Resolution and simplification of Dombi-fuzzy relational equations and latticized optimization programming on Dombi FREs

In this paper, we introduce a type of latticized optimization problem whose objective function is the maximum component function and the feasible region is defined as a system of fuzzy relational equalities (FRE) defined by the Dombi t-norm. Dombi family of t-norms includes a parametric family of continuous strict t-norms, whose members are increasing functions of the parameter. This family of t-norms covers the whole spectrum of t-norms when the parameter is changed from zero to infinity. Since the feasible solutions set of FREs is non-convex and the finding of all minimal solutions is an NP-hard problem, designing an efficient solution procedure for solving such problems is not a trivial job. Some necessary and sufficient conditions are derived to determine the feasibility of the problem. The feasible solution set is characterized in terms of a finite number of closed convex cells. An algorithm is presented for solving this nonlinear problem. It is proved that the algorithm can find the exact optimal solution and an example is presented to illustrate the proposed algorithm.Comment: arXiv admin note: text overlap with arXiv:2206.09716, arXiv:2207.0637

An exact algorithm for linear optimization problem subject to max-product fuzzy relational inequalities with fuzzy constraints

Fuzzy relational inequalities with fuzzy constraints (FRI-FC) are the generalized form of fuzzy relational inequalities (FRI) in which fuzzy inequality replaces ordinary inequality in the constraints. Fuzzy constraints enable us to attain optimal points (called super-optima) that are better solutions than those resulted from the resolution of the similar problems with ordinary inequality constraints. This paper considers the linear objective function optimization with respect to max-product FRI-FC problems. It is proved that there is a set of optimization problems equivalent to the primal problem. Based on the algebraic structure of the primal problem and its equivalent forms, some simplification operations are presented to convert the main problem into a more simplified one. Finally, by some appropriate mathematical manipulations, the main problem is transformed into an optimization model whose constraints are linear. The proposed linearization method not only provides a super-optimum (that is better solution than ordinary feasible optimal solutions) but also finds the best super-optimum for the main problem. The current approach is compared with our previous work and some well-known heuristic algorithms by applying them to random test problems in different sizes.Comment: 29 pages, 8 figures, 7 table

Geometric Programming Subject to System of Fuzzy Relation Inequalities

In this paper, an optimization model with geometric objective function is presented. Geometric programming is widely used; many objective functions in optimization problems can be analyzed by geometric programming. We often encounter these in resource allocation and structure optimization and technology management, etc. On the other hand, fuzzy relation equalities and inequalities are also used in many areas. We here present a geometric programming model with a monomial objective function subject to the fuzzy relation inequality constraints with maxproduct composition. Simplification operations have been given to accelerate the resolution of the problem by removing the components having no effect on the solution process. Also, an algorithm and two practical examples are presented to abbreviate and illustrate the steps of the problem resolution

Modelo fuzzy genético para a estimação de forças em correntes a partir da medição das frequências naturais

Orientador: Milton Dias JuniorDissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia MecânicaResumo: As instalações em alto mar possuem linhas de ancoragem, chamadas de amarras, para proporcionar estabilidade, suporte e sustentação às estruturas. Essas linhas de ancoragem são geralmente compostas por cabos, correntes e cordas de fibra sintética. Quando a solicitação de carga é alta, as linhas de ancoragem devem ser constituídas por corrente. O monitoramento da força atuando nestas correntes é vital para a confiabilidade e segurança da produção de energia. Os métodos atuais para supervisionar as cargas nas amarras são caros e têm muitas incertezas envolvidas. Nesse contexto, propõe-se uma nova metodologia para a estimativa de força em correntes através da medição de suas frequências naturais. Um sistema de inferência difuso e otimizado por um algoritmo genético foi desenvolvido para estimar da carga nas correntes. As entradas dos modelos difusos são as frequências naturais das correntes e a saída é a força estimada. As metodologias Mamdani e Sugeno foram implementadas e comparadas. Funções de pertinência triangular e gaussiana foram usadas para modelar as entradas e a saída. As regras foram definidas de acordo com as relações entre as frequências naturais e a força na corrente. Para otimizar o sistema, o algoritmo genético pode usar como dados de treinamento os resultados fornecidos por um modelo matemático ou por um conjunto de medições. O modelo matemático desenvolvido apresenta boa concordância com os dados experimentais. O modelo genético difuso foi simulado e testado, fornecendo boa precisão na estimativa da força. Finalmente, demonstrou-se que a fuzzificação não singleton pode ser uma ferramenta útil quando as entradas são ruidosasAbstract: Offshore facilities have mooring lines to provide stability, support and holding to the structures. These mooring lines are commonly made up of synthetic fiber ropes, cables and chains. When the load solicitation is high, the mooring lines must be made up of chain. The monitoring of the strength of these chains is vital for the reliability and security of the production of energy. The current methods for supervising the loads on the chains are expensive and have many uncertainties involved. In this context, it is proposed a new methodology for the force estimation in chains through the measurements of their natural frequencies. The present dissertation arises as an improvement of this approach. A fuzzy inference system optimized by a genetic algorithm is introduced to enhance the estimation of the load on the chains. The inputs of the fuzzy models are the natural frequencies of the chains and the output is the estimated force. The Mamdani and Sugeno methodologies were implemented and compared. Triangular and Gaussian membership functions were used to model the inputs and the output. The rules were set according to the relations between the natural frequencies and the force on the chain. To optimize the system, the genetic algorithm can use the results provided by a mathematical model or by a set of measurements as training data. The mathematical model has good agreement with the experimental data. The fuzzy genetic model was simulated and tested providing good accuracy in estimating the force. In addition, the non-singleton fuzzification demonstrated that can be a helpful tool when the entries are noisyMestradoMecanica de Solidos e Projeto MecanicoMestre em Engenharia Mecânica33003017CAPE

Advances in Evolutionary Algorithms

With the recent trends towards massive data sets and significant computational power, combined with evolutionary algorithmic advances evolutionary computation is becoming much more relevant to practice. Aim of the book is to present recent improvements, innovative ideas and concepts in a part of a huge EA field

Measurements, Models, Systems and Design

531 s.

Numerical and Evolutionary Optimization 2020

This book was established after the 8th International Workshop on Numerical and Evolutionary Optimization (NEO), representing a collection of papers on the intersection of the two research areas covered at this workshop: numerical optimization and evolutionary search techniques. While focusing on the design of fast and reliable methods lying across these two paradigms, the resulting techniques are strongly applicable to a broad class of real-world problems, such as pattern recognition, routing, energy, lines of production, prediction, and modeling, among others. This volume is intended to serve as a useful reference for mathematicians, engineers, and computer scientists to explore current issues and solutions emerging from these mathematical and computational methods and their applications

Particle Swarm Optimization

Particle swarm optimization (PSO) is a population based stochastic optimization technique influenced by the social behavior of bird flocking or fish schooling.PSO shares many similarities with evolutionary computation techniques such as Genetic Algorithms (GA). The system is initialized with a population of random solutions and searches for optima by updating generations. However, unlike GA, PSO has no evolution operators such as crossover and mutation. In PSO, the potential solutions, called particles, fly through the problem space by following the current optimum particles. This book represents the contributions of the top researchers in this field and will serve as a valuable tool for professionals in this interdisciplinary field

Applied Metaheuristic Computing

For decades, Applied Metaheuristic Computing (AMC) has been a prevailing optimization technique for tackling perplexing engineering and business problems, such as scheduling, routing, ordering, bin packing, assignment, facility layout planning, among others. This is partly because the classic exact methods are constrained with prior assumptions, and partly due to the heuristics being problem-dependent and lacking generalization. AMC, on the contrary, guides the course of low-level heuristics to search beyond the local optimality, which impairs the capability of traditional computation methods. This topic series has collected quality papers proposing cutting-edge methodology and innovative applications which drive the advances of AMC

Automatic Control and Routing of Marine Vessels

Due to the intensive development of the global economy, many problems are constantly emerging connected to the safety of ships’ motion in the context of increasing marine traffic. These problems seem to be especially significant for the further development of marine transportation services, with the need to considerably increase their efficiency and reliability. One of the most commonly used approaches to ensuring safety and efficiency is the wide implementation of various automated systems for guidance and control, including such popular systems as marine autopilots, dynamic positioning systems, speed control systems, automatic routing installations, etc. This Special Issue focuses on various problems related to the analysis, design, modelling, and operation of the aforementioned systems. It covers such actual problems as tracking control, path following control, ship weather routing, course keeping control, control of autonomous underwater vehicles, ship collision avoidance. These problems are investigated using methods such as neural networks, sliding mode control, genetic algorithms, L2-gain approach, optimal damping concept, fuzzy logic and others. This Special Issue is intended to present and discuss significant contemporary problems in the areas of automatic control and the routing of marine vessels