In this study, to search the optimum solution of multimodal function in high accuracy and high speed, a new hybrid evolutionary algorithm is suggested, which combines the merits of the popular algorithms such as GA, TS, RSM and SM. This algorithm, in order to improve the convergent speed that is thought to be the demerit of GA, uses RSM and SM. Though mutation of GA offers random variety, systematic variety can be secured through the use of a tabu list of TS. Especially, in the initial phase, GA's convergent speed can be improved by using RSM which is using the information on the objective function acquired through the GA process and then making response surface (approximate function) and optimizing this. The optimum solution was calculated without the evaluation of an additional actual objective function, and the GA’s convergent speed could be improved. The efficiency of this method has been proven by applying traditional test functions and comparing the results to GA. It also confirmed that the global opti

mum solution is being searched efficiently by applying the proposed algorithm to weight minimization where avoiding resonance of the fresh water tank located on the rear of the ship was considered.   

2. Integrated evolutionary optimization algorithm (IEOA) 

2.1 Structure of IEOA 

The main idea is to reduce the number for evaluation of the objective function by using RSM which is one among the designed experiments to reduce the repetitive number, since it is one of the demerits of optimum design. The IEOA consists of four main parts: (i) GA for governing the general algorithm, (ii) tabu-list for systematic variety of solution, (iii) RSM for improving convergent speed for getting a candidate solution, and (iv) modified SM for local search. Figure 1 represents the flowchart of the IEOA. The left side of the flowchart shows global search region that is similar to the flowchart of standard GA, excluding the function assurance criterion (FAC), a set of history, tabu-list, and RSM. These parts offer candidate solutions, which are considered as initial search points in the local search region. The right side represents the local search region. This part finds the optimum solution by the modified SM, which uses the final solution by results of the global search as initial search point. Fig. 1-1~Fig. 1-3 show the detail process of Part A, B, and C in Fig. 1  

Fig. 1. Flowchart of proposed algorithm (IEOA).

Fig. 1-1. Flowchart of Part A (update Sh).

Fig. 1-2. Flowchart of Part B (check tabu list).

Part A shown in detail in Fig. 1-1 shows a set of history Sh region which provides the well distributed points to make a response surface. The Sh is constructed according to the following procedures:

 Step 1: Read inpiduals from the current population 

Step 2: NSh = NSh + Psize   

Fig. 1-3. Flowchart of Part C (RSM).

where NSh and Psize mean the size of a set of history and size of population, respectively.

Step 3: if NSh ≤ NShmax, then go to step 7 

where NShmax means maximum size in Sh. 

Step 4: Evaluate the dense grade Dg for each inpidual. 

Dg = max (dik) + mean (dik)  

where dik is Euclidian distance between i and k;  

||x(i)-x(k)||, i = 1, …, NSh; i ≠ k  

Step 5: Rank the inpiduals for Dg. 

Step 6: Select the higher ranked first NShmax inpiduals. 

Step 7: Store the solutions in Sh and go out. 

Part B shown detail in Fig. 1-2 represents checking the tabu-list to have a persity of solution. The one inpidual which is selected in GA’s inpiduals after crossover process is reviewed to ensure the persity of solution. If the persity of solution is ensured, the inpidual is selected and if not, the crossover process is repeated. That is, the inpidual is selected when it is located far away from the dense area. A dense grade criterion of solution and acceptance criteria of inpidual are D ⊂ RN for normalized domain and V ⊂ RN for a domain having the equally pided by NShmax from D where N is number of design variables. Let |V| is the size of V, then