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A multi-objective Monte Carlo tree search for forest harvest scheduling

EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2020年第3期282卷 1115-1126页

作者： Neto, Teresa Constantino, Miguel Martins, Isabel Pedroso, Joao Pedro Inst Politecn Viseu Escola Super Tecnol & Gestao P-3504510 Viseu Portugal Univ Lisbon Fac Ciencias Ctr Matemat Aplicacoes Fundamentals & Invest Oper P-1749016 Lisbon Portugal Univ Lisboa Tapada Ajuda Inst Super Agron Ctr Matemat Aplicacoes Fundamentals & Invest Oper P-1349017 Lisbon Portugal Univ Porto INESC TEC Fac Ciencias Rua Campo Alegre P-4169007 Porto Portugal

While the objectives of forest management vary widely and include the protection of resources in protected forests and nature reserves, the primary objective has often been the production of wood products. However, even in this case, forests play a key role in the conservation of living resources. Constraining the areas of clearcuts contributes to this conservation, but if it is too restrictive, a dispersion of small clearcuts across the forest might occur, and forest fragmentation might be a serious ecological problem. Forest fragmentation leads to habitat loss, not only because the forest area is reduced, but also because the core area of the habitats and the connectivity between them decreases. This study presents a Monte Carlo tree search method to solve a bi-objective harvest scheduling problem with constraints on the clearcut area, total habitat area and total core area inside habitats. The two objectives are the maximization of both the net present value and the probability of connectivity index. The method is presented as an approach to assist the decision maker in estimating efficient alternative solutions and the corresponding trade-offs. This approach was tested with instances for forests ranging from some dozens to over a thousand stands and temporal horizons from three to eight periods. In general, multi-objective Monte Carlo tree search was able to find several efficient alternative solutions in a reasonable time, even for medium and large instances. (C) 2019 Elsevier B.V. All rights reserved.

关键词： multiple objective programming Forest planning Core area Connectivity Tree search

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Dynamic formulation for humanitarian response operations incorporating multiple organisations

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INTERNATIONAL JOURNAL OF PRODUCTION ECONOMICS 2018年 204卷 83-98页

作者： Rodriguez-Espindola, Oscar Albores, Pavel Brewster, Christopher Aston Univ Aston Business Sch Birmingham W Midlands England TNO Data Sci Grp The Hague Netherlands

Disasters represent a significant challenge for countries globally. Balancing human and material resources during these situations is not a trivial issue, and that is further complicated by the participation of several actors at multiple periods. However, there is an absence of articles considering the importance of deploying only the required organisations for response activities depending on the conditions and the stage of the disaster. This research proposes a dynamic model to support disaster response which incorporates human and material resources from multiple organisations. The multi-modal, multi-commodity optimisation model supports resource allocation and relief distribution decisions through the maximisation of the level of service provided to disaster victims and the minimisation of cost. The model is the first dynamic formulation in the literature with the ability to optimise the number, type and stage of deployment of organisations required according to the circumstances of the emergency. The model has been applied to two major floods that have occurred in Mexico in recent years. Each case was tested using three different scenarios to investigate the ability of the model to handle different conditions. The results of both cases were compared to scenarios with independent participation from each organisation and an instance capturing the real decisions made by Mexican authorities. The results showed the inefficiency stemming from independent decision-making, an excess of actors involved in the real instances of both cases, the applicability of the model to different circumstances, and the value of the ability to modify the number of organisations involved per stage.

关键词： Emergency logistics multiple objective programming Disaster response Resource allocation

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A multiplicative version of Promethee II applied to multiobjective optimization problems

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2007年第2期183卷 729-740页

作者： Parreiras, R. O. Vasconcelos, J. A. Univ Fed Minas Gerais Dept Elect Engn BR-31270010 Belo Horizonte MG Brazil

The method Promethee II has produced attractive results in the choice of the most satisfactory optimal solution of convex multiobjective problems. However, according to the current literature, it may not work properly with nonconvex problems. A modified version of this method, called multiplicative Promethee, is proposed in this paper. Both versions are applied to some analytical problems, previously optimized by an evolutionary algorithm. The multiplicative Promethee got much better results than the original Promethee II, being capable of solving convex and nonconvex problems, with continuous and discontinuous Pareto fronts. (c) 2006 Elsevier B.V. All rights reserved.

关键词： multiple criteria analysis multiple objective programming decision analysis

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A novel elitist multiobjective optimization algorithm: Multiobjective extremal optimization

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2008年第3期188卷 637-651页

作者： Chen, Min-Rong Lu, Yong-Zal Shanghai Jiao Tong Univ Dept Automat Shanghai 200240 Peoples R China

Recently, a general-purpose local-search heuristic method called extremal optimization (EO) has been successfully applied to some NP-hard combinatorial optimization problems. This paper presents an investigation on EO with its application in numerical multiobjective optimization and proposes a new novel elitist (1 + lambda) multiobjective algorithm, called multiobjective extremal optimization (MOEO). In order to extend EO to solve the multiobjective optimization problems, the Pareto dominance strategy is introduced to the fitness assignment of the proposed approach. We also present a new hybrid mutation operator that enhances the exploratory capabilities of our algorithm. The proposed approach is validated using five popular benchmark functions. The simulation results indicate that the proposed approach is highly competitive with the state-of-the-art multiobjective evolutionary algorithms. Thus MOEO can be considered a good alternative to solve numerical multiobjective optimization problems. (C) 2007 Elsevier B.V. All rights reserved.

关键词： multiple objective programming metaheuristics extremal optimization self-organized criticality

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Tradeoff directions in multiobjective optimization problems

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MATHEMATICAL programming 1997年第3期78卷 357-374页

作者： Henig, MI Buchanan, JT UNIV WAIKATO DEPT MANAGEMENT SYSTHAMILTONNEW ZEALAND TEL AVIV UNIV FAC MANAGEMENTIL-69978 TEL AVIVISRAEL

Multiobjective optimization problems (MOP) typically have conflicting objectives wherein a gain in one objective is at the expense of another. Tradeoff directions, which measure the change in some objectives relative to changes in others, provide important information as to the best direction of improvement from the current solution. In this paper we present a general definition of tradeoffs as a cone of directions and provide a general method of calculating tradeoffs al every Pareto optimal point of a convex MOP. This extends current definitions of tradeoffs which assume certain conditions on the feasible set and the objective functions. Two comprehensive numerical examples are provided to illustrate the tradeoff directions and the methods used to calculate them. (C) 1997 The Mathematical programming Society, Inc. published by Elsevier Science B.V.

关键词： multiple objective programming tradeoff directions Pareto optimal

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Synchronous approach in interactive multiobjective optimization

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2006年第3期170卷 909-922页

作者： Miettinen, K Mäkelä, MM Helsinki Sch Econ FIN-00101 Helsinki Finland Univ Jyvaskyla Dept Math Informat Technol FIN-40014 Jyvaskyla Finland

We introduce a new approach in the methodology development for interactive multiobjective optimization. Thepresentation is given in the context of the interactive NIMBUS method, where the solution process is based on the classification of objective functions. The idea is to formulate several scalarizing functions, all using the same preference information of the decision maker. Thus, opposed to fixing one scalarizing function (as is done in most methods), we utilize several scalarizing functions in a synchronous way. This means that we as method developers do not make the choice between different scalarizing functions but calculate the results of different scalarizing functions and leave the final decision to the expert, the decision maker. Simultaneously, (s)he obtains a better view of the solutions corresponding to her/his preferences expressed once during each iteration. In this paper, we describe a synchronous variant of the NIMBUS method. In addition, we introduce a new version of its implementation WWW-NIMBUS operating on the Internet. WWW-NIMBUS is a software system capable of solving even computationally demanding nonlinear problems. The new version of WWW-NIMBUS can handle versatile types of multiobjective optimization problems and includes new desirable features increasing its user-friendliness. (c) 2004 Elsevier B.V. All rights reserved.

关键词： multiple objective programming MCDM Internet interactive methods NIMBUS WWW-NIMBUS nonlinear programming

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Evaluation of nondominated solution sets for k-objective optimization problems:: An exact method and approximations

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2006年第2期173卷 565-582页

作者： Kim, B. Gel, E. S. Fowler, J. W. Carlyle, W. M. Wallenius, J. Arizona State Univ Tempe AZ 85287 USA USN Postgrad Sch Monterey CA 93943 USA Helsinki Sch Econ FIN-00100 Helsinki Finland

Integrated Preference Functional (IPF) is a set functional that, given a discrete set of points for a multiple objective optimization problem, assigns a numerical value to that point set. This value provides a quantitative measure for comparing different sets of points generated by solution procedures for difficult multiple objective optimization problems. We introduced the IPF for bi-criteria optimization problems in [Carlyle, W.M., Fowler, J.W., Gel, E., Kim, B., 2003. Quantitative comparison of approximate solution sets for bi-criteria optimization problems. Decision Sciences 34 (1), 63-82]. As indicated in that paper, the computational effort to obtain IPF is negligible for bi-criteria problems. For three or more objective function cases, however, the exact calculation of IPF is computationally demanding, since this requires k (>= 3) dimensional integration. In this paper, we suggest a theoretical framework for obtaining IPF for k (>= 3) objectives. The exact method includes solving two main sub-problems: (1) finding the optimality region of weights for all potentially optimal points, and (2) computing volumes of k dimensional convex polytopes. Several different algorithms for both sub-problems can be found in the literature. We use existing methods from computational geometry (i.e., triangulation and convex hull algorithms) to develop a reasonable exact method for obtaining IPF. We have also experimented with a Monte Carlo approximation method and compared the results to those with the exact IPF method. (c) 2005 Elsevier B.V. All rights reserved.

关键词： multiple objective programming combinatorial optimization metaheuristics

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NAUTILUS method: An interactive technique in multiobjective optimization based on the nadir point

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2010年第2期206卷 426-434页

作者： Miettinen, Kaisa Eskelinen, Petri Ruiz, Francisco Luque, Mariano Univ Jyvaskyla Dept Math Informat Technol FI-40014 Jyvaskyla Finland Univ Malaga Dept Appl Econ Math E-29071 Malaga Spain

Most interactive methods developed for solving multiobjective optimization problems sequentially generate Pareto optimal or nondominated vectors and the decision maker must always allow impairment in at least one objective function to get a new solution. The NAUTILUS method proposed is based on the assumptions that past experiences affect decision makers' hopes and that people do not react symmetrically to gains and losses. Therefore, some decision makers may prefer to start from the worst possible objective values and to improve every objective step by step according to their preferences. In NAUTILUS, starting from the nadir point, a solution is obtained at each iteration which dominates the previous one. Although only the last solution will be Pareto optimal, the decision maker never looses sight of the Pareto optimal set, and the search is oriented so that (s)he progressively focusses on the preferred part of the Pareto optimal set. Each new solution is obtained by minimizing an achievement scalarizing function including preferences about desired improvements in objective function values. NAUTILUS is specially suitable for avoiding undesired anchoring effects, for example in negotiation support problems, or just as a means of finding an initial Pareto optimal solution for any interactive procedure. An illustrative example demonstrates how this new method iterates. (C) 2010 Elsevier B.V. All rights reserved.

关键词： multiple objective programming Interactive methods Reference point methods Preference information Pareto optimality

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Multi-criteria optimization and decision-making in radiotherapy

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2019年第1期277卷 1-19页

作者： Breedveld, Sebastiaan Craft, David van Haveren, Rens Heijmen, Ben Univ Med Ctr Rotterdam Dept Radiat Oncol Erasmus MC Canc Inst Rotterdam Netherlands Massachusetts Gen Hosp Boston MA 02114 USA Harvard Med Sch Dept Radiat Oncol Boston MA 02115 USA

Radiotherapy (radiation therapy) is one of the main treatments for cancer. The aim is to deliver a prescribed radiation dose to the tumor, while keeping the unavoidable dose to the surrounding healthy organs as low as possible to minimize the probability of developing radiation induced complications. Radio-therapy treatment plan optimization strives to find machine parameters that result in desirable treatment plans. This is a large scale nonconvex multi-criteria optimization problem. In this review, we focus on the multi-criteria and decision-making aspects of radiotherapy treatment plan optimization. Shaping the 3D dose distribution within the patient involves balancing 10-30 highly correlated criteria, subject to the (in general) nonconvex mechanical machine parameters and time constraints, both in plan generation and delivery time of the treatment itself. Furthermore, each patient has a unique anatomy and unique (but unknown) radiosensitivity levels for each organ. This complicates decision-making, as the trade-offs are different for each patient, the patient-specific "safe" levels are unknown, and the interplay between different damaged organs to a physical complication is not always clear. There is no "best" plan for a patient, and decisions made are based on the insights and experience of the treating physician. In this review we describe the use of multi-criteria and decision-making methods used in modern radiotherapy. To understand the difficulties and the many levels in which multi-criteria optimization and decision-making are involved, a thorough background is given. We also provide basic treatment planning guidelines and directions to datasets for those who wish to further explore the field of radiotherapy. (C) 2018 Elsevier B.V. All rights reserved.

关键词： multiple objective programming Decision processes OR in health services Radiotherapy

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Unequal probability sampling from a finite population: A multicriteria approach

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2010年第2期201卷 500-504页

作者： Carrizosa, Emilio Univ Seville Fac Matemat E-41012 Seville Spain

In this note we address the problem of determining selection probabilities for multipurpose surveys, when the aim is the simultaneous minimization of variances for each variable under study. A characterization of the set of Pareto-optimal designs is given for designs with replacement and also for a class of designs without replacement, namely, Poisson designs. As an application, we describe a problem encountered in Auditing, where both the fraction of misstatements, and the average amount of such misstatements are of interest. (C) 2009 Elsevier B.V. All rights reserved.

关键词： multiple objective programming Auditing Hansen Hurwitz estimator

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