A Posynomial Geometric Programming Restricted to a System of Fuzzy Relation Equations

AbstractA posynomial geometric optimization problem subjected to a system of max-min fuzzy relational equations (FRE) constraints is considered. The complete solution set of FRE is characterized by unique maximal solution and finite number of minimal solutions. A two stage procedure has been suggested to compute the optimal solution for the problem. Firstly all the minimal solutions of fuzzy relation equations are determined. Then a domain specific evolutionary algorithm (EA) is designed to solve the optimization problems obtained after considering the individual sub-feasible region formed with the help of unique maximum solution and each of the minimal solutions separately as the feasible domain with same objective function. A single optimal solution for the problem is determined after solving these optimization problems. The whole procedure is illustrated with a numerical example

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

Mono and Multi-Objective Optimization and Modeling of Machining Performance in Face Milling of Ti6Al4V Alloy

Titanium alloys are extensively used in numerous industries like aerospace, automotive, military, etc., due to their exclusive characteristics. But machining these alloys has always been challenging for manufacturers. This research investigates the effect of radial depth of cut on cutting forces, tool life, surface roughness (Ra), and material removal rate (MRR) during face milling of Ti6Al4V alloy. It also aims to perform mono and multi-objective optimization of response characteristics to determine the optimal input parameters, namely cutting speed, feed rate, and radial depth of cut. Taguchi method and analysis of variance (ANOVA) have been used for mono-objective optimization, whereas Taguchi-based Grey relational analysis (GRA) and Genetic algorithm (GA) have been used for multi-objective optimization. Regression analysis has been performed for developing mathematical models to predict Ra, tool life, average cutting forces, and MRR. According to ANOVA analysis, the most significant parameter for tool life is cutting speed. For MRR and average cutting force (Avg. FY), the most influential parameter is the radial depth of cut. On the other hand, feed rate is the most significant parameter for Ra and average feed force (Avg. FX). The optimal combination of input parameters for tool life and Avg. FY is 50 m/min cutting speed, 0.2 mm/rev feed rate, and 7.5 mm radial depth of cut. However, the optimal parameters for Ra are 65 m/min cutting speed, 0.2 mm/rev feed rate, and 7.5 mm radial depth of cut. For Avg. FX, the optimal conditions are 57.5 m/min cutting speed, 0.2 mm/rev feed rate, and 7.5 mm radial depth of cut. Similarly, for MRR, the optimal parameters are 65 m/min cutting speed, 0.3 mm/rev feed rate, and 12.5 mm radial depth of cut. A validation experiment has been conducted at the optimal Ra parameters, which shows an improvement of 31.29% compared to the Ra measured at the initial condition. A minor error has been found while comparing the experimental data with the predicted values calculated from the mathematical models. GRA for multi-objective (3 objectives: tool life, Ra, and Avg. FY) optimization has improved 55.81% tool life, 6.12% Ra, and 23.98% Avg. FY. ANOVA analysis based on grey relational grade has demonstrated that radial depth of cut is the most significant parameter for multi-objective (three objectives) optimization during the face milling of Ti6Al4V. The results obtained from the GRA considering four output characteristics (tool life, Ra, Avg. FY, and MRR) are compared with GA optimization results for both roughing and finishing, and a negligible deviation has been observed

Computer science: the hardware software and heart of IT

1st edition, 201

The Third Air Force/NASA Symposium on Recent Advances in Multidisciplinary Analysis and Optimization

The third Air Force/NASA Symposium on Recent Advances in Multidisciplinary Analysis and Optimization was held on 24-26 Sept. 1990. Sessions were on the following topics: dynamics and controls; multilevel optimization; sensitivity analysis; aerodynamic design software systems; optimization theory; analysis and design; shape optimization; vehicle components; structural optimization; aeroelasticity; artificial intelligence; multidisciplinary optimization; and composites