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An efficient, adaptive parameter variation scheme for metaheuristics based on the epsilon-constraint method

EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2006年第3期169卷 932-942页

作者： Laumanns, M Thiele, L Zitzler, E ETH Zentrum Swiss Fed Inst Technol Inst Operat Res CH-8092 Zurich Switzerland ETH Zentrum Swiss Fed Inst Technol Comp Engn & Networks Lab CH-8092 Zurich Switzerland

This paper discusses methods for generating or approximating the Pareto set of multiobjective optimization problems by solving a sequence of constrained single-objective problems. The necessity of determining the constraint value a priori is shown to be a serious drawback of the original epsilon-constraint method. We therefore propose a new, adaptive scheme to generate appropriate constraint values during the run. A simple example problem is presented, where the running time (measured by the number of constrained single-objective sub-problems to be solved) of the original epsilon-constraint method is exponential in the problem size (number of decision variables), although the size of the Pareto set grows only linearly. We prove that-independent of the problem or the problem size-the time complexity of the new scheme is O(k(m-1)), where k is the number of Pareto-optimal solutions to be found and m the number of objectives. Simulation results for the example problem as well as for different instances of the multiobjective knapsack problem demonstrate the behavior of the method, and links to reference implementations are provided. (c) 2004 Elsevier B.V. All rights reserved.

关键词： multiple objective optimization non-dominated set Pareto set Epsilon-constraint method generating methods

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Min-Max quickest path problems

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NETWORKS 2012年第4期60卷 253-258页

作者： Ruzika, Stefan Thiemann, Markus Univ Kaiserslautern D-67653 Kaiserslautern Germany

In a dynamic network, the quickest path problem asks for a path such that a given amount of flow can be sent from source to sink via this path in minimal time. In practical settings, for example, in evacuation or transportation planning, the problem parameters might not be known exactly a priori. It is therefore of interest to consider robust versions of these problems in which travel times and/or capacities of arcs depend on a certain scenario. In this article, minmax versions of robust quickest path problems are investigated and, depending on their complexity status, exact algorithms or fully polynomial-time approximation schemes are proposed. (c) 2012 Wiley Periodicals, Inc. NETWORKS, Vol. 60(4), 253-258 2012

关键词： quickest path problem robust network flows optimization FPTAS polynomial algorithms multiple objective optimization

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A parametric simplex algorithm for linear vector optimization problems

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MATHEMATICAL PROGRAMMING 2017年第1-2期163卷 213-242页

作者： Rudloff, Birgit Ulus, Firdevs Vanderbei, Robert Vienna Univ Econ & Business Inst Stat & Math A-1020 Vienna Austria Bilkent Univ Dept Ind Engn TR-06800 Ankara Turkey Princeton Univ Dept Operat Res & Financial Engn Princeton NJ 08544 USA

In this paper, a parametric simplex algorithm for solving linear vector optimization problems (LVOPs) is presented. This algorithm can be seen as a variant of the multi-objective simplex (the Evans-Steuer) algorithm (Math Program 5(1):54-72, 1973). Different from it, the proposed algorithm works in the parameter space and does not aim to find the set of all efficient solutions. Instead, it finds a solution in the sense of Lohne (Vector optimization with infimum and supremum. Springer, Berlin, 2011), that is, it finds a subset of efficient solutions that allows to generate the whole efficient frontier. In that sense, it can also be seen as a generalization of the parametric self-dual simplex algorithm, which originally is designed for solving single objective linear optimization problems, and is modified to solve two objective bounded LVOPs with the positive orthant as the ordering cone in RuszczyA"ski and Vanderbei (Econometrica 71(4):1287-1297, 2003). The algorithm proposed here works for any dimension, any solid pointed polyhedral ordering cone C and for bounded as well as unbounded problems. Numerical results are provided to compare the proposed algorithm with an objective space based LVOP algorithm [Benson's algorithm in Hamel et al. (J Global Optim 59(4):811-836, 2014)], that also provides a solution in the sense of Lohne (2011), and with the Evans-Steuer algorithm (1973). The results show that for non-degenerate problems the proposed algorithm outperforms Benson's algorithm and is on par with the Evans-Steuer algorithm. For highly degenerate problems Benson's algorithm (Hamel et al. 2014) outperforms the simplex-type algorithms;however, the parametric simplex algorithm is for these problems computationally much more efficient than the Evans-Steuer algorithm.

关键词： Linear vector optimization multiple objective optimization Algorithms Parameter space segmentation

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multiple objective Compromised Method for Power Management in Virtual Power Plants

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ENERGIES 2011年第4期4卷 700-716页

作者： Gong, Jinxia Xie, Da Jiang, Chuanwen Zhang, Yanchi Shanghai Jiao Tong Univ Sch Elect Informat & Elect Engn Shanghai 200240 Peoples R China E China Univ Sci & Technol Dept Automat Shanghai 200237 Peoples R China

In practical optimization, a priority requirement for different objectives of multiple objective optimization problems should be considered. In this paper, the distributed power management of a Virtual Power Plant (VPP) with priority requirement is optimized by the compromised method. The operation optimization model of VPP is formulated as a fuzzy multiple objective optimization problem considering the satisfaction of customers and suppliers, the system stability, the power quality, and costs with operation limitations. The multiple objective optimization algorithm with the compromise of the satisfactory degree and the priority of objectives is studied based on the principle of two-step interactive satisfactory optimization. This method is also applied in a test system.

关键词： multiple objective optimization VPP satisfaction decision making priority

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Multi-objective energy aware multiprocessor scheduling using bat intelligence

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JOURNAL OF INTELLIGENT MANUFACTURING 2013年第4期24卷 805-819页

作者： Malakooti, Behnam Sheikh, Shaya Al-Najjar, Camelia Kim, Hyun Case Western Reserve Univ Dept Elect Engn & Comp Sci Cleveland OH 44106 USA

In this paper, a new heuristic called bat intelligence (BI) is introduced for solving energy aware multiprocessor scheduling problems. Bat intelligence is a novel optimization method that models prey hunting behaviors of bats. Bat intelligence and genetic algorithm (GA) are used to solve single-objective multiprocessor scheduling problem using, makespan, tardiness, and energy consumption as objective functions. Bat intelligence shows considerable improvement in terms of solution quality when compared with GA. Different combinations of these objectives are used to solve bi-objective multiprocessor scheduling problems, (makespan vs. energy, and also tardiness vs. energy). Tri-objective multiprocessor scheduling problem is also presented at the end. To generate desirable efficient alternatives, a Normalized Weighted Additive Utility Function is used. Simulation shows that BI identifies a set of efficient solutions that correspond to the assigned weights. The computational simulation also shows conflicting relationships between makespan and energy, and also between tardiness and energy.

关键词： Energy-aware multiprocessor scheduling problem Heuristic multiple objective optimization Hunting behavior

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Study on milling technology of Waspaloy superalloy internal threads with a small diameter

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INTERNATIONAL JOURNAL OF ADVANCED MANUFACTURING TECHNOLOGY 2021年第9-10期113卷 2925-2941页

作者： Dong, Liangliang Wang, Jing Li, Tian Xie, Xutao Li, Kun Zhang, Shengwei Southwest Petr Univ Sch Mechatron Engn Chengdu 610500 Peoples R China AECC Chengdu Engine Co Ltd Chengdu 610503 Peoples R China

Small-diameter thread is widely used in the connection of aeroengine, nuclear equipment, and petrochemical equipment parts due to its advantages of high connection strength, simple structure, and convenient loading and unloading. Manual tapping is its main production method. But, the stability of product quality is poor;the qualified rate of one-time machining is less than 20%, resulting in a large number of repeated machining and scrap. The existing thread milling method is difficult to adapt to the small-diameter internal thread processing of Waspaloy high-temperature alloy. The deformation of the tool during the processing and the difficulty in heat dissipation from the unreasonable processing technology are the main reasons for the processing accuracy not meeting the standard. In this paper, a 3-D numerical simulation model of small-diameter internal thread milling is established based on the flow stress control theory. The influence of structure parameters and milling machining parameters on milling force and milling temperature is studied by orthogonal experiment, and the range analysis is carried out. The mathematical model of milling force and temperature is calculated by nonlinear regression analysis. Based on Pareto genetic algorithm, multiple objective optimization method, the cutter structure, and machining parameters are optimized. The better machining parameters and cutting cutter parameters are obtained;the deformation of thread milling cutter in X, Y, and Z direction is obtained, and a new structure of thread milling cutter is designed;the feasibility of the new type of thread milling cutter and the machining scheme is verified by the trial cutting experiment of the thread milling cutter.

关键词： Waspaloy superalloy Small-diameter internal thread Thermal coupling Orthogonal experiment multiple objective optimization Machining technology

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Improving fuel economy and performance of a fuel-cell hybrid electric vehicle (fuel-cell, battery, and ultra-capacitor) using optimized energy management strategy

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ENERGY CONVERSION AND MANAGEMENT 2018年第Mar.期160卷 74-84页

作者： Ahmadi, Saman Bathaee, S. M. T. Hosseinpour, Amir H. KN Toosi Univ Technol Tehran Iran

Fuel-Cell System (FCS) is the primary energy supply of a Fuel-Cell Vehicle (FCV). Battery or Ultra-Capacitor (UC), as a secondary power source, is used along the FCS to improve the FCV's power response. Battery and UC composition, as a hybrid power source presenting the term of Fuel-Cell Hybrid Electric Vehicle (FCHEV), provides the FCV with the advantages of high energy density and high dynamic response. The supervisory system of the FCHEV could be managed efficiently to exploit the benefits of battery and UC at the same time. As a matter of fact, in such a combination, the performance of the hybrid powertrain largely depends on how to distribute the requested power through different types of energy sources. In this paper, we design the powertrain elements of an FCHEV in advance, with FCS/Battery/UC considerations. The energy management strategy (EMS) is achieved by presenting a novel power sharing method and by implementing an intelligent control technique constructed based on Fuzzy Logic Control (FLC). The control parameters are accurately adjusted by the genetic algorithm (GA) while considering targets and restrictions within a multi-objective optimization function over a combined city/highway driving cycle. This optimized supervisory system is examined by Advanced Vehicle Simulator (ADVISOR) to evaluate the performance of the proposed EMS over 22 different driving cycles and some specific performance tests. The results of simulation show that the presented strategy progressively affects the vehicle characteristics. Fuel economy enhancement, vehicle performance improvement, battery charge-sustaining capability, and optimal energy distribution are some of the significant outcomes achieved by the optimized FLC-based EMS.

关键词： Energy management strategy Fuel-cell hybrid electric vehicle Fuzzy logic control Genetic algorithm multiple objective optimization

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Proposal of Torque-Correct-by-Construction optimization Method for Axial Flux Machines

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IEEE TRANSACTIONS ON ENERGY CONVERSION 2023年第3期38卷 1511-1520页

作者： Zhou, Hao Gerling, Dieter Univ Bundeswehr Munich Inst Elect Drives D-85577 Neubiberg Germany

We propose an innovative optimization method for axial flux machine that keeps the output torque constant in the process of weight reduction. A concept of framework is introduced that provides guidance for optimization design on how to choose and redesign the relevant parameters. Unlike the conventional algorithms that search candidates in sample space, new designs with reduced weight are directly determined by following the developed optimization strategy using two-dimensional finite element analysis (FEA). The torque error is restricted by a maximum allowable error introduced in the framework. A single-sided axial flux permanent magnet synchronous machine is used as a starting design. A total of 29 new designs are derived with gradually varying optimization variables. The optimization trend and limit are investigated with respect to the redesigned parameters as well as the resulting weights, which provide an overview for selecting optimal design. At last, the torque of every design is verified by both two-dimensional and three-dimensional FEA. The effectiveness of proposed method is demonstrated by the result that the weight is significantly and continuously reduced as the independent optimization variable increases while the torque error remains in a small extent.

关键词： Axial flux permanent magnet machine constant torque finite element analysis multiple objective optimization weight reduction

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DP Pareto optimal balanced orthogonal subplot designs

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QUALITY TECHNOLOGY AND QUANTITATIVE MANAGEMENT 2020年第4期17卷 486-500页

作者： Wulff, Shaun S. Cao, Yongtao Robinson, Timothy J. Univ Wyoming Dept Math & Stat Laramie WY 82071 USA Indiana Univ Penn Math Dept Indiana PA USA

This paper considers the problem of identifying optimal Split-Plot Designs (SPDs) using traditional design criteria along with pure error degrees of freedom. An optimal SPD is of little use if it does not allow for suitable variance estimation of the whole plot and subplot variance components. The proposed approach incorporates a multi-criterion version of DP-optimality to represent the conflicting criteria involving the D-criterion and the replication at each design level. A set of Pareto optimal designs can then be obtained that consists of the optimal design with respect to each criterion and which cannot be dominated with respect to all the criteria. Key to this development is the notion of Orthogonal Subplot Designs (OSUBD) since this class of SPDs leads to a clear representation of DP-optimality. A number of common SPD design scenarios are provided to demonstrate the approach and to highlight the benefits of using the proposed multi-objective criterion.

关键词： D-criterion equivalent estimation design multiple objective optimization pure error replication

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A multiple objective integer programming approach for planning franchise expansion

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COMPUTERS & INDUSTRIAL ENGINEERING 1999年第3期37卷 543-561页

作者： Kolli, S Evans, GW Amer Airlines Eagle Finance Dept Dallas TX 76155 USA Univ Louisville Dept Ind Engn Louisville KY 40292 USA

The number and configuration of franchise outlets in a market de tines the distribution strategy of a franchise company. The introduction of new franchise outlets contributes to conflict between the franchisee and franchisor over the degree of market penetration. The selection of sites for new franchises is an important factor in the long-term profitability of many types of franchises, This selection process requires consideration of objectives of the franchisee and franchisor which are often conflicting in nature. This paper deals with the problem of locating new franchises in an existing franchise network using multiple objective integer programming models and methods, (C) 2000 Elsevier Science Ltd. All rights reserved.

关键词： facility location marketing integer programming multiple objective optimization

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