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3.2 Simulation results
Fig. 3 shows the convergence trend of objective function for each test function. According to the results, GRSM (GA+RSM) and IEOA (GA+RSM+tabu list) algorithms which are based on RSM have faster convergent speed and more accurate solutions than standard GA, which validated the efficiency of RSM on the calculation. Also, the tabu list enables convergence to solutions quickly on the multimodal function due to the systematic persity of solution. The setting parameters for each algorithm are listed in Table 1. Table 2 shows the comparison of optimization results for the above stated three test functions. The evaluation number means total evaluation number of the objective function used in optimization procedure, and it is directly proportional to the total calculation time. According to the results, for all test functions, IEOA can give better solutions than GA on accuracy and convergent speed. For the Rastrigin function, which is very useful to evaluate the global search ability because there are many local minima around the global minimum, IEOA found a global minimum with higher accuracy and less elapsed time compared to GA. According to these results, the proposed hybrid algorithm is a powerful global optimization algorithm from the view of convergent speed and global search ability.
Table 1. Set parameters for GA and IEOA.
Parameters Value Remarks
No. of generation
Population size, Psize
Crossover probability, Pc
Mutation probability, Pm 100
100
0.5
0.1 GA & IEOA
Size of Sh for RSM, NShmax
Step size for TS
Count number for TS 1000
10
3 IEOA only
Fig. 3. Convergent trend of objective function.
Table 2. Comparison of optimization results.
Test function Exact solutions Methods
Results No. of evaluation
f(x) x1, x2
Four-peak
function f(x) = 1.9543
x1 = x2 = 0.0 GA
IEOA 1.927
1.927 2.403×10-3,2.787×10-3
2.736×10-3,2.736×10-3 2353
459
Rosenbrock
function f(x) = 0.0
x1 = x2 = 1.0 GA
IEOA 1.640×10-5
0.0 0.996, 0.996
1.0, 1.0 1046
419
Rastrigin
function f(x) = 0.0
x1 = x2 = 0.0 GA
IEOA 1.586×10-4
0.0 1.408×10-4, 8.15×10-4
−3.076×10-9, −7.747×10-10 2109
514
4. Optimum design of fresh water tank of ship
In the engine room and the rear region of a ship, there are many tank structures that contact fresh and sea water or fuel and lubricating oil. Also, these are possibly subject to the excessive vibration during voyage because they are arranged around the main excitation sources of the ship such as the main engine and propeller. If problems occur, it takes a considerable cost, time and effort to improve the situation because the reinforcement work for emptying the fluid out of the tanks, additional welding and special painting and so on is required. It is very important to predict the precise vibration characteristics of the tank structures at the design stage. Optimum design needs to be applied. Especially when the structure is in contact with fluid, much analysis time must be taken. Therefore, a new optimization algorithm is required for getting a short analysis time and accurate solution. In this study, optimum design of a fresh water tank in an actual ship is carried out to verify the validity of the proposed algorithm (IEOA) and the results are compared to that of standard GA.