Fuzzy Optimization of Complex Systems Using Approximation Concepts

1997 ◽  
Vol 50 (11S) ◽  
pp. S97-S104 ◽  
Author(s):  
Hector A. Jensen ◽  
Abdon E. Sepulveda
Keyword(s):  
Original Problem ◽  
Optimization Problems ◽  
Fuzzy Optimization ◽  
Optimization Techniques ◽  
System Response ◽  
Optimization Approach ◽  
Design Variables ◽  
Intermediate Response ◽  
Intermediate Variables ◽  
Approximation Concepts

This paper presents a methodology for the efficient solution of fuzzy optimization problems. Design variables, as well as system parameters are modeled as fuzzy numbers characterized by membership functions. An optimization approach based on approximation concepts is introduced. High quality approximations for system response functions are constructed using the concepts of intermediate response quantities and intermediate variables. These approximations are used to replace the solution of the original problem by a sequence of approximate problems. Optimization techniques for non-differentiable problems which arise in fuzzy optimization are used to solve the approximate optimization problems. Example problems are presented to illustrate the ideas set forth.

Innovative Hybrid Genetic Algorithms and Line Search Method for Industrial Production Management

2010 ◽  
pp. 142-160 ◽  
Author(s):  
Pandian M. Vasant
Keyword(s):  
Production Management ◽  
Optimization Problems ◽  
Fuzzy Optimization ◽  
Computational Techniques ◽  
Optimization Approach ◽  
Non Linear Programming ◽  
Decision Variables ◽  
Line Search Method ◽  
Non Linear ◽  
Management Optimization

Many engineering, science, information technology and management optimization problems can be considered as non linear programming real world problems where the all or some of the parameters and variables involved are uncertain in nature. These can only be quantified using intelligent computational techniques such as evolutionary computation and fuzzy logic. The main objective of this research chapter is to solve non linear fuzzy optimization problem where the technological coefficient in the constraints involved are fuzzy numbers which was represented by logistic membership functions by using hybrid evolutionary optimization approach. To explore the applicability of the present study a numerical example is considered to determine the production planning for the decision variables and profit of the company.

An Agent Based Optimization Approach to Manufacturing Process Planning

2001 ◽  
Author(s):  
Saurabh Deshpande ◽  
Jonathan Cagan
Keyword(s):  
Stochastic Optimization ◽  
Process Planning ◽  
Manufacturing Process ◽  
Optimization Problems ◽  
Search Space ◽  
Optimization Techniques ◽  
Process Models ◽  
Optimization Approach ◽  
Agent Based ◽  
Manufacturing Process Planning

Abstract Many optimization problems, such as manufacturing process planning optimization, are difficult problems due to the large number of potential configurations (process sequences) and associated (process) parameters. In addition, the search space is highly discontinuous and multi-modal. This paper introduces an agent based optimization algorithm that combines stochastic optimization techniques with knowledge based search. The motivation is that such a merging takes advantage of the benefits of stochastic optimization and accelerates the search process using domain knowledge. The result of applying this algorithm to computerized manufacturing process models is presented.

Feasibility Robust Optimization via Scenario Generation and Reduction

2018 ◽  
Author(s):  
Eliot Rudnick-Cohen ◽  
Jeffrey W. Herrmann ◽  
Shapour Azarm
Keyword(s):  
Robust Optimization ◽  
Optimization Problems ◽  
Computational Cost ◽  
Optimization Techniques ◽  
Scenario Generation ◽  
Test Problems ◽  
Optimization Approach ◽  
Uncertain Parameters ◽  
Worst Case ◽  
Robust Solution

Feasibility robust optimization techniques solve optimization problems with uncertain parameters that appear only in their constraint functions. Solving such problems requires finding an optimal solution that is feasible for all realizations of the uncertain parameters. This paper presents a new feasibility robust optimization approach involving uncertain parameters defined on continuous domains without any known probability distributions. The proposed approach integrates a new sampling-based scenario generation scheme with a new scenario reduction approach in order to solve feasibility robust optimization problems. An analysis of the computational cost of the proposed approach was performed to provide worst case bounds on its computational cost. The new proposed approach was applied to three test problems and compared against other scenario-based robust optimization approaches. A test was conducted on one of the test problems to demonstrate that the computational cost of the proposed approach does not significantly increase as additional uncertain parameters are introduced. The results show that the proposed approach converges to a robust solution faster than conventional robust optimization approaches that discretize the uncertain parameters.

scholarly journals Extended Duality in Fuzzy Optimization Problems

2015 ◽  
Vol 2015 ◽  
pp. 1-11 ◽  
Author(s):  
Tingting Zou
Keyword(s):  
Nonlinear Programming ◽  
Original Problem ◽  
Dual Problem ◽  
Optimization Problems ◽  
Fuzzy Optimization ◽  
Duality Gap ◽  
Continuous Variables ◽  
Objective Functions ◽  
Duality Theorems ◽  
Fuzzy Nonlinear Programming

Duality theorem is an attractive approach for solving fuzzy optimization problems. However, the duality gap is generally nonzero for nonconvex problems. So far, most of the studies focus on continuous variables in fuzzy optimization problems. And, in real problems and models, fuzzy optimization problems also involve discrete and mixed variables. To address the above problems, we improve the extended duality theory by adding fuzzy objective functions. In this paper, we first define continuous fuzzy nonlinear programming problems, discrete fuzzy nonlinear programming problems, and mixed fuzzy nonlinear programming problems and then provide the extended dual problems, respectively. Finally we prove the weak and strong extended duality theorems, and the results show no duality gap between the original problem and extended dual problem.

Study on Vibration Reduction Design of Steel-Composite Material Hybrid Mounting for Ship Based on Material Selection Optimization

2013 ◽  
Vol 694-697 ◽  
pp. 415-424
Author(s):  
Wei Wang ◽  
Lu Yun Chen ◽  
Yu Fang Zhang
Keyword(s):  
Power Flow ◽  
Optimization Problems ◽  
Material Selection ◽  
Vibration Reduction ◽  
Optimization Method ◽  
Optimization Approach ◽  
Structural Dynamic ◽  
Level Difference ◽  
Design Variables ◽  
Steel Composite

The material selection optimization for vibration reduction design is studied present article. By introducing the stacking sequence hypothesis of metal material, taking into account the power flow level difference and vibration level difference parameter, the mechanical parameters of the material and plies number are defined as design variables, and the mathematical model of structural dynamic optimization based on material selection optimization approach is established. Finally, a naval hybrid steel-composite mounting structure for example, by introducing genetic algorithm, the optimization problems is solved. The numerical results show that the optimization method is effective and feasible.

Isogeometric shape optimization for design dependent loads

2021 ◽  
pp. 1-13
Author(s):  
Arkaprabho Pal ◽  
Sourav Rakshit
Keyword(s):  
Shape Optimization ◽  
Optimization Problems ◽  
Minimum Weight ◽  
Control Point ◽  
Optimization Approach ◽  
Shape Sensitivity ◽  
Body Forces ◽  
Design Variables ◽  
Design Dependent Loads ◽  
Material Layout

Abstract This paper presents a new isogeometric formulation for shape optimization of structures subjected to design dependent loads. This work considers two types of design dependent loads, namely surface loads like pressure where the direction and/or magnitude of force changes with the variation of boundary shape, and body forces that depend on the material layout. These problems have been mostly solved by topology optimization methods which are prone to difficulties in determination of the loading surface for pressure loads and problems associated with non-monotonous behaviour of compliance and low density regions for body forces. This work uses an isogeometric shape optimization approach where the geometry is defined using NURBS and the control point coordinates and control weights of the boundary are chosen as design variables. This approach accommodates the design dependent loads easily, in addition to its other advantages like exact geometry representation, local control, fewer design variables, excellent shape sensitivity, efficient mesh refinement strategies, and smooth results that can be integrated with CAD. Two classes of optimization problems have been discussed, they are minimum compliance problems subject to volume constraint and minimum weight problems subjected to local stress constraints. These problems are solved using convex optimization programs. Hence, expressions for full sensitivities are derived which is new for structural shape optimization problems with design dependent loads. Some representative engineering examples are solved and compared with existing literature to demonstrate the application of the proposed method.

Particle Swarm Methodologies for Engineering Design Optimization

2009 ◽  
Author(s):  
Singiresu S. Rao ◽  
Kiran K. Annamdas
Keyword(s):  
Particle Swarm Optimization ◽  
Optimization Problems ◽  
Particle Swarm ◽  
Multiple Objective ◽  
Optimization Approach ◽  
Objective Functions ◽  
Mixed Design ◽  
Swarm Optimization ◽  
Design Variables ◽  
Mixed Design Variables

Particle swarm methodologies are presented for the solution of constrained mechanical and structural system optimization problems involving single or multiple objective functions with continuous or mixed design variables. The particle swarm optimization presented is a modified particle swarm optimization approach, with better computational efficiency and solution accuracy, is based on the use of dynamic maximum velocity function and bounce method. The constraints of the optimization problem are handled using a dynamic penalty function approach. To handle the discrete design variables, the closest discrete approach is used. Multiple objective functions are handled using a modified cooperative game theory approach. The applicability and computational efficiency of the proposed particle swarm optimization approach are demonstrated through illustrate examples involving single and multiple objectives as well as continuous and mixed design variables. The present methodology is expected to be useful for the solution of a variety of practical engineering design optimization problems.

A Fuzzy Query Optimization Approach for Multidatabase Systems

1997 ◽  
Vol 05 (06) ◽  
pp. 701-722 ◽  
Author(s):  
Qiang Zhu ◽  
Per-Åke Larson
Keyword(s):  
Query Optimization ◽  
Cost Model ◽  
Fuzzy Optimization ◽  
Optimization Criterion ◽  
Optimization Techniques ◽  
Optimization Approach ◽  
Fuzzy Query ◽  
Execution Strategy ◽  
Fuzzy Cost ◽  
Global Query

A crucial challenge for global query optimization in a multidatabase system (MDBS) is that some local optimization information, such as local cost parameters, may not be accurately known at the global level because of local autonomy. Traditional query optimization techniques using a crisp cost model may not be suitable for an MDBS because precise information is required. In this paper we present a new approach that performs global query optimization using a fuzzy cost model that allows fuzzy information. We suggest methods for establishing a fuzzy cost model and introduce a fuzzy optimization criterion that can be used with a fuzzy cost model. We discuss the relationship between the fuzzy optimization approach and the traditional (crisp) optimization approach and show that the former has a better chance to find a good execution strategy for a query in an MDBS environment, but its complexity may grow exponentially compared with the complexity of the later. To reduce the complexity, we suggest to use so-called k-approximate fuzzy values to approximate all fuzzy values during fuzzy query optimization. It is proven that the improved fuzzy approach has the same order of complexity as the crisp approach.

scholarly journals Non-Convex Feasibility Robust Optimization Via Scenario Generation and Local Refinement

2019 ◽  
Vol 142 (5) ◽  
Author(s):  
Eliot Rudnick-Cohen ◽  
Jeffrey W. Herrmann ◽  
Shapour Azarm
Keyword(s):  
Robust Optimization ◽  
Optimization Problems ◽  
Computational Cost ◽  
Optimal Solution ◽  
Optimization Techniques ◽  
Scenario Generation ◽  
Test Problems ◽  
Optimization Approach ◽  
Uncertain Parameters ◽  
Worst Case

Abstract Feasibility robust optimization techniques solve optimization problems with uncertain parameters that appear only in their constraint functions. Solving such problems requires finding an optimal solution that is feasible for all realizations of the uncertain parameters. This paper presents a new feasibility robust optimization approach involving uncertain parameters defined on continuous domains. The proposed approach is based on an integration of two techniques: (i) a sampling-based scenario generation scheme and (ii) a local robust optimization approach. An analysis of the computational cost of this integrated approach is performed to provide worst-case bounds on its computational cost. The proposed approach is applied to several non-convex engineering test problems and compared against two existing robust optimization approaches. The results show that the proposed approach can efficiently find a robust optimal solution across the test problems, even when existing methods for non-convex robust optimization are unable to find a robust optimal solution. A scalable test problem is solved by the approach, demonstrating that its computational cost scales with problem size as predicted by an analysis of the worst-case computational cost bounds.

scholarly journals Optimization of Polymer Processing: A Review (Part II- Molding Technologies)

2021 ◽  
Author(s):  
António Gaspar-Cunha ◽  
Janusz Sikora ◽  
José A. Covas
Keyword(s):  
Optimization Problems ◽  
Polymer Processing ◽  
Optimization Techniques ◽  
Function Optimization ◽  
Optimization Approach ◽  
Processing Technologies ◽  
Twin Screw Extruders ◽  
Extrusion Dies ◽  
Twin Screw ◽  
Processing Optimization

The application of optimization techniques to improve the performance of polymer processing technologies is of great practical consequence, since it may result in significant savings of materials and energy resources, assist recycling schemes and generate products with better properties. The present review aims at identifying and discussing the most important characteristics of polymer processing optimization problems in terms of the nature of the objective function, optimization algorithm, and process modelling approach that is used to evaluate the solutions and the parameters to optimize. Taking into account the research efforts developed so far, it is shown that several optimization methodologies can be applied to polymer processing with good results, without demanding important computational requirements. Also, within the field of artificial intelligence, several approaches can be reach significant success. The first part of this review demonstrated the advantages of the optimization approach in polymer processing, discussed some concepts on multi-objective optimization and reported the application of optimization methodologies in single and twin screw extruders, extrusion dies and calibrators. This second part focus on injection molding, blow molding and thermoforming technologies.

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