Some Difficulties in Applying Interactive Compromise Programming Illustrated by a Recent Method and a Case Study

The paper presents some of the difficulties in applying interactive, and interactive compromise, programming methods to real-life problems. These include the problem of dominated solutions when multiple optimal solutions exist to single objective function optimization, cycling, and the depiction of the analyst as a silent spectator in the decision making process. By taking as an example a recently proposed interactive compromise programming method, these difficulties are illustrated and necessary modifications are proposed to overcome these difficulties. These are further elucidated by a case study.     

Multi-Objective Interactive Programming

This paper proposes a method for finding optimal, or near optimal, solutions for problems involving m objective functions, where there is an overall criterion which is a weighted sum of the m objective functions, but where the weights are, initially, unknown. The process is an interactive one, beginning with a set within which the actual weighting vector is known to lie, and progressively cutting down the size of the set until an acceptable solution is found. A by-product of the procedure is an iterative method for finding the generators of the polyhedral cones, within which the weighting vector must lie, at each stage.     

Portfolio Selection: A Compromise Programming Solution

A surrogate for an investor's bi-criteria utility function (profitability, safety) is proposed as an alternative methodology for selecting portfolios. The optimum is approximated by resorting to a recent utility theorem expounded in multi-criteria analysis. This method is developed for an ‘average’ investor and could be used as a routine procedure by investment consultants with incomplete information of the client's utility function.     

Interactive Sequential Goal Programming

This paper introduces a new solution method based on Goal Programming for Multiple Objective Decision Making (MODM) problems. The method, called Interactive Sequential Goal Programming (ISGP), combines and extends the attractive features of both Goal Programming and interactive solution approaches for MODM problems. ISGP is applicable to both linear and non-linear problems. It uses existing single objective optimization techniques and, hence, available computer codes utilizing these techniques can be adapted for use in ISGP. The non-dominance of the "best-compromise" solution is assured. The information required from the decision maker in each iteration is simple. The proposed method is illustrated by solving a nutrition problem.     

多目标线性规划模糊算法与折衷算法分析

本分析了多目标线性规划中“min”算子的非补偿性和“算术平均”算子的不平衡性,并在此基础上论述了两阶段模糊算法与经典折衷算法之间的内在联系。     

双层规划的递阶交互决策有效化方法

本文讨论了协调集上双层规划问题解的性质,所得结论表明上层将所得利益全部让给下层,或下层将所得利益全部让给上层.当决策者不满足此种有效化方式时,必须寻找体现递阶结构的有效化方法.本文给出了一种保持递阶结构的递阶交互决策有效化方法.该方法适用于下层有多个平行子问题的双层线性规划.     

多目标交互可行方向法

对于多目标非线性规划问题，本文借助修正Zoutendijk法的可行方向思想，利用ε－约束问题的K－T乘子和决策者提供的权衡比产生变形标量化问题的可行下降方向，逐步求得决策者满意的有效解．     

多目标非线性规划的可行方向交互算法

本文提出一个求解多目标非线性规划问题的交互规划算法．在每一轮迭代中,此法仅要求决策者提供目标间权衡比的局部信息．算法中的可行方向是基于求解非线性规划问题的Topkis－Veinott法构千的．我们证明,在一定条件下,此算法收敛于问题的有效解．     

Interactive Multi-Objective Programming: Its Aims,Applications and Demands

The past decade has seen a considerable development of techniques designed to help decision makers faced with problems involving conflicting objectives. In particular, a family of methods known collectively as interactive multi-objective programming has come to the fore. This paper presents the underlying rationale of such methods, albeit as seen by a devil's advocate, briefly surveys some areas of application, but then questions the validity of these methods because their assumptions are not supported by the empirical results of behavioural decision theory.     

两人交叉决策联合最优解的存在性

本文探讨了两人交叉规划问题联合最优解的存在性．交叉规划问题来源于具有冲突的经济均衡问题,它的研究在理论和应用上具有重要的意义．     

基于交互式模糊规划方法的可持续闭环供应链网络规划

在市场需求、设施开设成本和产品回收率不确定的条件下,采用一种交互式可能性规划方法,研究由多个工厂、分销点、市场和废旧点构成的可持续闭环供应链网络设计问题。基于可持续闭环供应链网络结构,构建以企业运营成本和环境伤害最小、社会效益最大为目标的混合整数规划模型。同时,引入改进Epsilon约束方法将多目标优化问题转化为单目标优化问题,在此基础上提出一种两阶段可能性规划方法,基于TH模糊方法对不确定性参数进行处理。最后,通过数值实例,验证本文所建可持续闭环供应链网络模型的有效性,并对悲观-乐观值、不确定参数最低可接受水平β、可调参数γ进行敏感性分析;通过与其他模糊方法对比表明,采用TH模糊方法能得到稳定的最优解。     

Application of Compromise Programming to a semi-detached housing development in order to balance economic and environmental criteria

European Energy Performance of Buildings Directives DE promote energy efficiency in buildings. Under these Directives, the European Union States must apply minimum requirements regarding the energy performance of buildings and ensure the certification of their energy performance. The Directives set only the basic principles and requirements, leaving a significant amount of room for the Member States to establish their specific mechanisms, numeric requirements and ways to implement them, taking into account local conditions. With respect to the Spanish case, the search for buildings that are more energy efficient results in a conflict between users’ economic objectives and society's environmental objectives. In this paper, Compromise Programming is applied to help in the decision-making process. An appropriate distribution of types of dwellings, according to their energy performance and to the climatic zone considered in Spain, will be suggested. Results provide a compromise solution between both objectives.     

Interactive Goal Programming on the Microcomputer to Establish Priorities for Small Business

This paper presents an application of interactive goal programming on the microcomputer for small business. The illustrative application in this paper is based on real data obtained from a small business in Wisconsin, U.S.A. The microcomputer-based interactive system indicates that the goal programming approach enables the small-business manager/owner to test a variety of alternative strategies reflected by goal levels and priority structures.     

An Interactive Method as an Aid in Solving Bicriterion Mathematical Programming Problems

In this paper, a man-machine interactive method is presented as an aid in solving the bicriterion mathematical programming problem. It is assumed that the two objective functions are real-valued functions of the decision variables which are themselves constrained to some compact and nonempty set. The overall utility function is assumed to be unknown explicitly to the decision-maker but is assumed to be a real-valued function defined on the pairs of feasible values of the objective functions and monotone non-decreasing in each argument. The decision-maker is required only to provide yes or no answers to questions regarding the desirability of increase or decrease in objective function values of solutions that he will not accept as optimal. Convergence of the method is indicated and a numerical example is presented in order to demonstrate its applicability.     

Unified Interactive Multiple Objective Programming: An Open Architecture For Accommodating New Procedures

It has previously been shown that nine of the most prominent procedures of interactive multiple objective programming can be considered as special cases of a common procedure called the unified algorithm. In this paper, we show how four additional procedures can be similarly included in the unified approach. Also, the paper presents a procedure-switching matrix that depicts the possibilities for switching from one procedure to another, one iteration to the next, in the unified algorithm if so directed by a user.     

Global Optimization in Practice: An Application to Interactive Multiple Objective Linear Programming

A multiple objective linear programming problem (P) involves the simultaneous maximization of two or more conflicting linear objective functions over a nonempty polyhedron X. Many of the most popular methods for solving this type of problem, including many well-known interactive methods, involve searching the efficient set X _E of the problem. Generally, however, X _E is a complicated, nonconvex set. As a result, concepts and methods from global optimization may be useful in searching X _E. In this paper, we will explain in theory, and show via an actual application to citrus rootstock selection in Florida, how the potential usefulness of the well-known interactive method STEM for solving problem (P) in this way, can depend crucially upon how accurately certain global optimization problems involving minimizations over X _E are solved. In particular, we will show both in theory and in practice that the choice of whether to use the popular but unreliable payoff table approach or to use one of the lesser known, more accurate global optimization methods to solve these problems can determine whether STEM succeeds or fails as a decision aid. Several lessons and conclusions of transferable value derived from this research are also given.     

MAGIC: The Design and Use of an Interactive Modelling Language for Mathematical Programming

The desirability of computer aids for the building as well asthe solving of Mathematical Programming models is argued. Ashort survey is given of some of the distinct approaches possiblein designing matrix generators/languages for such a role. Itis then suggested that the approach most suited to general modelsis to design a language close to widely used mathematical notation.The facilities needed in such a language are discussed and theimplementation using the MAGIC (MAtrix Generator InstructionConvertor) language described.     

Minimum Cost Compromise Mixed Allocation

When more than one (say p) characteristics in multivariate stratified population are defined on each unit of the population, the individual optimum allocations may differ widely and can not be used practically. Moreover, there may be a situation such that no standard allocation is advisable to all the strata, for one reason or another. In such a situation, Clark and Steel (J R Stat Soc, Ser D Stat 49(2):197–207, 2000) suggested that different allocations may be used for different groups of strata having some common characteristics for double sampling in stratification. Later on, Ahsan et al. (Aligarh J Stat 25:87–97, 2005) used the same concept in univariate stratified sampling. They minimized the variance of the stratified sample mean for a fixed cost to obtain an allocation and called this allocation “mixed allocation”. In the present paper, a “compromise mixed allocation” is worked out for the fixed precisions of the estimates of the p-population means of a multivariate stratified population. A numerical example is also presented.