Interactive Fuzzy Random Two-level Linear Programming through Fractile Criterion Optimization

This paper considers two-level linear programming problems involving fuzzy random variables. Having introduced level sets of fuzzy random variables and fuzzy goals of decision makers, following fractile criterion optimization, fuzzy random two-level programming problems are transformed into deterministic ones. Interactive fuzzy programming is presented for deriving a satisfactory solution efficiently with considerations of overall satisfactory balance

A Hierachical Evolutionary Algorithm for Multiobjective Optimization in IMRT

Purpose: Current inverse planning methods for IMRT are limited because they are not designed to explore the trade-offs between the competing objectives between the tumor and normal tissues. Our goal was to develop an efficient multiobjective optimization algorithm that was flexible enough to handle any form of objective function and that resulted in a set of Pareto optimal plans. Methods: We developed a hierarchical evolutionary multiobjective algorithm designed to quickly generate a diverse Pareto optimal set of IMRT plans that meet all clinical constraints and reflect the trade-offs in the plans. The top level of the hierarchical algorithm is a multiobjective evolutionary algorithm (MOEA). The genes of the individuals generated in the MOEA are the parameters that define the penalty function minimized during an accelerated deterministic IMRT optimization that represents the bottom level of the hierarchy. The MOEA incorporates clinical criteria to restrict the search space through protocol objectives and then uses Pareto optimality among the fitness objectives to select individuals. Results: Acceleration techniques implemented on both levels of the hierarchical algorithm resulted in short, practical runtimes for optimizations. The MOEA improvements were evaluated for example prostate cases with one target and two OARs. The modified MOEA dominated 11.3% of plans using a standard genetic algorithm package. By implementing domination advantage and protocol objectives, small diverse populations of clinically acceptable plans that were only dominated 0.2% by the Pareto front could be generated in a fraction of an hour. Conclusions: Our MOEA produces a diverse Pareto optimal set of plans that meet all dosimetric protocol criteria in a feasible amount of time. It optimizes not only beamlet intensities but also objective function parameters on a patient-specific basis

Aspiration Based Decision Analysis and Support Part I: Theoretical and Methodological Backgrounds

In the interdisciplinary and intercultural systems analysis that constitutes the main theme of research in IIASA, a basic question is how to analyze and support decisions with help of mathematical models and logical procedures. This question -- particularly in its multi-criteria and multi-cultural dimensions -- has been investigated in System and Decision Sciences Program (SDS) since the beginning of IIASA. Researchers working both at IIASA and in a large international network of cooperating institutions contributed to a deeper understanding of this question. Around 1980, the concept of reference point multiobjective optimization was developed in SDS. This concept determined an international trend of research pursued in many countries cooperating with IIASA as well as in many research programs at IIASA -- such as energy, agricultural, environmental research. SDS organized since this time numerous international workshops, summer schools, seminar days and cooperative research agreements in the field of decision analysis and support. By this international and interdisciplinary cooperation, the concept of reference point multiobjective optimization has matured and was generalized into a framework of aspiration based decision analysis and support that can be understood as a synthesis of several known, antithetical approaches to this subject -- such as utility maximization approach, or satisficing approach, or goal -- program -- oriented planning approach. Jointly, the name of quasisatisficing approach can be also used, since the concept of aspirations comes from the satisficing approach. Both authors of the Working Paper contributed actively to this research: Andrzej Wierzbicki originated the concept of reference point multiobjective optimization and quasisatisficing approach, while Andrzej Lewandowski, working from the beginning in the numerous applications and extensions of this concept, has had the main contribution to its generalization into the framework of aspiration based decision analysis and support systems. This paper constitutes a draft of the first part of a book being prepared by these two authors. Part I, devoted to theoretical foundations and methodological background, written mostly by Andrzej Wierzbicki, will be followed by Part II, devoted to computer implementations and applications of decision support systems based on mathematical programming models, written mostly by Andrzej Lewandowski. Part III, devoted to decision support systems for the case of subjective evaluations of discrete decision alternatives, will be written by both authors

Domination and Decomposition in Multiobjective Programming

During the last few decades, multiobjective programming has received much attention for both its numerous theoretical advances as well as its continued success in modeling and solving real-life decision problems in business and engineering. In extension of the traditionally adopted concept of Pareto optimality, this research investigates the more general notion of domination and establishes various theoretical results that lead to new optimization methods and support decision making. After a preparatory discussion of some preliminaries and a review of the relevant literature, several new findings are presented that characterize the nondominated set of a general vector optimization problem for which the underlying domination structure is defined in terms of different cones. Using concepts from linear algebra and convex analysis, a well known result relating nondominated points for polyhedral cones with Pareto solutions is generalized to nonpolyhedral cones that are induced by positively homogeneous functions, and to translated polyhedral cones that are used to describe a notion of approximate nondominance. Pareto-oriented scalarization methods are modified and several new solution approaches are proposed for these two classes of cones. In addition, necessary and sufficient conditions for nondominance with respect to a variable domination cone are developed, and some more specific results for the case of Bishop-Phelps cones are derived. Based on the above findings, a decomposition framework is proposed for the solution of multi-scenario and large-scale multiobjective programs and analyzed in terms of the efficiency relationships between the original and the decomposed subproblems. Using the concept of approximate nondominance, an interactive decision making procedure is formulated to coordinate tradeoffs between these subproblems and applied to selected problems from portfolio optimization and engineering design. Some introductory remarks and concluding comments together with ideas and research directions for possible future work complete this dissertation

Fuzzy Goal Programming Procedure to Bilevel Multiobjective Linear Fractional Programming Problems

This paper presents a fuzzy goal programming (FGP) procedure for solving bilevel multiobjective linear fractional programming (BL-MOLFP) problems. It makes an extension work of Moitra and Pal (2002) and Pal et al. (2003). In the proposed procedure, the membership functions for the defined fuzzy goals of the decision makers (DMs) objective functions at both levels as well as the membership functions for vector of fuzzy goals of the decision variables controlled by first-level decision maker are developed first in the model formulation of the problem. Then a fuzzy goal programming model to minimize the group regret of degree of satisfactions of both the decision makers is developed to achieve the highest degree (unity) of each of the defined membership function goals to the extent possible by minimizing their deviational variables and thereby obtaining the most satisfactory solution for both decision makers. The method of variable change on the under- and over-deviational variables of the membership goals associated with the fuzzy goals of the model is introduced to solve the problem efficiently by using linear goal programming (LGP) methodology. Illustrative numerical example is given to demonstrate the procedure

A REVIEW OF APPLICATIONS OF MULTIPLE - CRITERIA DECISION-MAKING TECHNIQUES TO FISHERIES

Management of public resources, such as fisheries, is a complex task. Society, in general, has a number of goals that it hopes to achieve from the use of public resources. These include conservation, economic, and social objectives. However, these objectives often conflict, due to the varying opinions of the many stakeholders. It would appear that the techniques available in the field of multiple-criteria decision-making (MCDM) are well suited to the analysis and determination of fisheries management regimes. However, to date, relatively few publications exist using such MCDM methods compared to other applicational fields, such as forestry, agriculture, and finance. This paper reviews MCDM applied to fishery management by providing an overview of the research published to date. Conclusions are drawn regarding the success and applicability of these techniques to analyzing fisheries management problems.Resource /Energy Economics and Policy,