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

Optimisation problems as decision problems: The case of fuzzy optimisation problems

The importance that decision-making problems and optimisation problems have today in all aspects of life is beyond all doubt. Despite that importance, both problems tend to be thought of as following different routes, when they have, in fact, a “symbiotic” relation. Here, we consider the different decision problems that arise when different kinds of information and framework of behaviour are considered, and we explore the corresponding optimisation problems that can be derived for searching the best possible decision. We explore the case where Fuzzy Mathematical Programming problems are obtained as well as other new ones in the fuzzy context.Research supported by the project TIN2014-55024-P from the Spanish Govern as well as by the project TIC-8001 from the Andalusian Govern (both financed with FEDER funds)

Determination of Cost-Effective Range in Surface Finish for Single Pass Turning

Surface finish is considered a critical characteristic for manufacturing components when manufacturers strive to produce components with high-quality characteristics predefined by design engineers. The objective of this research is to provide a cost-effective range in surface finish for single pass turning that enables the design engineers to explore a wider spectrum of alternative solutions without significantly affecting the functionality of the part. Apart from the one optimal solution, the proposed methodology, which is based on Geometric Programming, would provide a range of cutting conditions solutions that satisfy the economic and functional needs for the designer. This can be achieved by switching cost reduction focus from tooling to labor cost, particularly by adjusting variables values such as spindle speed and feed. An algorithm has been developed to find the new variables values. In addition, a sensitivity analysis model, based on metaheuristic techniques, will also be developed to further give a set of possible solutions that are practically preferable to the practitioners. In addition, the developed methodology can be applied to other engineering applications. The proposed methodology will provide a tool that enhances the design for manufacturability for companies to become more competitive