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 ...
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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.
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...
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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.
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 severa...
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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.
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 ...
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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.
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...
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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.
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 ...
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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.
Integrated Preference Functional (IPF) is a set functional that, given a discrete set of points for a multipleobjective optimization problem, assigns a numerical value to that point set. This value provides a quantit...
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Integrated Preference Functional (IPF) is a set functional that, given a discrete set of points for a multipleobjective 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 multipleobjective 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.
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 obje...
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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.
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...
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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.
Energy planning for individual large energy consumers becomes increasingly important due to several supply options competing and/or complementing each other and the high uncertainty associated with fuel prices. Hotel ...
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Energy planning for individual large energy consumers becomes increasingly important due to several supply options competing and/or complementing each other and the high uncertainty associated with fuel prices. Hotel units are among the largest energy consumers in the building sector, where energy planning may greatly facilitate investment decisions for efficiently meeting energy demand. The present paper presents a linear programming model, including both continuous and integer variables, which represent energy flows and discrete energy technologies, respectively. Furthermore, the model comprises fuzzy parameters in order to handle adequately the uncertainties regarding energy costs. The obtained fuzzy linear programming model is then translated into the equivalent multipleobjective linear programming model, which provides a set of efficient solutions, each one characterized by quantification of the risk associated with the uncertain energy costs. The proposed methodology is illustrated with a case study referring to a large hotel unit located nearby Athens. (C) 2002 Elsevier Science Ltd. All rights reserved.
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