Solving Multi-Objective Linear Programming Problem by Statistical Averaging Method with the Help of Fuzzy Programming Method

A multi-objective linear programming problem is made from fuzzy linear programming problem. It is due the fact that it is used fuzzy programming method during the solution. The Multi objective linear programming problem can be converted into the single objective function by various methods as Chandra Sen’s method, weighted sum method, ranking function method, statistical averaging method. In this paper, Chandra Sen’s method and statistical averaging method both are used here for making single objective function from multi-objective function. Two multi-objective programming problems are solved to verify the result. One is numerical example and the other is real life example. Then the problems are solved by ordinary simplex method and fuzzy programming method. It can be seen that fuzzy programming method gives better optimal values than the ordinary simplex method.

Roughly <i>B</i>-invex Multi-Objective Programming Problems

In this paper, we shall be interested in characterization of efficient solutions for special classes of problems. These classes consider roughly B-invexity of involved functions. Sufficient and necessary conditions for a feasible solution to be an efficient or properly efficient solution are obtained.

Solving Fuzzy Multi-Objective Linear Programming Problem by Applying Statistical Method

In this paper, the statistical averaging method and the new statistical averaging methods have been used to solve the fuzzy multi-objective linear programming problems. These methods have been applied to form a single objective function from the fuzzy multi-objective linear programming problems. At first, a numerical example of solving fuzzy multi-objective linear programming problem has been provided to validate the maximum risk reduction by the proposed method. The proposed method has been applied to assess the risk of damage due to natural calamities like flood, cyclone, sidor, and storms at the coastal areas in Bangladesh. The proposed method of solving the fuzzy multi-objective linear programming problems by the statistical method has been compared with the Chandra Sen’s method. The numerical results show that the proposed method maximizes the risk reduction capacity better than Chandra Sen’s method.

Global convergent algorithm for the bilevel linear fractional-linear programming based on modified convex simplex method

A global convergent algorithm is proposed to solve bilevel linear fractional-linear programming, which is a special class of bilevel programming. In our algorithm, replacing the lower level problem by its dual gap equaling to zero, the bilevel linear fractional-linear programming is transformed into a traditional sin- gle level programming problem, which can be transformed into a series of linear fractional programming problem. Thus, the modi- fied convex simplex method is used to solve the infinite linear fractional programming to obtain the global convergent solution of the original bilevel linear fractional-linear programming. Finally, an example demonstrates the feasibility of the proposed algorithm.

Goal Programming for Solving Fractional Programming Problem in Fuzzy Environment

This paper is comprised of the modeling and optimization of a multi objective linear programming problem in fuzzy environment in which some goals are fractional and some are linear. Here, we present a new approach for its solution by using α-cut of fuzzy numbers. In this proposed method, we first define membership function for goals by introducing non-deviational variables for each of objective functions with effective use of α-cut intervals to deal with uncertain parameters being represented by fuzzy numbers. In the optimization process the under deviational variables are minimized for finding a most satisfactory solution. The developed method has also been implemented on a problem for illustration and comparison.

Fixed-Point Iteration Method for Solving the Convex Quadratic Programming with Mixed Constraints

The present paper is devoted to a novel smoothing function method for convex quadratic programming problem with mixed constrains, which has important application in mechanics and engineering science. The problem is reformulated as a system of non-smooth equations, and then a smoothing function for the system of non-smooth equations is proposed. The condition of convergences of this iteration algorithm is given. Theory analysis and primary numerical results illustrate that this method is feasible and effective.

Time variant multi-objective linear fractional interval-valued transportation problem

This paper studies a time-variant multi-objective linear fractional transportation problem. In reality, transported goods should reach in destinations within a specific time. Considering the importance of time, a time-variant multi-objective linear fractional transportation problem is formulated here. We take into account the parameters as cost, supply and demand are interval valued that involved in the proposed model, so we treat the model as a multi-objective linear fractional interval transportation problem. To solve the formulated model, we first convert it into a deterministic form using a new transformation technique and then apply fuzzy programming to solve it. The applicability of our proposed method is shown by considering two numerical examples. At last, conclusions and future research directions regarding our study is included.

Multi-Objective Optimization of Pilots’ FFS Recurrent Training Problem

Two multi-objective programming models are built to describe Pilots’ full flight simulator (FFS) recurrent training (PFRT) problem. There are two objectives for them. One is the best matching of captains and copilots in the same aircraft type. The other is that pilots could attend his training courses at proper month. Usually the two objectives are conflicting because there are copilots who will promote to captains or transfer to other aircraft type and new trainees will enter the company every year. The main theme in the research is to find the final non-inferior solutions of PFRT problem. Graph models are built to help to analyze the problem and we convert the original problem into a longest-route problem with weighted paths. An algorithm is designed with which we can obtain all the non-inferior solutions by a graphic method. A case study is present to demonstrate the effectiveness of the algorithm as well.

The Optimal Conditions of the Linear Fractional Programming Problem with Constraint

在这篇文章，作者讨论线性部分编程问题的最佳的条件并且证明一个局部地可选的答案是一个全球性可选的答案，局部地最佳的答案能与限制状况在一个基本可行答案被达到。

Solving a Class of Nonlinear Programming Problems via a Homotopy Continuation Method

In this paper we present a homotopy continuation method for finding the Karush-Kuhn-Tucker point of a class of nonlinear non-convex programming problems. Two numerical examples are given to show that this method is effective. It should be pointed out that we extend the results of Lin et al. （see Appl. Math. Comput., 80（1996）, 209-224） to a broader class of non-convex programming problems.

Multicut L-Shaped Algorithm for Stochastic Convex Programming with Fuzzy Probability Distribution

Two-stage problem of stochastic convex programming with fuzzy probability distribution is studied in this paper. Multicut L-shaped algorithm is proposed to solve the problem based on the fuzzy cutting and the minimax rule. Theorem of the convergence for the algorithm is proved. Finally, a numerical example about two-stage convex recourse problem shows the essential character and the efficiency.

Optimality Conditions for Generalized Convex Nonsmooth Uncertain Multi-objective Fractional Programming

This paper aims at studying optimality conditions of robust weak efficient solutions for a nonsmooth uncertain multi-objective fractional programming problem(NUMFP).The concepts of two types of generalized convex function pairs,called type-I functions and pseudo-quasi-type-I functions,are introduced in this paper for(NUMFP).Under the assumption that(NUMFP)satisfies the robust constraint qualification with respect to Clarke subdifferential,necessary optimality conditions of the robust weak efficient solution are given.Sufficient optimality conditions are obtained under pseudo-quasi-type-I generalized convexity assumption.Furthermore,we introduce the concept of robust weak saddle points to(NUMFP),and prove two theorems about robust weak saddle points.The main results in the present paper are verified by concrete examples.

ON ALTERNATIVE OPTIMAL SOLUTIONS TO QUASIMONOTONIC PROGRAMMING WITH LINEAR CONSTRAINTS

In this paper, the nonlinear programming problem with quasimonotonic （ both quasiconvex and quasiconcave ）objective function and linear constraints is considered. With the decomposition theorem of polyhedral sets, the structure of optimal solution set for the programming problem is depicted. Based on a simplified version of the convex simplex method, the uniqueness condition of optimal solution and the computational procedures to determine all optimal solutions are given, if the uniqueness condition is not satisfied. An illustrative example is also presented.

Solving the Binary Linear Programming Model in Polynomial Time

The paper presents a technique for solving the binary linear programming model in polynomial time. The general binary linear programming problem is transformed into a convex quadratic programming problem. The convex quadratic programming problem is then solved by interior point algorithms. This settles one of the open problems of whether P = NP or not. The worst case complexity of interior point algorithms for the convex quadratic problem is polynomial. It can also be shown that every liner integer problem can be converted into binary linear problem.

Resource Planning and Allocation Problem Under Uncertain Environment

This paper generalizes the classic resource allocation problem to the resource planning and allocation problem, in which the resource itself is a decision variable and the cost of each activity is uncertain when the resource is determined. The authors formulate this problem as a two-stage stochastic programming. The authors first propose an efficient algorithm for the case with finite states. Then, a sudgradient method is proposed for the general case and it is shown that the simple algorithm for the unique state case can be used to compute the subgradient of the objective function. Numerical experiments are conducted to show the effectiveness of the model.

Existence results for generalized vector equilibrium problems with applications

By a coincidence theorem, some existence theorems of solutions are proved for four types of generalized vector equilibrium problems with moving cones. Applications to the generalized semi-infinite programs with the generalized vector equilibrium constraints under the mild conditions are also given. The results of this paper unify and improve the corresponding results in the previous literature.

Duality for a Control Problem Involving Support Functions

Mond-Weir type duality for control problem with support functions is investigated under generalized convexity conditions. Special cases are derived. A relationship between our results and those of nonlinear programming problem containing support functions is outlined.

A NEW DUAL PROBLEM FOR NONDIFFERENTIABLE CONVEX PROGRAMMING

This paper gives a new dual problem for nondifferentiable convex programming and provesthe properties of weak duality and strong duality and offers a necessary and sufficient condition ofstrong duality.

Project Scheduling Problem with Uncertain Variables

Project scheduling problem is mainly to determine the schedule of allocating resources in order to balance the total cost and the completion time. This paper chiefly uses chance theory to introduce project scheduling problem with uncertain variables. First, two types of single-objective programming models with uncertain variables as uncertain chance-constrained model and uncertain maximization chance-constrained model are established to meet different management requirements, then they are extended to multi-objective programming model with uncertain variables.

An Efficient Random Algorithm for Box Constrained Weighted Maximin Dispersion Problem

The box-constrained weighted maximin dispersion problem is to find a point in an n-dimensional box such that the minimum of the weighted Euclidean distance from given m points is maximized. In this paper, we first reformulate the maximin dispersion problem as a non-convex quadratically constrained quadratic programming (QCQP) problem. We adopt the successive convex approximation (SCA) algorithm to solve the problem. Numerical results show that the proposed algorithm is efficient.