Bi-objective Linear Programming Problem Research Articles

(2012-6359) An approach based on -cuts and max-min technique to linear fractional programming with fuzzy coefficients

This paper presents an efficient and straightforward method with less computational complexities to address the linear fractional programming with fuzzy coefficients (FLFPP). To construct the approach, the concept of α-cut is used to tackle the fuzzy numbers in addition to rank them. Accordingly, the fuzzy problem is changed into a bi-objective linear fractional programming problem (BOLFPP) by the use of interval arithmetic. Afterwards, an equivalent BOLFPPis defined in terms of the membership functions of the objectives, which is transformed into a bi-objective linear programming problem (BOLPP) applying suitable non-linear variable transformations. Max-min theory is utilized to alter the BOLPP into a linear programming problem (LPP). It is proven that the optimal solution of the LPP is an ϵ-optimal solution for the fuzzy problem. Four numerical examples are given to illustrate the method and comparisonsare made to show the efficiency.

Solution approach to a special class of full fuzzy linear programming problems

A wide variety of solution approaches to linear programming problems in fuzzy environment are proposed in the recent literature. For this study we consider a linear programming problem with fuzzy inequality constraints, and both coefficients and decision variables described by trapezoidal fuzzy numbers. Our solution approach takes into consideration decision maker’s acceptance degree of the violated fuzzy constraints.We use the interval expectation of the trapezoidal fuzzy numbers to transform the original problem into an interval optimization problem. Then, using an order relation to rank the intervals; and handling the acceptance degree of the violated fuzzy constraints as a parameter in the optimization model, we analyze the Pareto optimal solutions to a parametric bi-objective linear programming problem. For a fixed value of the acceptance degree provided by the decision maker, but after a parametric analysis with respect to the parameter used for aggregating the two objectives, the decision maker becomes better informed about the nature of the problem he has to complete.We illustrate our new solution approach using numerical examples found in the literature, and emphasize its advantages.

An improved evolutionary algorithm for handling many-objective optimization problems

It has been shown that the multi-objective evolutionary algorithms (MOEAs) act poorly in solving many-objective optimization problems which include more than three objectives. The research emphasis, in recent years, has been put into improving the MOEAs to enable them to solve many-objective optimization problems efficiently. In this paper, we propose a new composite fitness evaluation function, in a novel way, to select quality solutions from the objective space of a many-objective optimization problem. Using this composite function, we develop a new algorithm on a well-known NSGA-II and call it FR-NSGA-II, a fast reference point based NSGA-II. The algorithm is evaluated for producing quality solutions measured in terms of proximity, diversity and computational time. The working logic of the algorithm is explained using a bi-objective linear programming problem. Then we test the algorithm using experiments with benchmark problems from DTLZ family. We also compare FR-NSGA-II with four competitive algorithms from the extant literature to show that FR-NSGA-II will produce quality solutions even if the number of objectives is as high as 20.

A parametric simplex algorithm for biobjective piecewise linear programming problems

In this paper we attempt to develop a parametric simplex algorithm for solving biobjective convex separable piecewise linear programming problems. The algorithm presented in this paper can be regarded as an extension of the parametric simplex algorithm for solving biobjective linear programming problems to the piecewise linear case. Analogous to the linear case, this parametric simplex algorithm provides a decomposition of parametric space. A numerical example is presented to illustrate the implementation of the algorithm.

Selecting new product development team members with knowledge sharing approach

Purpose – The purpose of this paper is to provide a method for selection of the new product development (NPD) project team members, in such a way to maximize the expertise level of team members and at the same time, optimize knowledge sharing in the organization. Design/methodology/approach – According to the motivation-opportunity-ability framework, knowledge sharing antecedents were determined. Then, the problem of selecting appropriate members of the project team was formulated as a bi-objective integer non-linear programming model. Due to the uncertainty conditions in the evaluation of candidates, the fuzzy sets approach was used for modeling. To solve the problem, first, the non-linear programming model was converted to a linear model. Subsequently, the fuzzy bi-objective linear programming problem was solved by using an approximate algorithm. Findings – Results of applying the proposed method to an Iranian ship-building company showed its effectiveness in selecting appropriate members of the project team. Practical implications – With the aid of the proposed approach, project managers will be able to form effective project teams that while increasing the success probability of the project, facilitate the maintenance of knowledge acquired during the project lifecycle. Originality/value – This paper, for the first time, has tried to provide a method for selecting the NPD project team members, in a way that while selecting candidates with highest expertise, maximizes the sharing of knowledge among them.

β-Pareto Set Prediction for Bi-Objective Reliability-Based Design Optimization

Abstract In this research, we investigate design optimization under uncertainties for problems with two objectives. Reliability-based design optimization (RBDO) that considers uncertainties as random variables and/or parameters and formulates constraints probabilistically has received extensive attention. However, research to date has focused primarily on single-objective problems only. We extend RBDO to problems for which multiple objectives are optimized simultaneously. Each constraint reliability value results in a Pareto set. The set of all Pareto frontiers at the various reliability values is denoted as the β-Pareto set. We study the relations between the deterministic Pareto set and the β-Pareto set and then develop a method to systematically determine the exact β-Pareto set of bi-objective linear programming problems. The method is also extended to predict the β-Pareto set of nonlinear problems using the sandwich technique. As a result, we are able to accurately predict the β-Pareto set in the objective space without solving multiple multi-objective optimization problems at various reliability levels. In the early stage of the product design process, the proposed approach can help decision-makers efficiently to determine how product performance varies with reliability level.

Possibilistic linear programming for managing interest rate risk

Abstract In this study, we consider the linear programming problem with the objective of the investment discounted value, where the interest rate is imprecise and has a triangular possibilistic distribution. An (crisp) auxiliary bi-objective linear programming model is proposed to resolve this possibilistic nature. Furthermore, we develop an extended Zimmermann approach, called augmented max-min approach, for solving this auxiliary bi-objective linear programming problem and other multiple objective linear programming problems. Finally, a numerical bank balance sheet problem, where interest rates, price of futures contract, loan demand, deposit supply and ratio of desired loan to deposit are assumed to be fuzzy, is solved for illustrating the new approach.