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A normal boundary intersection approach to multiresponse robust optimization of the surface roughness in end milling process with combined arrays

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PRECISION ENGINEERING-JOURNAL OF THE INTERNATIONAL SOCIETIES FOR PRECISION ENGINEERING AND NANOTECHNOLOGY 2014年第3期38卷 628-638页

作者： Brito, T. G. Paiva, A. P. Ferreira, J. R. Gomes, J. H. F. Balestrassi, P. P. Univ Fed Itajuba Inst Ind Engn BR-37500903 Itajuba MG Brazil

Robust parameter design (RPD) has recently been applied in modern industries in a large deal of processes. This technique is occasionally employed as a multiobjective optimization approach using weighted sums as a trade-off strategy;in such cases, however, a considerable number of gaps have arisen. In this paper, the use of normal boundary intersection (NBI) method coupled with mean-squared error (MSE) functions is proposed. This approach is capable of generating equispaced Pareto frontiers for a bi-objective robust design model, independent of the relative scales of the objective functions. To verify the adequacy of this proposal, a central composite design (CCD) is developed with combined arrays for the AISI 1045 steel end milling process. In this case study, a CCD with three noise factors and four control factors are used to create the mean and variance equations for MSE of two quality characteristics. The numerical results indicate the NBI-MSE approach is capable of generating a convex and equispaced Pareto frontier to MSE functions of surface roughness, thus nullifying the drawbacks of weighted sums. Moreover, the results show that the achieved optimum lessens the sensitivity of the end milling process to the variability transmitted by the noise factors. (C) 2014 Elsevier Inc. All rights reserved.

关键词： multiple objective programming Robust parameter design (RPD) Normal boundary intersection (NBI) End milling process Surface roughness

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Solving discrete multi-objective optimization problems using modified augmented weighted Tchebychev scalarizations

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2018年第2期271卷 436-449页

作者： Holzmann, Tim Smith, J. C. Clemson Univ Dept Ind Engn 100B Freeman Hall Clemson SC 29634 USA

In this paper we present the modified augmented weighted Tchebychev norm, which can be used to generate a complete efficient set of solutions to a discrete multi-objective optimization problem. We contribute a generating algorithm that will, without supervision, generate the entire non-dominated set for any number of objectives. To our knowledge, this is the first generating method for general discrete multi objective problems that uses a variant of the Tchebychev norm. In a computational study, our algorithm's running times are comparable to previously proposed algorithms. (C) 2018 Elsevier B.V. All rights reserved.

关键词： multiple objective programming Tchebychev norm Computational optimization Generating methods

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Finding a representative nondominated set for multi-objective mixed integer programs

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2019年第1期272卷 61-77页

作者： Ceyhan, Gokhan Koksalan, Murat Lokman, Banu Middle East Tech Univ Dept Ind Engn TR-06800 Ankara Turkey

In this paper, we develop algorithms to find small representative sets of nondominated points that are well spread over the nondominated frontiers for multi-objective mixed integer programs. We evaluate the quality of representations of the sets by a Tchebycheff distance-based coverage gap measure. The first algorithm aims to substantially improve the computational efficiency of an existing algorithm that is designed to continue generating new points until the decision maker (DM) finds the generated set satisfactory. The algorithm improves the coverage gap value in each iteration by including the worst represented point into the set. The second algorithm, on the other hand, guarantees to achieve a desired coverage gap value imposed by the DM at the outset. In generating a new point, the algorithm constructs territories around the previously generated points that are inadmissible for the new point based on the desired coverage gap value. The third algorithm brings a holistic approach considering the solution space and the number of representative points that will be generated together. The algorithm first approximates the nondominated set by a hypersurface and uses it to plan the locations of the representative points. We conduct computational experiments on randomly generated instances of multi-objective knapsack, assignment, and mixed integer knapsack problems and show that the algorithms work well. (C) 2018 Elsevier B.V. All rights reserved.

关键词： multiple objective programming Mixed integer programming Nondominated point Representative subset

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Weak efficiency for multiobjective variational problems

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2004年第2期155卷 373-379页

作者： Arana-Jiménez, M Rufián-Lizana, A Osuna-Gómez, R IES Andres Benitez Cadiz 11407 Spain Univ Sevilla Dept Estadist & Invest Operat E-41012 Seville Spain

Sometimes, to locate efficient solutions for multiobjective variational problems (MVPs) is quite costly, so in this paper we tackle the study of weakly efficient solutions for MVPs. A new concept of weak vector critical point which generalizes other ones already existent, and a new class of pseudoinvex functions are introduced. We will apply a new approach to prove that the new class of pseudoinvex functions is equivalent to the class of functions whose weak vector critical points are weakly efficient solution for MVPs. (C) 2003 Published by Elsevier B.V.

关键词： nonlinear programming multiple objective programming variational problems pseudoinvexity weakly efficient solutions

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PROMISE/scenarios: An interactive method for multiobjective stochastic linear programming under partial uncertainty

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2004年第2期155卷 361-372页

作者： Urli, B Nadeau, R Univ Quebec Dept Econ & Gest Rimouski PQ G5L 3A1 Canada Univ Laval St Foy PQ G1K 7P4 Canada

In many real contexts where the multiobjective stochastic linear programming can be used as a modelling approach, the decision maker is in general placed in a situation of incomplete information concerning the uncertain parameters of the problem. A good way to express that incomplete information consists in resorting to the idea of scenarios relatively to the objectives and constraints of the stochastic program. While the authors who have suggested methods based on scenarios suppose that the probabilities of those scenarios are known, in this paper we propose a scenarios approach where the probabilities of scenarios is only incompletely specified according to a ranking. That interactive method, called PROMISE/scenarios, is presented and is illustrated by a didactic example. (C) 2003 Elsevier Ltd. All rights reserved.

关键词： multiple objective programming stochastic programming scenarios interactive method partial uncertainty

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Biobjective route planning of an unmanned air vehicle in continuous space

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TRANSPORTATION RESEARCH PART B-METHODOLOGICAL 2023年第1期168卷 151-169页

作者： Ozturk, Diclehan Tezcaner Koksalan, Murat Hacettepe Univ Dept Ind Engn TR-06800 Ankara Turkiye Univ Michigan Ross Sch Business Ann Arbor MI 48104 USA Middle East Tech Univ Dept Ind Engn TR-06800 Ankara Turkiye

We consider the route planning problem of an unmanned air vehicle (UAV) in a continuous space that is monitored by radars. The UAV visits multiple targets and returns to the base. The routes are constructed considering the total distance traveled and the total radar detection threat ob-jectives. The UAV is capable of moving to any point in the terrain. This leads to infinitely many efficient trajectories between target pairs and infinitely many efficient routes to visit all targets. We use a two stage approach in solving the complex problem of finding all efficient routes. In the first stage, we structure the nondominated frontiers of the efficient trajectories between all target pairs. For this, we first identify properties shared by efficient trajectories between target pairs that are protected by a radar. This helps to structure the nondominated frontier between any target pair by identifying at most four specific efficient trajectories. We develop a search-based algo-rithm that finds these efficient trajectories effectively. For the second stage, we develop a mixed integer nonlinear program that exploits the structured nondominated frontiers between target pairs to construct the efficient routes. We compare the nondominated front we generate in the continuous space with its counterpart in a terrain discretized with three different grid fidelities. The continuous space representation outperforms all discrete representations in terms of solution quality and computational times.

关键词： multiple objective programming UAV routing Continuous space

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Pareto solutions in multicriteria optimization under uncertainty

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2020年第2期281卷 357-368页

作者： Engau, Alexander Sigler, Devon Univ Lancaster Management Sch Lancaster LA1 4YX England Dalhousie Univ Rowe Sch Business Kenneth C Rowe Management Bldg6100 Univ Ave Halifax NS B3H 4R2 Canada Univ Colorado Dept Math & Stat Sci Campus Box 170POB 173364 Denver CO 80217 USA Natl Renewable Energy Lab 15013 Denver West Pkwy Golden CO 80401 USA

We present and analyze several definitions of Pareto optimality for multicriteria optimization or decision problems with uncertainty primarily in their objective function values. In comparison to related notions of Pareto robustness, we first provide a full characterization of an alternative efficient set hierarchy that is based on six different ordering relations both with respect to the multiple objectives and a possibly finite, countably infinite or uncountable number of scenarios. We then establish several scalarization results for the generation of the corresponding efficient points using generalized weighted-sum and epsilon-constraint techniques. Finally, we leverage these scalarization results to also derive more general conditions for the existence of efficient points in each of the corresponding optimality classes, under suitable assumptions. (C) 2019 Elsevier B.V. All rights reserved.

关键词： multiple objective programming Pareto solutions Optimization under uncertainty Efficient set hierarchy Scalarization methods

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Integration of electromagnetism with multi-objective evolutionary algorithms for RCPSP

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2016年第1期251卷 22-35页

作者： Xiao, Jing Wu, Zhou Hong, Xi-Xi Tang, Jian-Chao Tang, Yong S China Normal Univ Sch Comp Sci Guangzhou 510631 Guangdong Peoples R China

As one of the most challenging combinatorial optimization problems in scheduling, the resource-constrained project scheduling problem (RCPSP) has attracted numerous scholars' interest resulting in considerable research in the past few decades. However, most of these papers focused on the single objective RCPSP;only a few papers concentrated on the multi-objective resource-constrained project scheduling problems (MORCPSP). Inspired by a procedure called electromagnetism (EM), which can help a generic population based evolutionary search algorithm to obtain good results for single objective RCPSP, in this paper we attempt to extend EM and integrate it into three reputable state-of-the-art multi-objective evolutionary algorithms (MOEAs) i.e. non-dominated sorting based multi-objective evolutionary algorithm (NSGA-II), strength Pareto evolutionary algorithm (SPEA2) and multi-objective evolutionary algorithm based on decomposition (MOEA/D), for MORCPSP. We aim to optimize makespan and total tardiness. Empirical analysis based on standard benchmark datasets are conducted by comparing the versions of integrating EM to NSGA-II, SPEA2 and MOEND with the original algorithms without EM. The results demonstrate that EM can improve the performance of NSGA-II and SPEA2, especially for NSGA-II. (C) 2015 Elsevier B.V. All rights reserved.

关键词： multiple objective programming Heuristics Resource-constrained project scheduling Electromagnetism Evolutionary algorithms

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A fuzzy hybrid integrated framework for portfolio optimization in private banking

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EXPERT SYSTEMS WITH APPLICATIONS 2018年 92卷 350-362页

作者： Ferreira, Luciano Borenstein, Denis Righi, Marcelo Brutti de Almeida Filho, Adiel Teixeira Univ Fed Rio Grande do Sul Management Sch Porto Alegre RS Brazil Univ Fed Pernambuco CDSID Recife PE Brazil

Decision-making processes in private banking must comply with standards for risk management and transparency enforced by banking regulations. Therefore, investors must be supported throughout a risk informed decision process. This paper contributes to the literature by presenting a hybrid integrated framework that considers personal features of the investor and additional characteristics imposed by regulations, for which linguistic evaluations are used with regard to risk exposure. The proposed approach for personal investment portfolios considers legal aspects and investor's preferences as an input to the novel fuzzy multiple-attribute decision making approach for sorting problems proposed in this paper, called FTOPSIS-Class. Then, the next step of the proposed framework uses the sorting results for a fuzzy multi-objective optimization model that considers the risk and return associated with the investor's profile over three objectives. The contributions of this paper are illustrated and validated by using a numerical application in line with a new trend for modern portfolio theory which enables a real world investor's characteristics to be considered throughout the decision-making process. (C) 2017 Elsevier Ltd. All rights reserved.

关键词： OR in banking Investment analysis Fuzzy sets multiple attribute decision making multiple objective programming

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Redistribution of funds for teaching and research among universities: The case of North Rhine-Westphalia

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2001年第1期130卷 111-120页

作者： Fandel, G Gal, T Fern Univ Hagen Dept Econ D-58084 Hagen Germany

This paper reports on a real application of a performance and success based system for redistribution of funds for teaching and research among universities in North Rhine-Westphalia, After a precise description of the decision situation, we show how goal programming and distance minimization were applied in order to find a solution on the basis of real data. Some comments on the results and the quality of the redistribution process conclude the paper. (C) 2001 Elsevier Science B.V. All rights reserved.

关键词： group decisions and negotiations multiple criteria analysis multiple objective programming resource allocation

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