A relaxed cutting plane algorithm for solving fuzzy inequality systems

This paper studies a system of infinitely many fuzzy inequalities with concavemembership functions. By using the tolerance approach, we show that solving such system can be reduced to a semi-infinite programming problem. A relaxed cutting plane algorithm is proposed. In each iteration, we solve a finite convex optimization problem and add one or two more constraints. The proposed algorithm chooses a point at which the infinite constraints are violated to a degree rather than at which the violation is maximized. The iterative process ends when an optimal solution is identified. A convergence proof, under some mild conditions, is given. An efficient implementation based on the "method of centres" with "entropic regularization" techniques is also included. Some computational results confirm the efficiency of the proposed method and show its potential for solving large scale problems.     

Revised multi-choice goal programming

Chang [C.-T. Chang, Multi-choice goal programming, Omega, The Inter. J. Manage. Sci. 35 (2007) 389–396] has recently proposed a new method namely multi-choice goal programming (MCGP) for multi-objective decision problems. The multi-choice goal programming allows the decision maker to set multi-choice aspiration levels for each goal to avoid underestimation of the decision. However, to express the multi-choice aspiration levels, multiplicative terms of binary variables are involved in their model. This leads to difficult implementation and it is not easily understood by industrial participants. In this paper, we propose an alternative method to formulate the multi-choice aspiration levels with two contributions: (1) the alternative approach does not involve multiplicative terms of binary variables, this leads to more efficient use of MCGP and is easily understood by industrial participants, and (2) the alternative approach represents a linear form of MCGP which can easily be solved by common linear programming packages, not requiring the use of integer programming packages. In addition, a new concept of constrained MCGP is introduced for constructing the relationships between goals in this paper. Finally, to demonstrate the usefulness of the proposed method, an illustrate example is included.     

Combining simulation and goal programming for healthcare planning in a medical assessment unit

This paper describes a detailed simulation model for healthcare planning in a medical assessment unit (MAU) of a general hospital belonging to the national health service (NHS), UK. The MAU is established to improve the quality of care given to acute medical patients on admission, and to provide the organisational means of rapid assessment and investigation in order to avoid unnecessary admissions. The simulation model enables different scenarios to be tested to eliminate bottlenecks in order to achieve optimal clinical workflow. The link between goal programming (GP) and simulation for efficient resource planning is explored. A GP model is developed for trade-off analysis of the results obtained from the simulation. The implications of MAU management preferences to various objectives are presented.     

Satisfying optimization method based on goal programming for fuzzy multiple objective optimization problem

This paper proposes a satisfying optimization method based on goal programming for fuzzy multiple objective optimization problem. The aim of this presented approach is to make the more important objective achieving the higher desirable satisfying degree. For different fuzzy relations and fuzzy importance, the reformulated optimization models based on goal programming is proposed. Not only the satisfying results of all the objectives can be acquired, but also the fuzzy importance requirement can be simultaneously actualized. The balance between optimization and relative importance is realized. We demonstrate the efficiency, flexibility and sensitivity of the proposed method by numerical examples.     

含模糊变量的水污染控制系统研究

在水流量为模糊变量且河流中工业污水含量标准给定的条件下,分别建立了水污染控制系统问题的模糊期望值模型和模糊机会约束规划模型来满足不同的优化需求.为了有效求解优化模型,采用了将模糊模拟、神经元网络及遗传算法相结合的混合智能算法.最后用算例进行了验证,结果表明该算法是有效可行的.     

The mixing set with divisible capacities: A simple approach

We give a simple algorithm for linear optimization over the mixing set with divisible capacities, and derive a compact extended formulation from such an algorithm. The main idea is to apply a suitable unimodular transformation to obtain an equivalent problem that is easier to analyze.     

模糊关系几何规划

提出一类目标函数为正项式,约束是模糊关系方程的优化问题。阐述模糊关系方程解集的结构以及求解的方法,基于目标函数中每个单项式的指数取值情况讨论最优解,并且给出解决此类优化问题的一个程序,为了说明该方法的有效性给出具体例子。