A CHIM-based interactive Tchebycheff procedure for multiple objective decision making

This study presents a new solution procedure for multiple objective programming (MOP). It applies the concept of the normal boundary intersection (NBI) within the framework of the interactive weighted Tchebycheff procedure (IWTP). The proposed procedure is a collaborative approach to overcome the weak points inherent in both the NBI method and IWTP. In order to control the solution procedure of pinpointing a final solution properly, we parameterized the Pareto-frontier via a set of reference point vectors based on the convex hull of individual maxima (CHIM) instead of using the varying weights of each objective. Using well-distributed reference point vectors, we could identify well-distributed Pareto-optimal solutions, thereby eliminating the IWTP filtering stages and reducing the chance of missing the best compromise solution from the decision maker (DM)'s utility point of view. Moreover, by working with a sequence of progressively smaller subsets of reference point vectors, the DM can identify a final solution at earlier stages than with the IWTP.     

An extension of interactive method for solving multiple objective linear programming with fuzzy parameters

In this paper, we propose a method which introduce a relative distance from an ideal value as a criterion that assist the decision maker(DM)'s judgement in pair of comparisons. Further, to consider the fuzziness of each coefficients in modelling the multiple objective linear programming(MOLP) problem and the fuzziness of satisfaction toward the attainment of the goals, we introduce a fuzzy number to the coefficients and fuzzy goals, respectively.     

Solving multiple objective quasi-convex goal programming problems by linear programming

This study presents a novel means of resolving multiple objective goal programming (GP) problems with quasi-convex linear penalty functions. The proposed method initially expresses a quasi-convex function by the maximum operator of two convex functions, then solves it via a linear programming technique. The proposed method does not contain any zero–one variables; nor does it require dividing the multi-objective quasi-convex GP problem into large sub-problems as in conventional methods. Some illustrative examples are provided.     

Interactive multiple objective linear programming system implemented on a microcomputer

Linear programming is one of the most widely used Operations Research/Management Science techniques. Recently, multiple objective decision making has been well established as a practical approach to seek a satisfactory solution to a decision making problem. Much attention has been focused on a microcomputer as an economical management tool.

In this paper we propose an interactive goal attainment method using the eigenvector algorithm for solving a multiple objective linear programming problem interactively on microcomputers. In the software package Micro-LPS based on the method proposed, we design a conversational and user-friendly system in which the user commands are involved.     

An exponential membership function for fuzzy multiple objective linear programming

The operator “min” is one of the most frequently used aggregation operators in fuzzy decision. However, this operator is the softest operator and no allowance is made for any compensation. The “product” and other operators, some of them may be compensatory, are seldom used because of the nonlinearity of the resulting problem. In this paper, an exponential, instead of linear membership function is proposed. The advantages of using exponential membership are two fold. First, the resulting problems can be transformed to linear ones when the “product” and several other nonlinear aggregate operators are used. Secondly, exponential representation is more realistic than the linear ones usually used for some practical applications.     

一类基于多目标规划的线性鉴别准则

两类Fisher鉴别准则、大间距线性投影准则以及最大散度差鉴别准则都是直接用于模式分类的两类线性鉴别准则,它们的共同点是将“投影后数据的可分性达到最大的方向”作为最优投影方向。区别在于它们对数据可分性的定义有所不同。过去的研究成果表明,大间距线性投影分类器与支持向量机之间、大间距线性投影准则与最大散度差鉴别准则之间以及最大散度差鉴别准则与两类Fisher鉴别准则之间,均存在着这样或那样的联系。论文试图在以往研究成果的基础上进一步理清这些两类线性鉴别准则之间的内在关系,并建立一个统一的理论框架从而将基于投影后数据可分性的这些两类线性鉴别准则都纳入其中。     

A modified weighted tchebycheff metric for multiple objective programming

We show how to determine nondominated criterion vectors (and then nondominated solutions, if necessary) by a modified weighted Tchebycheff metric in cases when sets of all criterion vectors are finite or polyhedral.     

A multiple objective integer programming approach for planning franchise expansion

The number and configuration of franchise outlets in a market defines the distribution strategy of a franchise company. The introduction of new franchise outlets contributes to conflict between the franchisee and franchisor over the degree of market penetration. The selection of sites for new franchises is an important factor in the long-term profitability of many types of franchises. This selection process requires consideration of objectives of the franchisee and franchisor which are often conflicting in nature. This paper deals with the problem of locating new franchises in an existing franchise network using multiple objective integer programming models and methods.     

A combined fuzzy linear regression and fuzzy multiple objective programming approach for setting target levels in quality function deployment

Quality function deployment (QFD) is a systematic process for translating customer needs into engineering characteristics, and then communicating them throughout the enterprise in a way to ensure that details are quantified and controlled. The inherent fuzziness of relationships in QFD modeling justifies the use of fuzzy regression for estimating the relationships between both customer needs and engineering characteristics, and among engineering characteristics. Albeit QFD aims to maximize customer satisfaction, requirements related to enterprise satisfaction such as cost budget, extendibility, and technical difficulty also need to be considered. This paper presents a fuzzy multiple objective decision framework that includes not only fulfillment of engineering characteristics to maximize customer satisfaction, but also maximization of extendibility and minimization of technical difficulty of engineering characteristics as objectives subject to a financial budget constraint to determine target levels of engineering characteristics in product design. A real-world quality improvement problem is presented to illustrate the application of the decision approach.     

Combining interactive multiple goal linear programming with an inter-stakeholder communication matrix to generate land use options

An Interactive Multiple Goal Linear Programming (IMGLP) model is developed that considers objectives of multiple stakeholders, i.e. different farmer groups, district agricultural officers and agricultural scientists for agricultural land use analysis. The analysis focuses on crop selection; considering irrigated and non-irrigated crops such as rice, sugarcane, sorghum, cotton, millet, pulses and groundnut. Interests of the most important stakeholders, farmers, policy makers and water users association are investigated. Important objectives of the farmers are increased income and retaining paddy area; of the policy makers (Agricultural Department) increased farmers' income, maintaining rural employment, improve water-use efficiency, reduce fertiliser and biocide use and discourage farmers from cultivating marginal lands; of the water users association optimising water use. Scenarios have been constructed by combining objectives and constraints. A Stakeholder Communication Matrix (SCM) indicating the level of communication and information flow among stakeholders in the district was generated after a Participatory Rural Appraisal (PRA). Results of the scenarios generated with the IMGLP model were compared with the matrix. The relevance of analysing the results of the scenarios generated with the IMGLP model in the context of the SCM is illustrated for a sample set of scenarios. Scenario 1 (S1), where both the paddy area and the agricultural area are retained at the current level, is preferred by the farmers. However, the Agricultural Department would identify more easily with S10 in which the paddy area is reduced by 50% and the agricultural area by 20%, in accordance with the policy of limiting the area of high water-demanding crops and dissuading farmers from cultivating marginal lands, while the water users association would prefer S12, where water use is minimised by expanding the area of crops that are relatively less water-demanding. Income in S12 is 22% lower than in S1, while water use is 36% lower, and there is a significant reduction in biocide use. The conflict between S1 and S10 is compounded by the fact that communication between small-scale farmers and the Agricultural Department is relatively weak. Analysing the scenarios in the context of the SCM is useful to gain insight into the interactions among stakeholders in the system and take curative measures if required for improved communication. While the IMGLP model considers the bio-economics of the land use system, the SCM describes its social aspects, which may be critical for successful implementation of the IMGLP model.     

Using objective reduction and interactive procedure to handle many-objective optimization problems

A number of practical optimization problems are posed as many-objective (more than three objectives) problems. Most of the existing evolutionary multi-objective optimization algorithms, which target the entire Pareto-front are not equipped to handle many-objective problems. Though there have been copious efforts to overcome the challenges posed by such problems, there does not exist a generic procedure to effectively handle them. This paper presents a simplify and solve framework for handling many-objective optimization problems. In that, a given problem is simplified by identification and elimination of the redundant objectives, before interactively engaging the decision maker to converge to the most preferred solution on the Pareto-optimal front. The merit of performing objective reduction before interacting with the decision maker is two fold. Firstly, the revelation that certain objectives are redundant, significantly reduces the complexity of the optimization problem, implying lower computational cost and higher search efficiency. Secondly, it is well known that human beings are not efficient in handling several factors (objectives in the current context) at a time. Hence, simplifying the problem a priori addresses the fundamental issue of cognitive overload for the decision maker, which may help avoid inconsistent preferences during the different stages of interactive engagement. The implementation of the proposed framework is first demonstrated on a three-objective problem, followed by its application on two real-world engineering problems.     

A linear programming procedure based on de la Vallée Poussin's minimax estimation procedure

It is shown that de la Vallée Poussin's 1911 procedure for the solution of linear minimax estimation problems can be adjusted to solve a class of linear programming problems. A general procedure of this type should have been accessible in the 1910s, but the historical record shows that no such procedure was developed before the work of Kantorovich, Koopmans, and Dantzig in the 1940s.     

集成供应链管理的多目标规划研究

目前,供应链管理已经成为学术研究的一个热点问题,也是企业战略管理的一项重要内容。为此首先使用多目标规划的方法描述了供应链及其成员的运作性能、供应链的协调运作、供应链成员的利润等,建立了由一个制造商和一个供应商构成的多产品、多阶段集成供应链管理绩效决策模型;其次通过应用算例的研究验证了模型的有效性和可行性;最后,针对各种参数的变化,对模型进行了灵敏度分析,并与分散供应链管理绩效决策模型进行了对照研究,为优化供应链绩效、拓展市场需求、开发原材料供应渠道提供了决策参考。     

Literate programming simplified

Literate programming tools let you arrange the parts of a program in any order and extract documentation and code from the same source file. The author argues that language-dependence and feature complexity have hampered acceptance of these tools, then offers a simpler alternative     

An interactive analytic center trade-off cutting plane algorithm for multiobjective linear programming

This paper proposes the use of an interior point algorithm for Multiobjective Linear Programming problems. At each iteration of the algorithm, the decision maker furnishes his precise trade-offs. From these trade-offs, a cut is formed in the objective space. This cut induces a cut in the decision space that defines a half-space of promising points. We compute the analytic center of the restricted feasible region in the decision space and then we calculate the trade-offs of the decision maker at the image of the analytic center in the objective space. Therefore, we obtain a trajectory of analytic centers that converges to the best compromise solution. Since the proposed algorithm moves through the interior of the feasible region, it avoids the combinatorial difficulties of visiting extreme points and is less sensitive to problem size. We illustrate the method through a numerical example and provide computational experience.     

Multi-instance classification based on regularized multiple criteria linear programming

Regularized multiple criteria linear programming (RMCLP) model is a new powerful method for classification and has been used in various real-life data mining problems. In this paper, a new Multi-instance Classification method based on RMCLP was proposed (called MI-RMCLP), which includes two algorithms for linearly separable case and nonlinearly case separately. The key point of this method, instead of a mixed integer quadratic programming in MI-SVM, is that it is able to deal with multi-instance learning problem by an iterative strategy solving sequential quadratic programming problems. All experiment results have shown that MI-RMCLP method can converge to the optimal value in limited iterative steps and be a competitive method in multi-instance learning classification.