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An Ant Colony Optimization algorithm to solve a 2-machine bicriteria flowshop scheduling problem

EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2002年第2期142卷 250-257页

作者： T'kindt, V Monmarché, N Tercinet, F Laügt, D Ecole Ingenieurs Informat Ind Lab Informat F-37200 Tours France

Consider the 2-machine flowshop scheduling problem with the objective of minimizing both the total completion time and the makespan criteria. The latter is assumed to be optimized prior to the former. In view of the N P-hardness of the problem an Ant Colony Optimization approach is proposed to solve it. The heuristic also uses feature of Simulated Annealing search and local search algorithms. Computational experiments show its effectiveness compared to existing heuristics. The extension to the total completion time problem is also studied. (C) 2002 Published by Elsevier Science B.V.

关键词： scheduling multiple objective programming Ant Colony Optimization

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On the Lexicographic Centre of multiple objective Optimization

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JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 2016年第2期168卷 600-614页

作者： Zhang Jiangao Yang, Shitao Chongqing Univ Fac Construct Management & Real Estate Chongqing 400045 Peoples R China Sichuan Univ State Key Lab Hydraul & Mt River Engn Chengdu 610064 Peoples R China Florida Inst Technol Nathan M Bisk Coll Business 150 W Univ Blvd Melbourne FL 32901 USA

We study the lexicographic centre of multiple objective optimization. Analysing the lexicographic-order properties yields the result that, if the multiple objective programming's lexicographic centre is not empty, then it is a subset of all efficient solutions. It exists if the image set of multiple objective programming is bounded below and closed. The multiple objective linear programming's lexicographic centre is nonempty if and only if there exists an efficient solution to the multiple objective linear programming. We propose a polynomial-time algorithm to determine whether there is an efficient solution to multiple objective linear programming, and we solve the multiple objective linear programming's lexicographic centre by calculating at most the same number of dual linear programs as the number of objective functions and a system of linear inequalities.

关键词： multiple objective programming Lexicographic order Lexicographic centre Efficient solution Image set theta-image set

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The maximal descriptor index set for a face of a convex polyhedral set and some applications

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JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS 2015年第1期429卷 395-414页

作者： Ta Van Tu Corvinus Univ Budapest Dept Operat Res H-1093 Budapest Hungary

A face of a convex polyhedral set can be investigated on the basis of only the maximal descriptor index set for it. This helps us reduce difficulties and computational efforts in solving many problems. In this paper, we consider a multiple objective linear programming (MOLP) problem in which the constraint polyhedron may have no extreme points and the variables may be negative. First we deal with determining the maximal descriptor index set for an arbitrary face of the constraint polyhedron, then we apply the maximal descriptor index sets for faces to compare descriptor sets for the faces and find all maximal efficient faces for the MOLP problem. The methods known so far compare descriptor sets at large computational cost (in terms of computing times and storage) because they require finding all extreme points and directions of them. Known top-down search methods have been devised to find the efficient set of the MOLP problem but they may fail to find all maximal efficient faces and the computational cost is considerable. We propose a new method to compare descriptor sets and a new top-down search method which finds all maximal efficient faces and requires less computational cost. A numerical example is given to illustrate how the method works. (C) 2015 Elsevier Inc. All rights reserved.

关键词： multiple objective programming Faces of a polyhedron Maximal efficient faces The maximal descriptor index set for a face

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Optimality, scalarization and duality in linear vector semi-infinite programming

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OPTIMIZATION 2018年第5期67卷 523-536页

作者： Kanzi, Nader Ardekani, Javad Shaker Caristi, Giuseppe Payam Noor Univ Dept Math Tehran Iran TVU Dept Basic Sci Fac Shahid Sadughi Tehran Iran Univ Messina Dept Econ Messina Italy

In this paper, we introduce some qualification conditions for a linear vector semi-infinite programming problem. The new qualification conditions are used for development of necessary conditions for weak efficient, isolated efficient and epsilon-efficient solutions of such a problem. Sufficient conditions for the existence of such solutions are also provided. In addition, a new general scalarization technique for solving the reference problem is presented. Finally, we propose a type of Wolf dual problem and examine weak\strong duality relations.

关键词： multiple objective programming linear programming semi-infinite optimization optimality condition constraint qualification

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Bi-objective reliability based optimization: an application to investment analysis

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ANNALS OF OPERATIONS RESEARCH 2024年第1期333卷 47-78页

作者： Sengupta, Raghu Nandan Gupta, Aditya Mukherjee, Subhankar Weiss, Gregor McKinsey & Co Inc Chennai Tamil Nadu India Indian Inst Technol Kanpur Dept Management Studies DoMS Kanpur Uttar Pradesh India Univ Leipzig Fac Econ & Management Leipzig Germany

Portfolio optimization problems are easy to address if single linear objective functions are considered, with the assumption of normality of asset returns distributions, subject to different risks, returns, and investment constraints. Higher complexities arise if combinations of multi-objective formulations, non-linear assets, non-normal asset return distributions, and uncertainty in parameter estimates are studied. In this paper, we solve two interesting variants of multi-objective investment analysis problems considering both non-normal asset return distributions and uncertainty in parameter estimates. Data used for the optimization models are pre-processed using ARCH/GARCH combined with extreme value asset returns distribution (EVD). The efficacy of our proposed multi-objective reliability-based portfolio optimization (MORBPO) problems is validated using Indian financial market data (Details of plan of codes, pseudo-codes and other set of detailed runs results (not discussed in this paper) are given in the open access link, https://***/RNSengupta/Bi-objective_RBDO_Paper). We present the optimal values of investment weights, portfolio returns, portfolio risks (variance, CVaR, EVaR), reliability indices (beta\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\beta$$\end{document}) as well as Pareto optimal frontiers and analyze the outputs in the context of their practical implications. The run results highlight the fact that investors' uncertainty levels (i.e., beta\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\beta$$\end{document}) play a crucial role in deciding the investment outcomes and thus faci

关键词： Investment analysis multiple objective programming Portfolio optimization Risk analysis

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A Mathematical programming Approach to Optimum Airspace Sectorisation Problem

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JOURNAL OF NAVIGATION 2020年第3期73卷 599-612页

作者： Oktal, Hakan Yaman, Kadriye Kasimbeyli, Refail Eskisehir Tech Univ Fac Aeronaut & Astronaut Eskisehir Turkey Eskisehir Tech Univ Fac Engn Eskisehir Turkey

The aim of this study is to provide a balanced distribution of air traffic controller workload (ATCW) across airspace sectors taking into account the complexity of airspace sectors and the factors affecting ATCW, both objective and perceived. Almost all the studies focusing on the airspace sectorisation problem use heuristic or metaheuristic algorithms in dynamic simulation environments instead of a mathematical modelling approach. The paper proposes a multi-objective mixed integer mathematical model for airspace sectorisation. The model is applied to the upper, en-route level of Turkish airspace. Geographical information systems (GIS) are used to advantage for airspace analysis. The multi-objective model developed in this paper is scalarised by using the conic scalarisation method. For solving the scalarised problem, the CPLEX and DICOPT solvers of GAMS software are implemented. Finally, the optimal sector boundaries of Turkish airspace are defined.

关键词： Air Transportation Airspace Sectorisation Air Traffic Controller Workload multiple objective programming Conic Scalarisation

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Generating properly efficient points in multi-objective programs by the nonlinear weighted sum scalarization method

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OPTIMIZATION 2014年第3期63卷 473-486页

作者： Zarepisheh, M. Khorram, E. Pardalos, Panos M. Amirkabir Univ Technol Fac Math & Comp Sci Tehran 15914 Iran Univ Florida Dept Ind & Syst Engn Ctr Appl Optimizat Gainesville FL 32611 USA Natl Res Univ Higher Sch Econ Lab Algorithms & Technol Networks Anal Moscow 101000 Russia

This article deals with the scalarization techniques in multi-objective optimization problems (MOPs). In this article, the nonlinear version of the weighted sum method is considered as the scalarization problem, and the relation of the set of properly efficient points and the set of scalarization solutions (optimal solutions of the scalarized problem) is studied. In particular, conditions are determined under which the optimal solutions of the scalarized problem are properly efficient points of the MOP, and the conditions under which the properly efficient points could be characterized in terms of the scalarization solutions are presented.

关键词： multiple objective programming scalarization techniques compromise programming properly efficient weighted p-power 90B50 90C29 90C30

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A multiobjective interval programming model to explore the trade-offs among different aspects of job satisfaction under different scenarios

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SOCIO-ECONOMIC PLANNING SCIENCES 2019年 66卷 35-46页

作者： Henriques, C. O. Luque, M. Marcenaro-Gutierrez, O. D. Lopez-Agudo, L. A. Polytech Inst Coimbra ISCAC Business Sch P-3040316 Coimbra Portugal Univ Coimbra Polo II INESC Coimbra R Silvio Lima P-3030290 Coimbra Portugal Univ Malaga Dept Appl Econ Math C Ejido 6 E-29071 Malaga Spain Univ Malaga Dept Appl Econ Stat & Econometr C Ejido 6 E-29071 Malaga Spain Univ Malaga Econ & Business Malaga Spain

The need for greater concern about job quality/satisfaction seems clear, due to its potential link with workers' productivity, to the extent it affects employees' quitting behaviour, absenteeism, turnover, and firms' productivity. In order to guide managers and policy makers when making decisions related to future hiring of human resources, a multiobjective interval programming model, based on the results of an econometric estimation, is suggested where different (and conflicting) aspects of job satisfaction are considered. The modelling framework thus obtained allows assessing the trade-offs among the different aspects of job satisfaction under different scenarios herein given within interval ranges. Data obtained from Spain are used to carry out the model's instantiation. Possibly efficient solutions are then generated with the help of scalarizing problems relying on reference point-based methods. The solution approach herein proposed allows computing with a lower computational effort the closest "possibly" efficient solutions attainable regarding their corresponding interval ideal solutions. Overall, the results obtained highlight the trade-off between earnings and quality of life, particularly under a pessimistic scenario, with the maximization of earnings leading to the lowest value of the working times. Conversely, the lowest value obtainable for earnings is reached with the consideration of both scenarios when the maximization of the satisfaction of the quality of life seekers is attained. Finally, the trade-off between less prone to risk workers and quality of life seekers is also revealed, with the lowest job security levels found in the solution that maximizes working times.

关键词： multiple objective programming Workers' satisfaction Econometric analysis Interval programming

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An exact approach for the Minimum-Cost Bounded-Error Calibration Tree problem

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ANNALS OF OPERATIONS RESEARCH 2020年第1期287卷 109-126页

作者： Carvalho, Iago A. Ribeiro, Marco A. Univ Fed Minas Gerais Dept Comp Sci Av Antonio Carlos 6627 BR-31270010 Belo Horizonte MG Brazil

The Minimum-Cost Bounded-Error Calibration Tree problem (MBCT) is a wireless network optimization problem that arises from the sensors' need of periodical calibration. The MBCT takes into account two objectives. The first is to minimize the communication distance between the network sensors, while the second is to reduce the maximum post-calibration error in the network. In this paper, we propose a mathematical formulation for the MBCT. Furthermore, we solve the problem using two different implementations of an Augmented epsilon that incorporate the proposed formulation. We also employed the Pareto-fronts obtained by aug epsilon-CM to evaluate the Node-depth Phylogenetic-based Non-dominated Sorting Artificial Immune System (NPE-NSAIS), the most recent heuristic in the literature for MBCT. Computational experiments showed that aug epsilon-CM can solve MBCT instances up to 50 nodes. Furthermore, a statistical test demonstrated that the running times of one of the aug epsilon-CM implementations was significantly smaller than those of the other. Finally, we show that NPE-NSAIS solutions are very close to the Pareto-fronts given by aug epsilon-CM, achieving good results on the evaluated metrics.

关键词： multiple objective programming Augmented epsilon-constraints Wireless sensors network Calibration error Spanning arborescence

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Recommendation of investment portfolio for peer-to-peer lending with additional consideration of bidding period

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ANNALS OF OPERATIONS RESEARCH 2022年第2期315卷 1083-1105页

作者： Park, Ki Taek Yang, Hyejeong Sohn, So Young Yonsei Univ Seoul South Korea

Peer-to-peer (P2P) lending has emerged as an alternative method of financing. Keeping pace with this development, many P2P lending studies have provided approaches to select investment portfolios for individual lenders. However, none of these approaches consider how long it takes for an individual loan to be fully funded so as to reduce the opportunity cost incurred due to delayed investment. In this paper, we propose a goal programming framework to develop an optimal P2P lending portfolio that considers not only the expected returns but also this opportunity cost for individual investors. First, for each loan proposal, a logistic regression model is used to predict the loan default probability while a Weibull regression is used to determine the opportunity cost incurred due to the time taken to obtain the loan. Next, goal programming is applied to construct a portfolio that minimizes the slack from the desired return on investment as well as the surplus from the preset opportunity cost due to a prolonged bidding period. The proposed approach is then applied to Prosper platform data and is expected to help investors' portfolio decisions in the P2P lending market.

关键词： Analytics in banking Goal programming multiple objective programming

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