Applications of fuzzy theories to multi-objective system optimization

Most of the computer aided design techniques developed so far deal with the optimization of a single objective function over the feasible design space. However, there often exist several engineering design problems which require a simultaneous consideration of several objective functions. This work presents several techniques of multiobjective optimization. In addition, a new formulation, based on fuzzy theories, is also introduced for the solution of multiobjective system optimization problems. The fuzzy formulation is useful in dealing with systems which are described imprecisely using fuzzy terms such as, 'sufficiently large', 'very strong', or 'satisfactory'. The proposed theory translates the imprecise linguistic statements and multiple objectives into equivalent crisp mathematical statements using fuzzy logic. The effectiveness of all the methodologies and theories presented is illustrated by formulating and solving two different engineering design problems. The first one involves the flight trajectory optimization and the main rotor design of helicopters. The second one is concerned with the integrated kinematic-dynamic synthesis of planar mechanisms. The use and effectiveness of nonlinear membership functions in fuzzy formulation is also demonstrated. The numerical results indicate that the fuzzy formulation could yield results which are qualitatively different from those provided by the crisp formulation. It is felt that the fuzzy formulation will handle real life design problems on a more rational basis

Decision support for build-to-order supply chain management through multiobjective optimization

This is the post-print version of the final paper published in International Journal of Production Economics. The published article is available from the link below. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. Copyright @ 2010 Elsevier B.V.This paper aims to identify the gaps in decision-making support based on multiobjective optimization (MOO) for build-to-order supply chain management (BTO-SCM). To this end, it reviews the literature available on modelling build-to-order supply chains (BTO-SC) with the focus on adopting MOO techniques as a decision support tool. The literature has been classified based on the nature of the decisions in different part of the supply chain, and the key decision areas across a typical BTO-SC are discussed in detail. Available software packages suitable for supporting decision making in BTO supply chains are also identified and their related solutions are outlined. The gap between the modelling and optimization techniques developed in the literature and the decision support needed in practice are highlighted. Future research directions to better exploit the decision support capabilities of MOO are proposed. These include: reformulation of the extant optimization models with a MOO perspective, development of decision supports for interfaces not involving manufacturers, development of scenarios around service-based objectives, development of efficient solution tools, considering the interests of each supply chain party as a separate objective to account for fair treatment of their requirements, and applying the existing methodologies on real-life data sets.Brunel Research Initiative and Enterprise Fund (BRIEF

Decision support for build-to-order supply chain management through multiobjective optimization

This paper aims to identify the gaps in decision-making support based on multiobjective optimization for build-to-order supply chain management (BTOSCM). To this end, it reviews the literature available on modelling build-to-order supply chains (BTO-SC) with the focus on adopting multiobjective optimization (MOO) techniques as a decision support tool. The literature has been classified based on the nature of the decisions in different part of the supply chain, and the key decision areas across a typical BTO-SC are discussed in detail. Available software packages suitable for supporting decision making in BTO supply chains are also identified and their related solutions are outlined. The gap between the modelling and optimization techniques developed in the literature and the decision support needed in practice are highlighted and future research directions to better exploit the decision support capabilities of MOO are proposed

An Interactive Fuzzy Satisficing Method for Multiobjective Nonlinear Programming Problems with Fuzzy Parameters

This paper presents an interactive fuzzy satisficing method for multiobjective nonlinear programming problems with fuzzy parameters. The fuzzy parameters in the objective functions and the constraints are characterized by the fuzzy numbers. On the basis of the alpha-level sets of the fuzzy numbers, the concept of alpha-multiobjective nonlinear programming and alpha-Pareto optimality is introduced. Through the interaction with the decision maker (DM), the fuzzy goals of the DM for each of the objective functions in alpha-multiobjective nonlinear programming are quantified by eliciting the corresponding membership functions. After determining the membership functions, in order to generate a candidate for the satisficing solution which is also alpha-Pareto optimal, if the DM specifies the degree alpha of the alpha-level sets and the reference membership values, the augmented minimax problem is solved and the DM is supplied with the corresponding alpha-Pareto optimal solution together with the trade-off rates among the values of the membership functions and the degree alpha. Then by considering the current values of the membership functions and as well as the trade-off rates, the DM responds by updating his reference membership values and/or the degree alpha. In this way the satisficing solution for the DM can be derived efficiently from among an alpha-Pareto optimal solution set. Based on the proposed method, a time-sharing computer program is written and an illustrative numerical example is demonstrated along with the corresponding computer outputs

An Interactive Fuzzy Satisficing Method for Multiobjective Stochastic Integer Programming Problems through Simple Recourse Model

Two major approaches to deal with randomness or impression involved in mathematical programming problems have been developed. The one is called stochastic programming, and the other is called fuzzy programming. In this paper, we focus on multiobjective integer programming problems involving random variable coefficients in constraints. Using the concept of simple recourse, such multiobjective stochastic integer programming problems are transformed into deterministic ones. As a fusion of stochastic programming and fuzzy one, after introducing fuzzy goals to reflect the ambiguity of the decision maker's judgments for objective functions, we propose an interactive fuzzy satisficing method to derive a satisficing solution for the decision maker by updating the reference membership levels

A Distance Based Method for Solving Multi-objective Optimization Problems

A new model for the weighted method of goal programming is proposed based on minimizing the distances between ideal objectives to feasible objective space. It provides the best compromised solution for Multi Objective Linear Programming Problems (MOLPP). The proposed model tackles MOLPP by solving a series of single objective sub-problems, where the objectives are transformed into constraints. The compromise solution so obtained may be improved by defining priorities in terms of the weight. A criterion is also proposed for deciding the best compromise solution. Applications of the algorithm are discussed for transportation and assignment problems involving multiple and conflicting objectives. Numerical illustrations are given for the proposed model

Multi-objective evolutionary–fuzzy augmented flight control for an F16 aircraft

In this article, the multi-objective design of a fuzzy logic augmented flight controller for a high performance fighter jet (the Lockheed-Martin F16) is described. A fuzzy logic controller is designed and its membership functions tuned by genetic algorithms in order to design a roll, pitch, and yaw flight controller with enhanced manoeuverability which still retains safety critical operation when combined with a standard inner-loop stabilizing controller. The controller is assessed in terms of pilot effort and thus reduction of pilot fatigue. The controller is incorporated into a six degree of freedom motion base real-time flight simulator, and flight tested by a qualified pilot instructor