Fuzzy linear programming problems : models and solutions

We investigate various types of fuzzy linear programming problems based on models and solution methods. First, we review fuzzy linear programming problems with fuzzy decision variables and fuzzy linear programming problems with fuzzy parameters (fuzzy numbers in the definition of the objective function or constraints) along with the associated duality results. Then, we review the fully fuzzy linear programming problems with all variables and parameters being allowed to be fuzzy. Most methods used for solving such problems are based on ranking functions, alpha-cuts, using duality results or penalty functions. In these methods, authors deal with crisp formulations of the fuzzy problems. Recently, some heuristic algorithms have also been proposed. In these methods, some authors solve the fuzzy problem directly, while others solve the crisp problems approximately

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

Evolutionary multi-objective decision support systems for conceptual design

Merged with duplicate record 10026.1/2328 on 07.20.2017 by CS (TIS)In this thesis the problem of conceptual engineering design and the possible use of adaptive search techniques and other machine based methods therein are explored. For the multi-objective optimisation (MOO) within conceptual design problem, genetic algorithms (GA) adapted to MOO are used and various techniques explored: weighted sums, lexicographic order, Pareto method with and without ranking, VEGA-like approaches etc. Large number of runs are performed for findingZ Dth e optimal configuration and setting of the GA parameters. A novel method, weighted Pareto method is introduced and applied to a real-world optimisation problem. Decision support methods within conceptual engineering design framework are discussed and a new preference method developed. The preference method for translating vague qualitative categories (such as "more important 91 , 4m.9u ch less important' 'etc. ) into quantitative values (numbers) is based on fuzzy preferences and graph theory methods. Several applications of preferences are presented and discussed: * in weighted sum based optimisation methods; s in weighted Pareto method; * for ordering and manipulating constraints and scenarios; e for a co-evolutionary, distributive GA-based MOO method; The issue of complexity and sensitivity is addressed as well as potential generalisations of presented preference methods. Interactive dynamical constraints in the form of design scenarios are introduced. These are based on a propositional logic and a fairly rich mathematical language. They can be added, deleted and modified on-line during the design session without need for recompiling the code. The use of machine-based agents in conceptual design process is investigated. They are classified into several different categories (e. g. interface agents, search agents, information agents). Several different categories of agents performing various specialised task are developed (mostly dealing with preferences, but also some filtering ones). They are integrated with the conceptual engineering design system to form a closed loop system that includes both computer and designer. All thesed ifferent aspectso f conceptuale ngineeringd esigna re applied within Plymouth Engineering Design Centre / British Aerospace conceptual airframe design project.British Aerospace Systems, Warto

Fuzzy sets and models of decision making

AbstractResults of research into the use of fuzzy sets for handling various forms of uncertainty in optimization problems related to the design and control of complex systems are presented. Much attention is given to considering the uncertainty of goals that is associated with a multicriteria character of many optimization problems. The application of a multicriteria approach is needed to solve 1.(1)|problems in which solution consequences cannot be estimated on the basis of a single criterion, that involves the necessity of analyzing a vector of criteria, and2.(2)|problems that may be considered on the basis of a single criterion but their unique solutions are not achieved because the uncertainty of information produces so-called decision uncertainty regions, and the application of additional criteria can serve as a convincing means to contract these regions.According to this, two classes of models (〈X, M〉 and 〈X, R〉 models) are considered with applying the Bellman-Zadeh approach and techniques of fuzzy preference relations to their analysis. The consideration of 〈X, R〉 models is associated with a general approach to solving a wide class of optimization problems with fuzzy coefficients. This approach consists in formulating and analyzing one and the same problem within the framework of interrelated models with constructing equivalent analogs with fuzzy coefficients in objective functions alone. It allows one to maximally cut off dominated alternatives. The subsequent contraction of the decision uncertainty region is associated with reduction of the problem to multicriteria decision making in a fuzzy environment with its analysis applying one of two techniques based on fuzzy preference relations. The results of the paper are of a universal character and are already being used to solve problems of power engineering

Redesign of a sustainable food bank supply chain

Thesis submitted for the degree of Doctor of Philosophy in Mathematics Applied to Economics and Management.Food rescue and delivery organizations target concurrently the environmental objective of reduc- ing food waste, and the social objective of supporting underprivileged segments of the population. They secure surplus and about-to-waste food items from producers, manufacturers and retailers, and redistribute them through charitable agencies and parish councils to support the population in need of food assistance. Inspired by the case of the Portuguese Federation of Food Banks, the study ad- dresses the redesign of a food bank supply chain from a multi-dimensional outlook on sustainability. Considering an initial network of food banks, strategic decisions include the opening and closing of food banks, as well as the installation or expansion of storage and transport resources, while tactical decisions comprise the selection of served charities and respective assignment to the operational food banks. Moreover, product flows across the network are also to be determined. The supply chain is formulated as a three-layer network involving the donors, the food banks, and the charities, where multiple products flow in vertical and lateral directions. Based on an extensive literature review, and supported by an in-depth field research, the problem is formulated as a dynamic and capacitated tri-objective mixed-integer linear programming model, accounting for environmental indicators such as the volume of food waste and CO2 emissions, and social metrics assessing, among others, equity, inclusion, and proximity. The tri-objective problem is studied for regional and national supply chain instances, developed to depict real-life based cases. Non-dominated solutions are obtained for the regional instances appealing to the lexicographic ordering method. Relevant managerial insights are derived from the analysis of the lexicographic solutions. Three decomposition based heuristics de- veloped in this study proved to be effective in solving the national instances. Trade-offs between the economic, environmental, and social objectives are discussed, and properties of the mathematical programming model are proven.As organizações de resgate e distribuição "alimentar perseguem paralelamente o objetivo ambiental de redução do desperdício alimentar e o objetivo social de apoio à população carenciada. Estas entidades angariam excedentes alimentares e produtos em vias de deterioração de produtores, indústrias e do comércio a retalho que redistribuem, através de instituições de solidariedade e autarquias locais, a pessoas com carências alimentares. Inspirado no caso da Federação Portuguesa de Bancos Alimentares, este estudo aborda o redesenho de uma cadeia de abastecimento de bancos alimentares numa perspectiva de sustentabilidade multi-dimensional. Considerando uma rede inicial de bancos alimentares, as decisões estratégicas envolvem a abertura e o encerramento de bancos alimentares, bem como a instalação ou expansão da capacidade de armazenamento e de transporte, ao passo que as decisões táticas compreendem a seleção das instituições servidas e a sua afetação a algum dos bancos em operação. Adicionalmente, são também determinados os fluxos de produtos que circulam na rede. A cadeia de abastecimento é formulada como uma rede de três níveis envolvendo os doadores, os bancos alimentares e as instituições beneficiárias. Nesta rede existem fluxos verticais e laterais de produtos. Com base numa extensa revisão bibliográfica e apoiado por um aprofundado trabalho de campo, o problema é formulado como um modelo de programação linear inteira-mista, dinâmico, com capacidades e tri-objetivo. Este problema considera indicadores ambientais como o volume de desperdício alimentar e as emissões de CO2, e como métricas sociais a equidade, a inclusão e a proximidade, entre outros. O problema é estudado para instâncias de cadeias de abastecimento regionais e nacionais, as quais foram desenvolvidas com o objetivo de retratar casos baseados na realidade. São obtidas soluções não dominadas para as instâncias regionais recorrendo ao método lexicográfico, cuja análise revela conclusões relevantes para a gestão. Foram desenvolvidas três heurísticas baseadas em decomposição que provaram ser eficazes na resolução das instâncias nacionais. São discutidos os compromissos existentes entre os objetivos económico, ambiental e social, e provadas propriedades do modelo de programação matemática.N/

Models for Oil Refinery Waste Management Using Determined and Fuzzy Conditions

This study developed models to solve problems of optimisation, production, and consumption in waste management based on methods of system analysis. Mathematical models of the problems of optimisation and sustainable waste management in deterministic conditions and in a fuzzy environment were formulated. The income from production was maximised considering environmental standards that apply to the field of macroeconomics and microeconomics. The proposed approach used MANAGER software to formalise and solve the problem of revenue optimisation with production waste management to optimise the production of oil products with waste management at a specific technological facility of the Atyrau oil refinery in Kazakhstan. Based on the combined application of the principles of maximin and Pareto optimality, a formulation of the problem of production optimisation with waste management was obtained and a heuristic algorithm for solving the formulated fuzzy optimisation problem with waste management was developed.info:eu-repo/semantics/publishedVersio

Solving multiobjective mathematical programming problems with fixed and fuzzy coefficients

Many concrete problems, ranging from Portfolio selection to Water resource management, may be cast into a multiobjective programming framework. The simplistic way of superseding blindly conflictual goals by one objective function let no chance to the model but to churn out meaningless outcomes. Hence interest of discussing ways for tackling Multiobjective Programming Problems. More than this, in many real-life situations, uncertainty and imprecision are in the state of affairs. In this dissertation we discuss ways for solving Multiobjective Programming Problems with fixed and fuzzy coefficients. No preference, a priori, a posteriori, interactive and metaheuristic methods are discussed for the deterministic case. As far as the fuzzy case is concerned, two approaches based respectively on possibility measures and on Embedding Theorem for fuzzy numbers are described. A case study is also carried out for the sake of illustration. We end up with some concluding remarks along with lines for further development, in this field.Operations ResearchM. Sc. (Operations Research

Computing leximin-optimal solutions in constraint networks

AbstractIn many real-world multiobjective optimization problems one needs to find solutions or alternatives that provide a fair compromise between different conflicting objective functions—which could be criteria in a multicriteria context, or agent utilities in a multiagent context—while being efficient (i.e. informally, ensuring the greatest possible overall agents' satisfaction). This is typically the case in problems implying human agents, where fairness and efficiency requirements must be met. Preference handling, resource allocation problems are another examples of the need for balanced compromises between several conflicting objectives. A way to characterize good solutions in such problems is to use the leximin preorder to compare the vectors of objective values, and to select the solutions which maximize this preorder. In this article, we describe five algorithms for finding leximin-optimal solutions using constraint programming. Three of these algorithms are original. Other ones are adapted, in constraint programming settings, from existing works. The algorithms are compared experimentally on three benchmark problems

A decade of application of the Choquet and Sugeno integrals in multi-criteria decision aid

The main advances regarding the use of the Choquet and Sugeno integrals in multi-criteria decision aid over the last decade are reviewed. They concern mainly a bipolar extension of both the Choquet integral and the Sugeno integral, interesting particular submodels, new learning techniques, a better interpretation of the models and a better use of the Choquet integral in multi-criteria decision aid. Parallel to these theoretical works, the Choquet integral has been applied to many new fields, and several softwares and libraries dedicated to this model have been developed.Choquet integral, Sugeno integral, capacity, bipolarity, preferences