From ranking fuzzy numbers to solving fuzzy linear programming: a comprehensive review

Solving fuzzy linear programming (FLP) requires the employment of a consistent ranking of fuzzy numbers. Ineffective fuzzy number ranking would lead to a flawed and erroneous solving approach. This paper presents a comprehensive and extensive review on fuzzy number ranking methods. Ranking techniques are categorised into six classes based on their characteristics. They include centroid methods, distance methods, area methods, lexicographical methods, methods based on decision maker's viewpoint, and methods based on left and right spreads. A survey on solving approaches to FLP is also reported. We then point out errors in several existing methods that are relevant to the ranking of fuzzy numbers and thence suggest an effective method to solve FLP. Consequently, FLP problems are converted into non-fuzzy single (or multiple) objective linear programming based on a consistent centroid-based ranking of fuzzy numbers. Solutions of FLP are then obtained by solving corresponding crisp single (or multiple) objective programming problems by conventional methods.

Solving fuzzy programming with a consistent fuzzy number ranking

 Some illustrative examples are provided to identify the ineffective and unrealistic characteristics of existing approaches to solving fuzzy linear programming (FLP) problems (with single or multiple objectives). We point out the error in existing methods concerning the ranking of fuzzy numbers and thence suggest an effective method to solve the FLP. Based on the consistent centroid-based ranking of fuzzy numbers, the FLP problems are transformed into non-fuzzy single (or multiple) objective linear programming. Solutions of FLP are then crisp single or multiple objective programming problems, which can respectively be obtained by conventional methods.

A multi-objective programming approach for the optimal operation of distributed generation considering uncertainty

Due to the renewed interest in distributed generation (DG), the number of DG units incorporated in distribution systems has been rapidly increasing in the past few years. This situation requires new analysis tools for understanding system performance, and taking advantage of the potential benefits of DG. This paper presents an evolutionary multi-objective programming approach to determine the optimal operation of DG in distribution systems. The objectives are the minimization of the system power losses and operation cost of the DG units. The proposed approach also considers the inherent stochasticity of DG technologies powered by renewable resources. Some tests were carried out on the IEEE 34 bus distribution test system showing the robustness and applicability of the proposed methodology. © 2011 IEEE.

A class of multiobjective control problems

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Constraint qualifications in linear vector semi-infinite optimization

Linear vector semi-infinite optimization deals with the simultaneous minimization of finitely many linear scalar functions subject to infinitely many linear constraints. This paper provides characterizations of the weakly efficient, efficient, properly efficient and strongly efficient points in terms of cones involving the data and Karush–Kuhn–Tucker conditions. The latter characterizations rely on different local and global constraint qualifications. The global constraint qualifications are illustrated on a collection of selected applications.

Mathematical programming model for heat exchanger design through optimization of partial objectives

Mathematical programming can be used for the optimal design of shell-and-tube heat exchangers (STHEs). This paper proposes a mixed integer non-linear programming (MINLP) model for the design of STHEs, following rigorously the standards of the Tubular Exchanger Manufacturers Association (TEMA). Bell–Delaware Method is used for the shell-side calculations. This approach produces a large and non-convex model that cannot be solved to global optimality with the current state of the art solvers. Notwithstanding, it is proposed to perform a sequential optimization approach of partial objective targets through the division of the problem into sets of related equations that are easier to solve. For each one of these problems a heuristic objective function is selected based on the physical behavior of the problem. The global optimal solution of the original problem cannot be ensured even in the case in which each of the sub-problems is solved to global optimality, but at least a very good solution is always guaranteed. Three cases extracted from the literature were studied. The results showed that in all cases the values obtained using the proposed MINLP model containing multiple objective functions improved the values presented in the literature.

Automatic evolution of conceptual building architectures

This thesis describes research in which genetic programming is used to automatically evolve shape grammars that construct three dimensional models of possible external building architectures. A completely automated fitness function is used, which evaluates the three dimensional building models according to different geometric properties such as surface normals, height, building footprint, and more. In order to evaluate the buildings on the different criteria, a multi-objective fitness function is used. The results obtained from the automated system were successful in satisfying the multiple objective criteria as well as creating interesting and unique designs that a human-aided system might not discover. In this study of evolutionary design, the architectures created are not meant to be fully functional and structurally sound blueprints for constructing a building, but are meant to be inspirational ideas for possible architectural designs. The evolved models are applicable for today's architectural industries as well as in the video game and movie industries. Many new avenues for future work have also been discovered and highlighted.

Multiobjective optimization of economic balances of sugarcane harvest biomass

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Optimization of Large-Scale Hydrothermal System Operation

This paper presents the development of a mathematical model to optimize the management and operation of the Brazilian hydrothermal system. The system consists of a large set of individual hydropower plants and a set of aggregated thermal plants. The energy generated in the system is interconnected by a transmission network so it can be transmitted to centers of consumption throughout the country. The optimization model offered is capable of handling different types of constraints, such as interbasin water transfers, water supply for various purposes, and environmental requirements. Its overall objective is to produce energy to meet the country's demand at a minimum cost. Called HIDROTERM, the model integrates a database with basic hydrological and technical information to run the optimization model, and provides an interface to manage the input and output data. The optimization model uses the General Algebraic Modeling System (GAMS) package and can invoke different linear as well as nonlinear programming solvers. The optimization model was applied to the Brazilian hydrothermal system, one of the largest in the world. The system is divided into four subsystems with 127 active hydropower plants. Preliminary results under different scenarios of inflow, demand, and installed capacity demonstrate the efficiency and utility of the model. From this and other case studies in Brazil, the results indicate that the methodology developed is suitable to different applications, such as planning operation, capacity expansion, and operational rule studies, and trade-off analysis among multiple water users. DOI: 10.1061/(ASCE)WR.1943-5452.0000149. (C) 2012 American Society of Civil Engineers.

Fuzzy optimization model for water quality management of a river system - Closure

A fuzzy waste-load allocation model, FWLAM, is developed for water quality management of a river system using fuzzy multiple-objective optimization. An important feature of this model is its capability to incorporate the aspirations and conflicting objectives of the pollution control agency and dischargers. The vagueness associated with specifying the water quality criteria and fraction removal levels is modeled in a fuzzy framework. The goals related to the pollution control agency and dischargers are expressed as fuzzy sets. The membership functions of these fuzzy sets are considered to represent the variation of satisfaction levels of the pollution control agency and dischargers in attaining their respective goals. Two formulations—namely, the MAX-MIN and MAX-BIAS formulations—are proposed for FWLAM. The MAX-MIN formulation maximizes the minimum satisfaction level in the system. The MAX-BIAS formulation maximizes a bias measure, giving a solution that favors the dischargers. Maximization of the bias measure attempts to keep the satisfaction levels of the dischargers away from the minimum satisfaction level and that of the pollution control agency close to the minimum satisfaction level. Most of the conventional water quality management models use waste treatment cost curves that are uncertain and nonlinear. Unlike such models, FWLAM avoids the use of cost curves. Further, the model provides the flexibility for the pollution control agency and dischargers to specify their aspirations independently.

Injection laryngoplasty with autologous fascia for treatment of unilateral vocal fold paralysis

The purpose of this dissertation was to study the applicability of minced autologous fascia graft for injection laryngoplasty of unilateral vocal fold paralysis (UVFP). Permanence of augmentation and host versus graft tissue reactions were of special interest. The topic deals with phonosurgery, which is a subdivision of the Ear, Nose and Throat-speciality of medicine. UVFP results from an injury to the recurrent or the vagal nerve. The main symptom is a hoarse and weak voice. Surgery is warranted for patients in whom spontaneous reinnervation and a course of voice therapy fails to improve the voice. Injection laryngoplasty is a widespread surgical technique which aims to restore glottic closure by augmenting the atrophied vocal muscle, and also by turning the paralyzed vocal fold towards midline. Currently, there exists a great diversity of synthetic, xenologous, homologous, and autologous substances available for injection. An autologous graft is perfect in terms of biocompatibility. Free fascia grafts have been successfully used in the head and neck surgery for decades, but fascia had not been previously applied into the vocal fold. The fascia is harvested from the lateral thigh under local anesthesia and minced into paste by scissors. Injection of the vocal fold is performed in laryngomicroscopy under general anesthesia. Three series of clinical trials of injection laryngoplasty with autologous fascia (ILAF) for patients with UVFP were conducted at the Department of Otorhinolaryngology of the Helsinki University Central Hospital. The follow-up ranged from a few months to ten years. The aim was to document the vocal results and possible morbidity related to graft harvesting and vocal fold injection. To address the tissue reactions and the degree of reabsoprtion of the graft, an animal study with a follow-up ranging from 3 days to 12 months was performed at the National Laboratory Animal Center, University of Kuopio. Harvesting of the graft and injection was met with minor morbidity. Histological analysis of the vocal fold tissue showed that fascia was well tolerated. Although some resorption or compaction of the graft during the first months is evident, graft volume is maintained well. When injected deep and laterally into the vocalis muscle, the fascia graft allows normal vibration of the vocal fold mucosa to occur during phonation. Improvement of voice quality was seen in all series by multiple objective parameters of voice evaluation. However, the vocal results were poor in cases where the nerve trauma was severe, such as UVFP after chest surgery. ILAF is most suitable for correction of mild to moderate glottic gaps related to less severe nerve damage. Our results indicate that autologous fascia is a feasible and safe new injection material with good and stable vocal results. It offers a practical solution for surgeons who treat this complex issue.

基于视觉和超声信息的机器人行为控制

随着机器人应用范围的不断扩展,机器人所面临的工作环境也越来越复杂,多数是未知的、动态的和非结构化的。通过对基于行为的机器人控制技术的研究,设计了一种用于完成多目标任务的移动机器人行为控制系统。将基于行为的控制技术融合进模糊控制的思想中,使移动机器人的行为通过运用模糊控制和基于优先度的行为决策来实现,并且通过视觉信息使机器人能够完成面向目标的任务。

水资源分配的决策模型及应用

水资源规划是一个复杂的系统规划问题,所以,在水资源规划中,含有大量的不精确的统计数据和模糊关系。由于这些特点,水资源规划必须用特殊的方法来解决。 本文将层次分析法(AHP)和模糊规划(Fuzzy Programming)方法相结合,形成了一种多目标规划的求解方法,并应用于大凌河流域水资源规划研究的课题中,通过实际分析可以看到,这种方法具有较好的实用性。