Abstract  This paper proposes an integrated evolutionary optimization algorithm (IEOA) which is combined with genetic algorithm (GA), random tabu search method (TS) and response surface methodology (RSM). This algorithm, in order to improve the convergent speed that is thought to be the demerit of GA, uses RSM and the simplex method. Though mutation of GA offers random variety, systematic variety can be secured through the use of tabu-list. Efficiency of this method has been proven by applying traditional test functions and comparing the results to GA. And it is an evidence that the newly suggested algorithm can effectively find the global optimum solution by applying it to minimize the weight of fresh water tank that is placed in the rear of ship designed to avoid resonance. According to the results, GA's convergent speed in initial phase has been improved by using RSM. An optimized solution was calculated without the evaluation of additional actual objective function. Finally, it can be concluded that IEOA is a very useful global optimization algorithm from the viewpoint of convergent speed and global search ability.  61820

Keywords: Evolutionary optimization algorithms; Genetic algorithm; Response surface methodology; Tabu search method; Simplex method; Fresh water tank

1. Introduction 

The focus of many dynamic analyses is to find the maximum response and avoid the resonance in a given structure under all excitation forces. Usually, these features provide the basis of a design limit and are thus employed to determine the dynamic characteristics of a structure and its weight. For this reason, weight minimization for reducing the response and avoiding resonance has always been a major concern of design engineers.

Many classic optimization methods and practical software have been developed and most of them are very effective, especially to solve practical problems. However, finding a global optimum 

for the system is difficult. To overcome this disadvantage, many search algorithms have been developed for searching a global optimum solution. One of the most popular methods is the genetic algorithm (GA) [1, 2]. The GA is a technique in the field of evolutionary computation, and it is a powerful and general global optimization method, which does not require the strict continuity of classical search techniques; instead, it allows non-linearity and discontinuity to appear in the solution space. Due to the evolutionary characteristics, the GA can handle all kinds of objective functions and constraints defined on discrete, continuous, or mixed search spaces. However, the global access of the GA requires a computationally random search. So, the convergent speed to the exact solution is slow. Furthermore, the coding of the chromosome for a 

large dimensional problem will be very long in order to get a more accurate solution. This results in a large search space and huge memory requirements for the computation. To overcome these demerits, many researchers have studied developing many hybrid genetic algorithms which combine the genetic algorithm with other ones [3-6]. These can save computation time and find the global solution as far as it goes. Therefore, the new algorithms are addressed to reach better accuracy and faster convergent speed to get an optimum solution in complicated and big structures like ships.  

Response surface methodology (RSM) [7] is an optimization tool that was introduced by Box and Wilson [8]. It is a collection of statistical and mathematical techniques that are useful for developing, improving, and optimizing processes. These techniques are employed in order to estimate the optimization function and to find search directions to sub-regions of the domain with improved and hopefully optimal solutions. The simplex method (SM) is a derivative-free method of optimization that uses regular patterns of search involving simplexes [9]. This well known technique has proven to be popular for unconstrained objective functions. Tabu search (TS) is one of the recent metaheuristics originally developed for combinatorial optimization problems. Since the first presentation of Glover [10, 11], many studies have emerged in this area, such as TS with random moves for constrained optimization problems [12].