A modification of the standard lexicographic method, used for linear multiobjective optimization problems, is presented. An algorithm for solving these kind of problems is developed, for the cases of two and three unknowns. The algorithm uses the general idea of indicating the lexicographic order to objective functions, combined with the graphical method of linear programming. Implementation de...

The hypervolume subset selection problem consists of finding a subset, with a given cardinality k, of a set of nondominated points that maximizes the hypervolume indicator. This problem arises in selection procedures of evolutionary algorithms for multiobjective optimization, for which practically efficient algorithms are required. In this article, two new formulations are provided for the two-...

In this paper we suggest an approach for solving a multiobjective stochastic linear programming problem with normal multivariate distributions. Our is combination between method and nonconvex technique. The first transformed into deterministic introducing the expected value criterion utility function that represents decision makers preferences. obtained reduced to mono-objective quadratic using...

This paper presents an application to the multi-objective stochastic transportation problem in fuzzy environment. In this paper, we focus on our attention to multiobjective stochastic transportation problem involving an inequality type of constraints in which all parameters ( supply and demand ) are log-normal random variable and the objectives are non-commensurable and conflicting in nature. A...

This paper presents an interval valued goal programming approach for solving multiobjective fractional programming problems. In the model formulation of the problem, the interval-valued system constraints are converted in to equivalent crisp system. The interval valued fractional objective goals are transformed into linear goals by employing the iterative parametric method which is an extension...

This paper focuses on multiobjective linear programming problems involving fuzzy random variable coefficients. A new decision making model and Pareto optimal solution concept are proposed using α-level cuts of membership function. It is shown that the problem including both randomness and fuzziness is equivalently transformed into a deterministic problem. An interactive algorithm is proposed in...

Genetic programming (GP) is applied to a multobjective optimisation problem and the advantages of its hierarchical tree encoding scheme are compared with an earlier use of a subset representation approach which used string-encoded genetic algorithms. The GP approach is applied to the identification of non-linear system polynomial models and provides a trade-off between the complexity and the pe...

We focus on fuzzy random multiobjective linear programming problems with variance covariance matrices, and propose a fuzzy decision making method to obtain a satisfactory solution. In the proposed method, it is assumed that the decision maker has fuzzy goals for both permissible levels and the corresponding objective functions for a probability maximization model or a fractile optimization mode...

We provide a comprehensive overview of the literature algorithmic approaches for multiobjective mixed-integer and integer linear optimization problems. More precisely, we categorize display exact methods problems with variables computing entire set nondominated images. Our review lists 108 articles is intended to serve as reference all researchers who are familiar basic concepts have an interes...

A fuzzy regression model is used in evaluating the functional relationship between the dependent and independent variables in a fuzzy environment. Most fuzzy regression models are considered to be fuzzy outputs and parameters but non-fuzzy (crisp) inputs. In general, there are two approaches in the analysis of fuzzy regression models: linear-programmingbased methods and fuzzy least-squares meth...