Robust optimization for interactive multiobjective programming with imprecise information applied to R&D project portfolio selection

A multiobjective binary integer programming model for R&D project portfolio selection with competing objectives is developed when problem coefficients in both objective functions and constraints are uncertain. Robust optimization is used in dealing with uncertainty while an interactive procedure is used in making tradeoffs among the multiple objectives. Robust nondominated solutions are generated by solving the linearized counterpart of the robust augmented weighted Tchebycheff programs. A decision maker’s most preferred solution is identified in the interactive robust weighted Tchebycheff procedure by progressively eliciting and incorporating the decision maker’s preference information into the solution process. An example is presented to illustrate the solution approach and performance. The developed approach can also be applied to general multiobjective mixed integer programming problems

Multiple-Objective Decision Analysis Applied to Chemical Engineering

The Interactive Decision Analysis Project at IIASA is studying both the theoretical basis of interactive decision support systems and their applications in a number of different fields. Such systems are of most use when decisions have to be made against a background of multiple and conflicting objectives, and they are therefore largely based on the theory of multiobjective decision analysis. This paper looks at the uses of multiobjective decision analysis in the chemical engineering industry. This is a particularly interesting area from the point of view of multiobjective decision making because recent developments have forced chemical plants to give increased weight to noneconomic criteria such as environmental quality and safety at the expense of economic criteria such as profit, capital investment, and operating costs. In addition, it is more necessary than ever for the industry to be able to adapt its production strategy to take into account changes in the economic situation (changing prices, patterns of demand, etc.). The complexity of this system is such that it is now no longer possible to determine the best course of action without some formal analysis. The techniques of multiobjective decision analysis can usefully be employed to help the plant manager find the best solution to these problems. Specific applications in process design, plant control, and production planning are described. Special emphasis is given to the reference-point approach to multiobjective decision making, and to an interactive software package (DIDASS) based on this approach which has been developed at IIASA

Robust Optimization for Multiobjective Programming Problems with Imprecise Information

AbstractA robust optimization approach is proposed for generating nondominated robust solutions for multiobjective linear programming problems with imprecise coefficients in the objective functions and constraints. Robust optimization is used in dealing with impreciseness while an interactive procedure is used in eliciting preference information from the decision maker and in making tradeoffs among the multiple objectives. Robust augmented weighted Tchebycheff programs are formulated from the multiobjective linear programming model using the concept of budget of uncertainty. A linear counterpart of the robust augmented weighted Tchebycheff program is derived. Robust nondominated solutions are generated by solving the linearized counterpart of the robust augmented weighted Tchebycheff programs

Robust Optimization for Multiobjective Programming Problems with Imprecise Information

A robust optimization approach is proposed for generating nondominated robust solutions for multiobjective linear programming problems with imprecise coefficients in the objective functions and constraints. Robust optimization is used in dealing with impreciseness while an interactive procedure is used in eliciting preference information from the decision maker and in making tradeoffs among the multiple objectives. Robust augmented weighted Tchebycheff programs are formulated from the multiobjective linear programming model using the concept of budget of uncertainty. A linear counterpart of the robust augmented weighted Tchebycheff program is derived. Robust nondominated solutions are generated by solving the linearized counterpart of the robust augmented weighted Tchebycheff programs

Fuzzy set based multiobjective allocation of resources and its applications

AbstractThis paper presents results of research into the use of the Bellman-Zadeh approach to decision making in a fuzzy environment for solving multiobjective optimization problems. Its application conforms to the principle of guaranteed result and provides constructive lines in obtaining harmonious solutions on the basis of analyzing associated maxmin problems. The use of the Bellman-Zadeh approach has served as a basis for solving a problem of multiobjective allocation of resources (or their shortages) and developing a corresponding adaptive interactive decision-making system (AIDMS1). Its calculating kernel permits one to solve maxmin problems using an algorithm based on a nonlocal search (modification of the Gelfand's and Tsetlin's “long valley” method). The AIDMS1 includes procedures for considering linguistic variables to reflect conditions that are difficult to formalize as well as procedures for constructing and correcting vectors of importance factors for goals. The use of these procedures permits one to realize an adaptive approach to processing information of a decision maker to provide successive improving of the solution quality. C++ windows of the AIDMS1 are presented for input, output, and special possibilities related to considering linguistic variables and constructing and correcting vectors of importance factors. The results of the paper are universally applicable and are already being used to solve power engineering problems

Ergonomic Chair Design by Fusing Qualitative and Quantitative Criteria using Interactive Genetic Algorithms

This paper emphasizes the necessity of formally bringing qualitative and quantitative criteria of ergonomic design together, and provides a novel complementary design framework with this aim. Within this framework, different design criteria are viewed as optimization objectives; and design solutions are iteratively improved through the cooperative efforts of computer and user. The framework is rooted in multi-objective optimization, genetic algorithms and interactive user evaluation. Three different algorithms based on the framework are developed, and tested with an ergonomic chair design problem. The parallel and multi-objective approaches show promising results in fitness convergence, design diversity and user satisfaction metrics

An Interactive Fuzzy Satisficing Method for Fuzzy Random Multiobjective 0-1 Programming Problems through Probability Maximization Using Possibility

In this paper, we focus on multiobjective 0-1 programming problems under the situation where stochastic uncertainty and vagueness exist at the same time. We formulate them as fuzzy random multiobjective 0-1 programming problems where coefficients of objective functions are fuzzy random variables. For the formulated problem, we propose an interactive fuzzy satisficing method through probability maximization using of possibility

Multiobjective optimization as a decision aid for managing build-to-order supply chains

This paper provides an overview of multiobjective optimization (MOO) as a decision aid in build-to-order supply chains (BTO-SC). The main features of BTO-SCs are discussed along with capabilities of MOO to enhance decision making at different points along the chain. Key decision points across a typical BTO-SC are identified and potential applications of MOO are discussed. A sample application is presented and future avenues for further research highlighted