Multi-objective Algorithm for Optimal Design Abubaker Mohamed Elbayoudi Abstract- Multiobjective optimization is progressively more applied as it allows being closer to real engineering problems that may be found in industrial applications. This paper proposes applied techniques to optimize the design of a pressure vessel for hollow cylinder and hemi-spherical head in terms of the cost of the material and manufacturing. The problem is studied with two objectives: minimise cost function equation and the variable vector of this function. The optimisation methodology to solve the problem of designing the vessel is tackled into three different stages by creating different models. The first model uses the simulated annealing technique; the second model uses the tabu search technique and last one uses the new hybrid technique. The results show some important improvements made by the hybrid method. Keywords: Simulated annealing, Tabu search, local search, multiobjective optimization. I. INTRODUCTION The computing obtainable from nature is described by the term Natural Computing, which means computing stimulated by nature. The computational process is viewed as complex phenomena when it is going on in nature basis. The real meaning of understanding the phenomena of computation is improved. In this way both of natural sciences and computer science will achieve valuable insight. The allegorical use of concepts, principles and mechanisms of natural systems is the characteristic of using the computing inspired by nature. An important methodological is found to show difference between a mixture of sub areas of natural computing, e.g., evolutionary algorithms and algorithms based on neural networks are currently applied on conservative computers. On the other hand, the computing is also aimed to implement the algorithms in biological hardware, e.g., using DNA molecules and enzymes. Moreover, quantum computing aims to change the traditional hardware and allow quantum effects to take place. Computer science is making an important transformation by trying to join the computer science with the computing observed in nature. Natural computing is a very important channel of this transformation, and it has a lot of promise for the future. Manuscript received March 18, 2012; This work was supported in part by the higher institute for instructors, Misurata,Libya. Multi-objective Algorithm for Optimal Design. Abubaker Elbayoudi is with the Higher Institute for Instructors, P.O Box 273 Misurata,Libya (corresponding author to provide Mobile: 00218-91 325 6645; e-mail: elbayudi@ yahoo.com). However, one of currently terms used in natural computing is called the optimization. Therefore, what the optimization mean? The optimization of function or process is that, “studies how to describe and attain what is best, once knows how to measure and alter what is good or bad … optimization theory encompasses the quantitative study of optima and methods for finding them. The optimization seeks to improve performance toward some optimal point or points.” [1].This definition has two parts, which are looking for improvement approach, and optimal points. It is clear; there is a distinction between the improvement process and the optimum itself. The commonly in judging of optimization procedures are focused solely upon convergence of an optimum method, and are forgotten entirely about interim performance. Therefore, if there are more requests on human like optimization tools, then the reordering of optimization priorities is led. As it seen clear, the most important goal of optimization is the improvement. In addition, to get some good (satisfying) level of performance quickly attainment of the optimum is much less important for complex systems. The objective of pressure vessel design is to avoid various possible failures and ensure safe operations of vessels. This is practically realized by limiting stresses, strains and design loads of vessels within the allowable values after the failure modes of vessels are determined. In this paper, adapt and apply natural computing techniques were done, to optimize the design of a pressure vessel in terms of the cost of the materials and manufacturing f(x); there are three methods implemented for this task, which are simulated annealing, tabu search and a new hybrid algorithm. All of them will use the same minimise cost function equation and the variable vector. II. MULTI-OBJECTIVE OPTIMIZATION In an early multi-objective combinatorial optimization survey paper,[1] proposed the application of metaheuristics, such as simulated annealing (SA), TS and Genetic Algorithms (GA), since they are comparatively easy to implement and gain good solutions in less time than classical optimization methods such as math programming or dynamic programming. A few years later, a complete survey on Proceedings of the World Congress on Engineering 2012 Vol II WCE 2012, July 4 - 6, 2012, London, U.K. ISBN: 978-988-19252-1-3 ISSN: 2078-0958 (Print); ISSN: 2078-0966 (Online) WCE 2012