Barao Ladarias-nIlha Cobras BR-20091000 Rio De Janeiro RJ Brazil Univ Fed Fluminense Dept Prod Engn Rua Passo Patria 156Sao Domingos BR-24210240 Niteroi RJ Brazil

The lack of discrimination power and the inappropriate multipliers schemes remain major issues in data envelopment analysis (DEA). To overcome these problems, the multiple criteria DEA (MCDEA) model was introduced in the late 1990s, drawing from a multiple objective perspective. However, because the objectives of the MCDEA model are generally conflicting, an optimal solution satisfying all objectives simultaneously often does not exist. Within this context, goal programming (GP) approaches were proposed to solve the MCDEA model. This paper focuses specifically on the GP formulation, known as GPDEA. However, recently, the GPDEA models were found to be invalid, and no alternative formulation, under a GP framework, was proposed. Therefore, the aim here is to develop a formulation for adequately solving the MCDEA model using weighted GP. In order to do so, we point out inconsistencies in the existing GPDEA models, and we present the WGP-MCDEA model. (C) 2016 Elsevier B.V. All rights reserved.

关键词： Data envelopment analysis multiple criteria analysis Goal programming multiple objective programming

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