multi-objective programming

In this paper, we present two methods to find the strictly efficient and weakly efficient points of multi-objective programming (MOP) problems in which their objective functions are pseudo-convex and their feasible sets are polyhedrons. The obtained efficient solutions in these methods are the extreme points. Since the pseudo-convex  functions are quasi-convex as well, therefore the presented methods can be used to find efficient solutions of the (MOP) problem with the quasi-convex objective functions and the polyhedron feasible set. Two experimental examples are presented.

It is a common characteristic of many multiobjective optimization problems that the efficient solution set can only be identified approximately. This study addresses scalarization techniques for solving multiobjective optimization problems. The min-max scalarization technique is considered, and efforts are made to overcome its weaknesses in studying approximate efficient solutions. To this end, two modifications of the min-max scalarization technique are proposed. First, an alternative form of the min-max method is introduced. Additionally, by using slack and surplus variables in the constraints and penalizing violations in the objective function, we obtain easy-to-check conditions for approximate efficiency. The established theorems clarify the relationship between \varepsilon-(weakly and properly) efficient solutions of the multiobjective optimization problem and \epsilon-optimal solutions of the proposed scalarized problems, without requiring any assumptions of convexity.

This paper is mainly concerned with some of the theoretical aspects of equitable multi-objective optimization. By using the equitability preference structure, we discuss some properties of the equitably nondominated set, such as nonemptiness, external stability and connectedness. Also, we introduce the concept of proper equitable nondominance, and show that these solutions can be obtained by minimizing a weighted sum of the sort of objective functions where all weights are positive and decreasing. Moreover, we present a hybrid scalarization problem to generate equitably nondominated solutions. This method also provides a necessary condition for the existence of properly equitable nondominated solutions.

This study proposes a method for solving mixed integer multi-objective fractional signomial geometric programming (MIMOFSGP) problems. A few methods have been applied in the recent past to convert a fractional signomial objective function into a non-fractional signomial objective function to find the optimal solution by use of some common mathematical programming techniques. In this paper, at first a multi-objective fractional signomial programming is converted into a non-fractional multi-objective signomial programming problem by a new convenient reformulation strategy. A convex relaxation is used to reach global solution and then fuzzy programming technique is applied to find the optimal compromise solution. A mixed integer compromise optimal solution of the convex programming problem can finally be found by use of nonlinear branch and bound algorithm. Then 0n using the Spacial branch and bound algorithm, we find a solution that has the shortest distance from the solution of original problem. Finally two illustrative examples are included to demonstrate the correctness and efficiency of the proposed strategy and compare the results with the other solutions obtained by the other methods.

Increasing the discrimination power the of data envelopment analysis method and choosing appropriate weights is one of the important issues in data envelopment analysis. One of the ways to overcome this problem is to use multi-objective data coverage analysis. In multi-objective problems, the goal of the objective functions is usually contradictory to each other, so it is not possible to find an optimal solution for all the objective functions simultaneously. In this article, we use the ideal programming approach to solve the problem of multi-criteria data envelopment analysis, and then we compare the presented method with previous methods in the framework of preferential voting.

In the last few decades there has been lots of discussion in the literature regarding robust optimization. Since Epsilon constraint is one of the most important technique in interactive problems, therefore in this paper, due to the importance of robust optimization and multi-objective programming problems, we consider Multi-Objective Linear Fractional Programming (MOLFP) problem in the presence of box-uncertainty in the coefficients of the objective functions. We propose an approach based on ε-constraint and Charnes-Cooper methods to obtain weakly robust efficient solutions, that have special importance in the literature, for a MOLFP problems in the presence of uncertain data. Charnes-cooper method is applied to reduce a fractional programm to a non fractional programm. At the end we write the robust counterpart of the UMOLFP model in the presence of the box-uncertainty and it's equivalent linear programming problem: Finally a numerical example is used to show the usefulness of the proposed approach.

In this paper, we introduce and discuss multi-objective interval-valued E-convex programming using gH-symmetrical differentiability. We prove nonlinear optimality conditions of Fritz John type for this context and construct an example to verify our results. Furthermore, we define LU-sE-pseudo convexity and LU-sE-quasi convexity for interval-valued functions and study some of their properties.

This paper presents a suitable solution procedure to solve the fully rough multi-objective multi-level linear fractional programming (FRMMFP) problem. First, an extension of interval method is presented to deal with roughness of the stated problem. Then, an iterative technique is proposed for linearization of fractional objectives. Finally, a modification of fuzzy approach is provided in the environment of the fully rough to solve the linear model. An example is provided for understanding the solution procedure of the proposed method.

The important issue of the aggregation preference is how to determine the weights associated with different ranking places and DEA models play an important role in this subject. DEA models use assignments of the same aggregate value (equal to unity) to evaluate multiple alternatives as efficient. Furthermore, overly diverse weights can appear, thus, the efficiency of different alternatives obtained by different sets of weights may be unable to be compared and ranked on the same basis. In order to solve two above problems, and rank all the alternatives on the same scale, in this paper, we propose a multiple objective programming (MOP) approach for generating a common set of weights in the DEA framework. Also, we develop a novel model to make a maximum discriminating among candidates’ rankings. Additionally, we present two scenarios to provide suitable strategies for solving the proposed MOP model.

Using fossil fuels in transportation sector has caused many environmental and economic problems. Therefore, the use of alternative fuel vehicles is necessary. Since such vehicles have limited fuel tank capacities, hence, frequent refueling is required. Regarding the possibility of the existence of different fuel costs in various refueling stations, the selection of suitable stations with the purpose of minimizing total cost of refueling is important. Moreover, minimizing the number of refuelings could be considered as another important criterion in refueling operations of a given trip. In this paper an integer bi-objective model is proposed to select suitable refueling stations considering two criteria of minimizing the total cost of refueling and minimizing the number of refuelings. To solve the proposed model, a new algorithm is suggested and its performance is compared with the weighted sum method of multi-objective optimization literature. The results show the superiority of the proposed solution approach.

Probabilistic or stochastic programming is a framework for modeling optimization problems that involve uncertainty.In this paper, we focus on multi-objective linear programmingproblems in which the coefficients of constraints and the righthand side vector are fuzzy random variables. There are several methodsin the literature that convert this problem to a stochastic orfuzzy problem. By using a special type of fuzzy inequality, wetransform the problem into a convenient stochastic problem. Thensome known methods are applied to obtain the optimal solution.Finally, the equivalent multi-objective problem is solved by aninteractive approach. A numerical example is provided to illustrate the procedure.

HLP (hub location problem) tries to find locations of hub facilities and assignment of nodes to extended facilities. Hubs are facilities to collect, arrange, and distribute commodities in telecommunication networks, cargo delivery systems, etc. Hubs are very crucial and their inaccessibility impresses on network whole levels. In this paper, first, total reliability of the network is defined based on considering the reliability values of nubs and arcs. Then, a reliable hub-and-spoke network design problem under uncertainty is introduced through the multi - objective programming method in which the parameters are random fuzzy variables. Indeed, we are making effort to either maximize the average reliability or minimize total cost. Then, the proposed reliable multi - objective hub-and-spoke network design problem under uncertainty is solved by a new method using Zimmermann fuzzy multi - objective programming and random fuzzy chance-constrained programming based on possibility theory. Finally, some benchmark problems are solved as numerical examples to clarify the described method and show its efficiency.

Traditional DEA models do not deal with imprecise data and assume that the data for all inputs and outputs are known exactly. Inverse DEA models can be used to estimate inputs for a DMU when some or all outputs and efficiency level of this DMU are increased or preserved. this paper studies the inverse DEA for fuzzy data. This paper proposes generalized inverse DEA in fuzzy data envelopment analysis.

Using alternative fuel vehicles is one of the ways to reduce the consumption of fossil fuels which have many negative environmental effects. An alternative fuel vehicle needs special planning for its refueling operations because of some reasons, e.g. limited number of refueling stations, uncertain refueling queue times in the stations, variable alternative fuel prices among the stations, etc. In this paper, a new problem as refueling an alternative fuel vehicle on a given path is formulated to minimize the cost of refueling and waiting times in the stations for refueling operations, simultaneously. To be more close to real-world situations, the waiting times are considered as intuitionistic fuzzy numbers in order to reflect uncertainty as well as hesitation due to various uncontrollable factors. To cope with the uncertainty of the problem, an intuitionistic fuzzy chance constrained method based on credibility measure is proposed to convert the fuzzy formulation to a crisp model. In order to tackle the bi-objective crisp formulation, a new interactive fuzzy solution method is proposed. A computational study on a real case from Turkey shows that the performance of the presented method is either better or the same as the approaches of the literature.}

Data envelopment analysis (DEA) is a nonparametric approach to estimate relative efficiency of Decision Making Units (DMUs). DEA and is one of the best quantitative approach and balanced scorecard (BSC) is one of the best qualitative method to measure efficiency of an organization. Since simultaneous evaluation of network performance of the quad areas of BSC model is considered as a necessity and separate use of DEA and BSC is not effective and leads to miscalculation of performance, integrated DEA-BSC model is applied. Regarding to multi-objective nature of the proposed model, two techniques including goal programming and weighted average method are used to solve such problems. At the end of the study, based on data relating to indexes of quad areas of BSC model, the results of the mentioned methods is compared. Besides assessing validation of the proposed model, the overall efficiency and each of the different stages of BSC is obtained. So that, finding a model for decision making units in various stages of BSC is the innovation of this research study.