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Box-constrained multi-objective optimization: A gradient-like method without "a priori" scalarization

EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2008年第3期188卷 662-682页

作者： Miglierina, E. Molho, E. Recchioni, M. C. Univ Politech Marche Piazza Martelli Dipartimento Sci Sociali D Serrani I-60121 Ancona Italy Univ Insubria Dipartimento Econ I-21100 Varese Italy Univ Pavia Dipartimento Ric Aziendali I-27100 Pavia Italy

The aim of this paper is the development of an algorithm to find the critical points of a box-constrained multi-objective optimization problem. The proposed algorithm is an interior point method based on suitable directions that play the role of gradient-like directions for the vector objective function. The method does not rely on an "a priori" scalarization and is based on a dynamic system defined by a vector field of descent directions in the considered box. The key tool to define the mentioned vector field is the notion of vector pseudogradient. We prove that the limit points of the solutions of the system satisfy the Karush-Kuhn-Tucker (KKT) first order necessary condition for the box-constrained multi-objective optimization problem. These results allow us to develop an algorithm to solve box-constrained multi-objective optimization problems. Finally, we consider some test problems where we apply the proposed computational method. The numerical experience shows that the algorithm generates an approximation of the local optimal Pareto front representative of all parts of optimal front. (C) 2007 Elsevier B.V. All rights reserved.

关键词： multiple objective programming gradient-like method interior point method descent directions pseudogradient

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Primal worst and dual best in robust vector optimization

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2019年第3期275卷 830-838页

作者： Caprari, Elisa Baiardi, Lorenzo Cerboni Molho, Elena Univ Pavia Dept Econ & Management Pavia Italy

We establish a relationship between the robust counterpart of an uncertain cone-convex vector problem and the optimistic counterpart of its uncertain dual. Along the line marked by Beck and Ben-Tal (2009) in the scalar case, we show that operating in the primal problem with a pessimistic view is equivalent to operating with an optimistic approach in its dual. (C) 2019 Elsevier B.V. All rights reserved.

关键词： multiple objective programming Vector optimization problems Lagrangian duality Robust optimization

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Incorporating additional meta-objectives into the extended lexicographic goal programming framework

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2013年第2期227卷 343-349页

作者： Jones, Dylan Jimenez, Mariano Univ Portsmouth Dept Math Logist & Management Math Grp Portsmouth PO1 3HF Hants England Univ Basque Country UPV EHU Dept Appl Econ 1 Bilbao Spain

This paper introduces two new meta-objectives into the extended goal programming framework. The first meta-objective is the number of unmet goals and the second is a measure of closeness to the pairwise comparisons given by the decision maker. These complement the original two meta-objectives of the weighted sum of deviations and the maximal weighted deviation to provide a flexible four meta-objective framework. Lexicographic and non-lexicographic representations of the framework are developed. An example relating to transportation is solved in both the lexicographic and non-lexicographic forms. Weight sensitivity analysis is applied to the meta-weight parameters for the non-lexicographic case in order to find a range of available distinct solutions. (C) 2013 Elsevier B.V. All rights reserved.

关键词： Extended goal programming Pairwise comparisons multiple objective programming Weight sensitivity analysis

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Experiments with classification-based scalarizing functions in interactive multiobjective optimization

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2006年第2期175卷 931-947页

作者： Miettinen, Kaisa Makela, Marko M. Kaario, Katja Helsinki Sch Econ FI-00101 Helsinki Finland Univ Jyvaskyla Dept Math Informat Technol FI-40014 Jyvaskyla Finland

In multiobjective optimization methods, the multiple conflicting objectives are typically converted into a single objective optimization problem with the help of scalarizing functions and such functions may be constructed in many ways. We compare both theoretically and numerically the performance of three classification-based scalarizing functions and pay attention to how well they obey the classification information. In particular, we devote special interest to the differences the scalarizing functions have in the computational cost of guaranteeing Pareto optimality. It turns out that scalarizing functions with or without so-called augmentation terms have significant differences in this respect. We also collect a set of mostly nonlinear benchmark test problems that we use in the numerical comparisons. (c) 2005 Elsevier B.V. All rights reserved.

关键词： multiple objective programming classification interactive methods test problems guaranteeing pareto optimality

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Multiobjective multiproduct parcel distribution timetabling: a real-world application

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INTERNATIONAL TRANSACTIONS IN OPERATIONAL RESEARCH 2012年第4期19卷 613-629页

作者： Ben-Ayed, Omar Hamzaoui, Salem Optimal Solut Ctr Management Sci Wichita KS USA Univ Kairouan Inst Comp Sci & Business Kairouan Tunisia Univ Sfax Coll Econ & Business Sfax Tunisia

Multiobjective multiproduct parcel distribution timetabling problem is concerned with generating effective timetables for parcel distribution companies that provide interdependent services (products) and have more than one objective. A parcel distribution timetabling problem is inherently multiobjective because of the multitude of criteria that can measure the performance of a timetable. This paper provides the mathematical formulation of the problem and applies the model to a real-world case study. The application shows that without a common ground with the practitioners, it would be impossible to define the actual requirements and objectives of the company;problem definition is as important as model construction and solution method.

关键词： scheduling multiple objective programming integer programming transportation distribution shipping industry postal services practice of OR

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A multi-objective approach to supply chain visibility and risk

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2014年第1期233卷 125-130页

作者： Yu, Min-Chun Goh, Mark Natl Kaohsiung Univ Appl Sci Dept Business Adm Kaohsiung 807 Taiwan Univ S Australia Sch Management Adelaide SA 5001 Australia

This paper investigates the twin effects of supply chain visibility (SCV) and supply chain risk (SCR) on supply chain performance. Operationally, SCV has been linked to the capability of sharing timely and accurate information on exogenous demand, quantity and location of inventory, transport related cost, and other logistics activities throughout an entire supply chain. Similarly, SCR can be viewed as the likelihood that an adverse event has occurred during a certain epoch within a supply chain and the associated consequences of that event which affects supply chain performance. Given the multi-faceted attributes of the decision making process which involves many stages, objectives, and stakeholders, it beckons research into this aspect of the supply chain to utilize a fuzzy multi-objective decision making approach to model SCV and SCR from an operational perspective. Hence, our model incorporates the objectives of SCV maximization, SCR minimization, and cost minimization under the constraints of budget, customer demand, production capacity, and supply availability. A numerical example is used to demonstrate the applicability of the model. Our results suggest that decision makers tend to mitigate SCR first then enhance SCV. (C) 2013 Elsevier B.V. All rights reserved.

关键词： Supply chain management multiple objective programming Supply chain visibility Supply chain risk

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An approach for solving nonlinear multi-objective separable discrete optimization problem with one constraint

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2005年第2期162卷 503-513页

作者： Isada, Y James, RJW Nakagawa, Y Tezukayama Gakuin Univ Fac Business Adm Nara 6318501 Japan

We propose an exact solution approach for solving nonlinear multi-objective optimization problems with separable discrete variables and a single constraint. The approach converts the multi-objective problem into a single objective problem by using surrogate multipliers from which we find all the solutions with objective values within a given range. We call this the surrogate target problem which is solved by using an algorithm based on the modular approach. Computational experiments demonstrate the effectiveness of this approach in solving large-scale problems. A simple example is presented to illustrate an interactive decision making process. (C) 2003 Elsevier B.V. All rights reserved.

关键词： multiple objective programming decision support systems target problem nonlinear discrete

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Satisfactory solution concepts and their relations for Stochastic Multiobjective programming problems

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2012年第2期220卷 430-442页

作者： Munoz, Maria M. Ben Abdelaziz, Fouad Univ Malaga Dept Appl Econ Math E-29071 Malaga Spain Amer Univ Sharjah Grad Program Coll Engn Sharjah U Arab Emirates

This work deals with the concept of satisfactory solution for Stochastic Multiobjective programming (SMP) problems. Based on previous literature, we will introduce different concepts of satisfactory solutions for SMP problems, define a new concept of solution (where the decision maker (DM) sets his/her preferences in terms of two aspiration levels for the stochastic objective and two probabilities to reach those levels), and establish some relationship between these concepts. The results will aim at featuring these concepts and determine the differences between them. Moreover, the paper proposes a new step by step procedure to exchange information between the analyst and DM prior to solving the problem. Thus, the DM will be able to choose the transformation criterion for each stochastic objective and the aspiration level. (C) 2012 Elsevier B.V. All rights reserved.

关键词： Stochastic programming multiple objective programming Goal programming Decision-maker's preferences Satisfactory solution Probabilistic goal

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A method for finding the set of non-dominated vectors for multiple objective integer linear programs

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2004年第1期158卷 46-55页

作者： Sylva, J Crema, A Cent Univ Venezuela Escuela Computac Fac Ciencias Caracas 1041 A Venezuela

An algorithm for enumerating all non-dominated vectors of multiple objective integer linear programs is presented. Using a straightforward theoretical approach, the problem is solved using a sequence of progressively more constrained integer linear programs generating a new solution at each step. The algorithm can also give subsets of efficient solutions that can be useful for designing interactive procedures for large, real-life problems. (C) 2003 Elsevier B.V. All rights reserved.

关键词： integer programming multiple objective programming parametric programming

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Weighted sum model with partial preference information: Application to multi-objective optimization

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2017年第2期260卷 665-679页

作者： Kaddani, Sami Vanderpooten, Daniel Vanpeperstraete, Jean-Michel Aissi, Hassene Univ Paris 09 PSL Res Univ CNRS UMR 7243LAMSADE F-75016 Paris France DCNS Res 280 Ave Aristide Briand F-92220 Bagneux France

Multi-objective optimization problems often lead to large nondominated sets, as the size of the problem or the number of objectives increases. Generating the whole nondominated set requires significant computation time, while most of the corresponding solutions are irrelevant to the decision maker (DM). Optimizing an aggregation function reduces the computation time and produces one or a very limited number of more focused solutions. This requires, however, the elicitation of precise preference parameters, which is often difficult and partly arbitrary, and might discard solutions of interest. An intermediate approach consists in using partial preference information with an aggregation function. In this work, we present a preference relation based on the weighted sum aggregation, where weights are not precisely defined. We give some properties of this preference relation and define the set of preferred points as the set of nondominated points with respect to this relation. We provide an efficient and generic way of generating this preferred set using any standard multi-objective optimization algorithm. This approach shows competitive performances both on computation time and quality of the generated preferred set. (C) 2017 Elsevier B.V. All rights reserved.

关键词： multiple objective programming Weighted sum Partial preference information

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