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.

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.

A Dimensional Reduction Approach Based on Essential Constraints in Linear Programming

This paper presents a new dimension reduction strategy for medium and large-scale linear programming problems. The proposed method uses a subset of the original constraints and combines two algorithms: the weighted average and the cosine simplex algorithm. The first approach identifies binding constraints by using the weighted average of each constraint, whereas the second algorithm is based on the cosine similarity between the vector of the objective function and the constraints. These two approaches are complementary, and when used together, they locate the essential subset of initial constraints required for solving medium and large-scale linear programming problems. After reducing the dimension of the linear programming problem using the subset of the essential constraints, the solution method can be chosen from any suitable method for linear programming. The proposed approach was applied to a set of well-known benchmarks as well as more than 2000 random medium and large-scale linear programming problems. The results are promising, indicating that the new approach contributes to the reduction of both the size of the problems and the total number of iterations required. A tree-based classification model also confirmed the need for combining the two approaches. A detailed numerical example, the general numerical results, and the statistical analysis for the decision tree procedure are presented.

A KIND OF FUZZY MULTI-OBJECTIVE LINEAR PROGRAMMING PSOBLEMS BASED ON INTER VALVALUED FUZZY SETS

This paper presents a general solution procedure and an interactive fuzzy satisfying method for a kind of fuzzy multi-objective linear programming-problems based on interval valued fuzzy sets. Firstly, a fuzzy set of the fuzzy solutions, which can be focused on providing complete information for the final decision, can be obtained by the proposed tolerance analysis of a non-dominated set. Secondly, the satisfying solution for the decisionmaker can be derived from Pareto optimal solutions by updating the current reference membership levels on the basis of the current levels of the membership functions together with the trade-off rates between the membership functions.

Determining Efficient Solutions of Multi-Objective Linear Fractional Programming Problems and Application

In this paper, a modified method to find the efficient solutions of multi-objective linear fractional programming (MOLFP) problems is presented. While some of the previously proposed methods provide only one efficient solution to the MOLFP problem, this modified method provides multiple efficient solutions to the problem. As a result, it provides the decision makers flexibility to choose a better option from alternatives according to their financial position and their level of satisfaction of objectives. A numerical example is provided to illustrate the modified method and also a real life oriented production problem is modeled and solved.

Principal-subordinate hierarchical multi-objective programming model of initial water rights allocation

The principal-subordinate hierarchical multi-objective programming model of initial water rights allocation was developed based on the principle of coordinated and sustainable development of different regions and water sectors within a basin. With the precondition of strictly controlling maximum emissions rights, initial water rights were allocated between the first and the second levels of the hierarchy in order to promote fair and coordinated development across different regions of the basin and coordinated and efficient water use across different water sectors, realize the maximum comprehensive benefits to the basin, promote the unity of quantity and quality of initial water rights allocation, and eliminate water conflict across different regions and water sectors. According to interactive decision-making theory, a principal-subordinate hierarchical interactive iterative algorithm based on the satisfaction degree was developed and used to solve the initial water rights allocation model. A case study verified the validity of the model.

Approach for uncertain multi-objective programming problems with correlated objective functions under C_(EV) criterion

An uncertain multi-objective programming problem is a special type of mathematical multi-objective programming involving uncertain variables. This type of problem is important because there are several uncertain variables in real-world problems.Therefore, research on the uncertain multi-objective programming problem is highly relevant, particularly those problems whose objective functions are correlated. In this paper, an approach that solves an uncertain multi-objective programming problem under the expected-variance value criterion is proposed. First, we define the basic framework of the approach and review concepts such as a Pareto efficient solution and expected-variance value criterion using an order relation between various uncertain variables.Second, the uncertain multi-objective problem is converted into an uncertain single-objective programming problem via a linear weighted method or ideal point method. Then the problem is transformed into a deterministic single objective programming problem under the expected-variance value criterion. Third, four lemmas and two theorems are proved to illustrate that the optimal solution of the deterministic single-objective programming problem is an efficient solution to the original uncertainty problem. Finally, two numerical examples are presented to validate the effectiveness of the proposed approach.

New approach for uncertain random multi-objective programming problems based on C_(ESD) criterion

To overcome the defects that the traditional ap-proach for multi-objective programming under uncertain ran-dom environment(URMOP)neglects the randomness and uncer-tainty of the problem and the volatility of the results,a new ap-proach is proposed based on expected value-standard devi-ation value criterion(C_(ESD) criterion).Firstly,the effective solution to the URMOP problem is defined;then,by applying sequence relationship between the uncertain random variables,the UR-MOP problem is transformed into a single-objective program-ming(SOP)under uncertain random environment(URSOP),which are transformed into a deterministic counterpart based on the C_(ESD) criterion.Then the validity of the new approach is proved that the optimal solution to the SOP problem is also effi-cient for the URMOP problem;finally,a numerical example and a case application are presented to show the effectiveness of the new approach.

MULTI-OBJECTIVE PROGRAMMING MODEL OF TROPICAL CROPS IN HAINAN ISLAND

According to Hainan Island's biological characteristics, and existing structure of productivity of tropical crops and local climatic conditions, this paper carries on regional division of tropical crops by fuzzy mathematics. Based on calculation of basic parameters for tl1e formation of production, near-tem optimum models of tropical crops structure of each region was established by means of multi-objective programming, and a far-term grey programming model was set up through the above-mentioned near-term model and prediction of future parameters. Conclusion shows that the near-term programming may raise the profit by 5. 1-55.7 percent and far-tem programming by 54-90 percent, both gainingobvious economic benefits.

MULTI-OBJECTIVE PROGRAMMING FOR AIRPORT GATE REASSIGNMENT

To improve the efficiency of gate reassignment and optimize the plan of gate reassignment,the concept of disruption management is introduced,and a multi-objective programming model for airport gate reassignment is proposed.Considering the interests of passengers and the airport,the model minimizes the total flight delay,the total passengers′walking distance and the number of flights reassigned to other gates different from the planned ones.According to the characteristics of the gate reassignment,the model is simplified.As the multi-objective programming model is hard to reach the optimal solutions simultaneously,a threshold of satisfactory solutions of the model is set.Then a simulated annealing algorithm is designed for the model.Case studies show that the model decreases the total flight delay to the satisfactory solutions,and minimizes the total passengers′walking distance.The least change of planned assignment is also reached.The results achieve the goals of disruption management.Therefore,the model is verified to be effective.

Estimating the Macroeconomic Costs of CO_2 Emission Reduction in China Based on Multi-objective Programming

This paper estimates the macroeconornic costs of CO2 emission reduction in China employing the input-output analysis with the multi-objective programming approach. The results show that the effect of reducing CO2 emissions on China＇s economy is significant. Under the present conditions, the estimated macroeconomic costs of CO2 emission reduction in 2010 for China are approximately 3,100-4,024 RMB t-1. The stronger the abatement actions, the higher the macroeconomic costs of per unit emission reduction would be. Excavation industry, oil industry, chemical industry, and metal smelting industry have high potential to abate their CO2 emissions.

Compactness, Contractibility and Fixed Point Properties of the Pareto Sets in Multi-Objective Programming

This paper presents the Pareto solutions in continuous multi-objective mathematical programming. We discuss the role of some assumptions on the objective functions and feasible domain, the relationship between them, and compactness, contractibility and fixed point properties of the Pareto sets. The authors have tried to remove the concavity assumptions on the objective functions which are usually used in multi-objective maximization problems. The results are based on constructing a retraction from the feasible domain onto the Pareto-optimal set.

Path Selection of Multimodal Transport Based on Multi-Objective Mixed Integer Programming

Based on “One Belt and One Road”, this paper studies the path selection of multimodal transport by using the method of multi-objective mixed integer programming. Therefore, this paper studies the factors of transportation time, transportation cost and transportation safety performance, and establishes a mathematical model. In addition, the method of multi-objective mixed integer programming is used to comprehensively consider the different emphasis and differences of customers on cargo transportation. Then we use planning tools of Microsoft Excel to solve path selection and to determine whether the chosen path is economical and reliable. Finally, a relatively complex road network is built as an example to verify the accuracy of this planning 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.

Generating Efficient Solutions in Bilevel Multi-Objective Programming Problems

In this paper, we address bilevel multi-objective programming problems (BMPP) in which the decision maker at each level has multiple objective functions conflicting with each other. Given a BMPP, we show how to construct two artificial multiobjective programming problems such that any point that is efficient for both the two problems is an efficient solution of the BMPP. Some necessary and sufficient conditions for which the obtained result is applicable are provided. A complete procedure of the implementation of an algorithm for generating efficient solutions for the linear case of BMPP is presented. A numerical example is provided to illustrate how the algorithm operates.

A Penalty Function Algorithm with Objective Parameters and Constraint Penalty Parameter for Multi-Objective Programming

In this paper, we present an algorithm to solve the inequality constrained multi-objective programming (MP) by using a penalty function with objective parameters and constraint penalty parameter. First, the penalty function with objective parameters and constraint penalty parameter for MP and the corresponding unconstraint penalty optimization problem (UPOP) is defined. Under some conditions, a Pareto efficient solution (or a weakly-efficient solution) to UPOP is proved to be a Pareto efficient solution (or a weakly-efficient solution) to MP. The penalty function is proved to be exact under a stable condition. Then, we design an algorithm to solve MP and prove its convergence. Finally, numerical examples show that the algorithm may help decision makers to find a satisfactory solution to MP.

Optimality for Multi-Objective Programming Involving Arcwise Connected d-Type-I Functions

This paper deals with the optimality conditions and dual theory of multi-objective programming problems involving generalized convexity. New classes of generalized type-I functions are introduced for arcwise connected functions, and examples are given to show the existence of these functions. By utilizing the new concepts, several sufficient optimality conditions and Mond-Weir type duality results are proposed for non-differentiable multi-objective programming problem.

A non-monotone Phase-1 method in linear programming

To gain superior computational efficiency, it might be necessary to change the underlying philosophy of the simplex method. In this paper, we propose a Phase-1 method along this line. We relax not only the conventional condition that some function value increases monotonically, but also the condition that all feasible variables remain feasible after basis change in Phase-1. That is, taking a purely combinatorial approach to achieving feasibility. This enables us to get rid of ratio test in pivoting, reducing computational cost per iteration to a large extent. Numerical results on a group of problems are encouraging.

Linear Programming建模研讨

研究用图解法、simplex method和匈牙利法建立Linear Programming的数学模型并求得了最优解.结果表明:对仅有两个变量的Linear Programming,既可通过图解法求得最优解;也可用单纯形表简便地求得最优解;而对任务和人数不等的assignment problem,则用匈牙利法求最优解.

Design of S-band photoinjector with high bunch charge and low emittance based on multi-objective genetic algorithm

High-brightness electron beams are required to drive LINAC-based free-electron lasers(FELs)and storage-ring-based synchrotron radiation light sources.The bunch charge and RMS bunch length at the exit of the LINAC play a crucial role in the peak current;the minimum transverse emittance is mainly determined by the injector of the LINAC.Thus,a photoin-jector with a high bunch charge and low emittance that can simultaneously provide high-quality beams for 4th generation synchrotron radiation sources and FELs is desirable.The design of a 1.6-cell S-band 2998-MHz RF gun and beam dynamics optimization of a relevant beamline are presented in this paper.Beam dynamics simulations were performed by combining ASTRA and the multi-objective genetic algorithm NSGA II.The effects of the laser pulse shape,half-cell length of the RF gun,and RF parameters on the output beam quality were analyzed and compared.The normalized transverse emittance was optimized to be as low as 0.65 and 0.92 mm·mrad when the bunch charge was as high as 1 and 2 nC,respectively.Finally,the beam stability properties of the photoinjector,considering misalignment and RF jitter,were simulated and analyzed.