一种新的基于预测的动态多目标进化算法

doi:10.19665/j.issn1001-2400.20230902

Abstract

Abstract:

Dynamic multi-objective optimization problems(DMOPs) where the environments change over time require that an evolutionary algorithm be able to continuously track the moving Pareto set or Pareto front.Response strategies based prediction has received much attention.However,these strategies mostly use historical environmental information for prediction,which will make the predicted results inaccurate.In this paper,we strengthen the mining and utilization of new environmental information and propose a new prediction strategy based evolutionary algorithm for dynamic multi-objective optimization(RAM),which includes mainly two core parts,namely,response mechanism and acceleration mechanism.The response mechanism reinitializes the population after the environmental changes,some individuals are generated by the prediction strategy,which is close to the new environmental PS to improve the optimization ability of this algorithm,and the remaining individuals are generated by the local search strategy to increase the population diversity.The acceleration mechanism is used in the static optimization process to accelerate the convergence speed of the RAM.Finally,the RAM is compared with other three advanced dynamic multi-objective optimization algorithms on a series of test functions with different dynamic characteristics.The results show that the RAM has more advantages than other three algorithms in solving dynamic multi-objective optimization problems.

Key words: evolutionary algorithm, dynamic multi-objective optimization, prediction strategy, new environment information

CLC Number:

WAN Mengyi, WU Yan. New prediction strategy based evolutionary algorithm for dynamic multi-objective optimization[J].Journal of Xidian University, 2024, 51(3): 124-135.

Figures/Tables 5

测试函数	(n_t,τ_t)	NSGA-Ⅱ-A mean(std)	Tr-MOEA mean(std)	DSS mean(std)	RAM mean(std)
F9	(10,5)	2.26e+0(3.16e-1)	2.74e+0(1.74e-2)	2.56e-1(3.38e-2)	1.84e-1(1.82e-2)
	(10,10)	1.27e+0(2.67e-1)	2.58e+0(5.18e-2)	9.99e-2(1.05e-2)	6.96e-2(8.60e-3)
	(10,20)	4.95e-1(1.60e-1)	2.24e+0(1.31e-1)	3.34e-2(4.00e-3)	4.39e-2(3.80e-3)
F10	(10,5)	2.56e+0(3.89e-1)	6.72e+0(5.71e-1)	2.02e-1(2.45e-2)	3.05e-1(4.79e-2)
	(10,10)	1.29e+0(2.27e-1)	4.52e+0(5.51e-1)	8.14e-2(8.00e-3)	1.02e-1(2.33e-2)
	(10,20)	5.79e-1(1.04e-1)	2.35e+0(4.32e-1)	3.52e-2(4.60e-3)	3.34e-2(6.30e-3)
F11	(10,5)	2.48e+0(3.69e-1)	4.47e+0(1.15e-1)	3.38e-1(1.32e-1)	3.93e-1(8.38e-2)
	(10,10)	1.40e+0(2.52e-1)	3.70e+0(1.76e-1)	1.27e-1(4.21e-2)	9.65e-2(2.08e-2)
	(10,20)	7.70e-1(1.22e-1)	3.13e+0(2.64e-1)	3.99e-2(1.27e-2)	2.75e-2(3.00e-3)
F12	(10,5)	2.34e+0(5.71e-1)	3.18e+0(2.40e-1)	2.19e-1(3.33e-2)	1.76e-1(2.94e-2)
	(10,10)	1.21e+0(3.49e-1)	2.85e+0(1.17e-1)	794e-2(9.20e-3)	5.29e-2(7.60e-3)
	(10,20)	5.02e-1(1.61e-1)	2.37e+0(1.45e-1)	2.73e-2(3.40e-3)	2.42e-2(2.30e-3)
DMOP3	(10,5)	1.04e-1(1.81e-2)	3.20e-2(8.90e-3)	6.27e-2(6.20e-3)	4.97e-2(5.50e-3)
	(10,10)	5.07e-2(2.80e-3)	2.56e-2(6.00e-3)	2.26e-2(3.70e-3)	1.84e-2(2.00e-3)
	(10,20)	3.62e-2(2.20e-3)	2.14e-2(2.20e-3)	1.02e-2(9.00e-3)	1.07e-2(2.00e-3)
ZJZ7	(10,5)	2.83e+0(3.14e-1)	3.92e-1(3.00e-2)	3.94e-1(1.65e-1)	3.36e-1(5.86e-2)
	(10,10)	1.18e+0(2.07e-1)	2.56e-1(1.76e-2)	1.35e-1(3.32e-2)	1.10e-1(1.75e-2)
	(10,20)	3.00e-1(8.76e-2)	1.95e-1(4.80e-3)	4.01e-2(5.70e-3)	3.26e-2(6.20e-3)
ZJZ8	(10,5)	1.25e+0(1.97e-1)	2.81e-1(2.24e-2)	3.37e-1(5.22e-2)	2.64e-1(6.15e-2)
	(10,10)	4.99e-1(1.33e-1)	2.50e-1(8.80e-3)	1.30e-1(2.69e-2)	1.12e-1(2.61e-2)
	(10,20)	1.54e-1(5.12e-2)	1.51e-1(9.80e-3)	3.97e-2(5.30e-3)	2.57e-2(6.50e-3)
JY10	(10,5)	2.38e+0(4.77e-1)	9.68e-1(6.32e-2)	4.28e-1(1.95e-1)	3.18e-1(2.17-1)
	(10,10)	1.26e+0(3.63e-1)	7.11e-1(4.07e-2)	3.10e-1(5.98e-2)	2.59e-1(8.45e-2)
	(10,20)	7.71e-1(2.85e-1)	5.87e-1(5.67e-2)	1.33e-1(5.20e-3)	1.28e-1(8.70e-3)

测试函数	(n_t,τ_t)	NSGA-Ⅱ-A mean(std)	Tr-MOEA mean(std)	DSS mean(std)	RAM mean(std)
F9	(5,10)	1.65e+0(2.12e-1)	2.63e+0(9.19e-2)	8.42e-2(1.77e-2)	7.59e-2(1.66e-2)
	(10,10)	1.26e+0(2.66e-1)	2.58e+0(5.18e-2)	9.99e-2(1.05e-2)	6.96e-2(8.6e-3)
	(20,10)	8.53e-1(2.60e-1)	2.56e+0(3.16e-2)	7.47e-2(1.09e-2)	6.46e-2(1.11e-2)
F10	(5,10)	1.88e+0(2.80e-1)	4.03e+0(5.02e-1)	1.24e-1(2.78e-2)	1.43e-1(4.40e-2)
	(10,10)	1.29e+0(2.27e-1)	4.52e+0(5.51e-1)	8.14e-2(8.00e-3)	1.02e-1(2.33e-2)
	(20,10)	7.75e-1(1.73e-1)	4.06e+0(5.34e-1)	8.83e-2(9.68e-1)	7.39e-2(1.43e-2)
F11	(5,10)	2.02e+0(3.52e-1)	3.99e+0(1.78e-1)	1.36e-1(2.70e-2)	1.45e-1(3.57e-2)
	(10,10)	1.40e+0(2.52e-1)	3.70e+0(1.76e-1)	1.27e-1(4.21e-2)	9.65e-2(2.08e-2)
	(20,10)	9.68e-1(2.31e-1)	3.54e+0(1.75e-1)	8.86e-2(3.78e-2)	6.67e-2(2.00e-2)
F12	(5,10)	1.88e+0(3.14e-1)	2.85e+0(1.23e-1)	1.24e-1(2.06e-2)	6.44e-2(6.60e-3)
	(10,10)	1.21e+0(3.49e-1)	2.85e+0(1.17e-1)	7.94e-2(9.20e-3)	5.29e-2(7.60e-3)
	(20,10)	9.61e-1(4.25e-1)	2.73e+0(2.78e-2)	5.97e-2(9.80e-3)	4.55e-2(7.5e-3)
DMOP3	(5,10)	8.72e-2(1.40e-2)	2.53e-2(1.26e-2)	2.55e-2(3.10e-3)	1.71e-2(2.50e-3)
	(10,10)	5.07e-2(2.81e-3)	2.56e-2(6.00e-3)	2.26e-2(3.70e-3)	1.84e-2(2.00e-3)
	(20,10)	3.81e-2(2.30e-3)	2.14e-2(2.20e-3)	2.13e-2(3.40e-3)	1.79e-2(2.40e-3)
ZJZ7	(5,10)	1.19e+0(2.02e+0)	3.11e-1(9.80e-3)	1.54e-1(5.63e-2)	1.02e-1(2.81e-2)
	(10,10)	1.18e+0(2.07e-1)	2.56e-1(1.76e-2)	1.35e-1(3.32e-2)	1.10e-1(1.75e-2)
	(20,10)	1.16e+0(2.09e-1)	3.10e-1(1.27e-2)	1.43e-1(5.16e-2)	1.07e-1(1.83e-2)
ZJZ8	(5,10)	5.15e-1(1.16e-1)	3.06e-1(1.28e-2)	1.61e-1(2.45e-2)	1.19e-1(2.53e-2)
	(10,10)	5.00e-1(1.33e-1)	2.50e-1(8.80e-3)	1.30e-1(2.69e-2)	1.12e-1(2.61e-2)
	(20,10)	5.42e-1(1.65e-1)	3.06e-1(1.11e-2)	1.36e-1(2.69e-2)	1.17e-1(3.30e-2)
JY10	(5,10)	7.28e-1(4.67e-1)	8.75e-1(5.17e-2)	5.37e-1(2.38e-1)	4.76e-1(2.28e-1)
	(10,10)	1.27e+0(3.63e-1)	7.11e-1(4.07e-2)	3.10e-1(5.89e-2)	2.60e-1(8.45e-2)
	(20,10)	1.01e+0(4.88e-1)	6.97e-1(6.24e-2)	2.94e-1(2.32e-1)	3.12e-1(2.69e-1)

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测试函数	(n_t,τ_t)	NSGA-Ⅱ-A mean(std)	Tr-MOEA mean(std)	DSS mean(std)	RAM mean(std)
FDA1	(10,10)	9.91e-2(2.22e-2)	1.58e-1(7.40e-3)	2.61e-2(1.90e-3)	2.02e-2(1.70e-3)
FDA1	(10,10)	9.91e-2(2.22e-2)	1.58e-1(7.40e-3)	2.61e-2(1.90e-3)	2.02e-2(1.70e-3)
FDA4	(10,10)	5.09e-2(4.20e-3)	5.74e-2(3.80e-3)	1.83e-1(6.00e-3)	1.83e-1(7.80e-3)
dMOP1	(10,10)	1.08e-1(2.24e-2)	6.67e-2(1.37e-2)	1.51e-1(8.60e-2)	6.52e-2(3.88e-2)
dMOP2	(10,10)	6.84e-2(4.40e-3)	9.33e-2(1.75e-2)	3.53e-2(4.70e-3)	3.59e-2(3.00e-3)
F5	(10,10)	9.06e+0(4.01e+0)	6.72e-1(1.49e-2)	2.86e-1(7.72e-2)	2.52e-1(7.49e-2)
F6	(10,10)	5.30e+0(2.13e+0)	7.01e-1(1.15e-2)	5.58e-1(4.95e-1)	2.47e-1(2.51e-1)
F7	(10,10)	7.49e+0(1.91e+0)	7.60e-1(1.02e-2)	2.47e-1(1.05e-1)	1.64e-1(8.84e-2)
F8	(10,10)	6.93e-2(3.70e-3)	6.52e-2(2.60e-3)	2.44e-1(1.92e-2)	2.42e-1(1.22e-2)
F9	(10,10)	9.26e+0(3.62e+0)	5.81e-1(1.12e-2)	3.40e-1(6.47e-2)	2.22e-1(3.70e-2)
F10	(10,10)	9.13e+0(3.62e+0)	5.98e-1(2.59e-2)	2.62e-1(7.01e-2)	3.75e-1(1.21e-1)
F11	(10,10)	9.30e+0(2.56e+0)	8.01e-1(7.00e-3)	8.40e-1(5.97e-1)	5.04e-1(2.44e-1)
F12	(10,10)	8.39e+0(4.03e+0)	7.06e-1(1.69e-2)	2.89e-1(5.77e-2)	1.92e-1(5.62e-2)
dMOP3	(10,10)	2.55e-1(1.01e-2)	2.78e-2(5.80e-3)	2.64e-2(4.90e-3)	1.58e-1(5.20e-3)
ZJZ7	(10,10)	8.24e+0(2.31e+0)	2.77e-1(1.72e-2)	4.12e-1(1.08e-1)	3.97e-1(1.16e-1)
ZJZ8	(10,10)	3.19e+0(7.83e-1)	2.71e-1(1.01e-2)	4.96e-1(2.14e-1)	3.89e-1(1.33e-1)
JY10	(10,10)	5.27e+0(7.33e-1)	4.23e-1(1.20e-1)	3.49e-1(2.96e-1)	3.64e-1(6.75e-1)

New prediction strategy based evolutionary algorithm for dynamic multi-objective optimization

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测试函数	(n_t,τ_t)	NSGA-Ⅱ-A mean(std)	Tr-MOEA mean(std)	DSS mean(std)	RAM mean(std)
FDA1	(10,10)	2.75e-2(1.18e-2)	1.75e-1(9.30e-3)	1.29e-2(9.00e-4)	9.90e-3(6.00e-4)
FDA4	(10,10)	6.74e-2(5.00e-4)	7.34e-2(1.25e-2)	6.58e-2(1.20e-3)	6.63e-2(1.60e-3)
dMOP1	(10,10)	3.16e-2(8.60e-3)	6.21e-2(1.74e-2)	7.44e-2(1.17e-2)	3.51e-2(2.33e-2)
dMOP2	(10,10)	4.47e-2(1.37e-2)	1.08e-1(2.75e-2)	1.58e-2(1.90e-3)	1.56e-2(1.10e-3)
F5	(10,10)	1.24e+0(3.13e-1)	2.67e+0(2.34e-1)	7.97e-2(9.40e-3)	6.62e-2(8.20-3)
F6	(10,10)	9.22e-1(1.59e-1)	2.37e+0(7.86e-2)	9.47e-2(1.20e-2)	5.07e-2(1.70e-2)
F7	(10,10)	1.12e+0(2.17e-1)	3.50e+0(1.12e-1)	6.94e-2(1.17e-2)	4.69e-2(1.13e-2)
F8	(10,10)	8.19e-2(1.60e-3)	9.11e-2(8.90e-3)	8.05e-2(1.60e-3)	7.70e-2(1.60e-3)
F9	(10,10)	1.26e+0(2.66e-1)	2.58e+0(5.18e-2)	9.99e-2(1.05e-2)	6.96e-2(8.60e-3)
F10	(10,10)	1.29e+0(2.27e-1)	4.51e+0(5.50e-1)	7.80e-2(1.24e-2)	1.02e-1(2.33e-2)
F11	(10,10)	1.40e+0(2.52e-1)	3.70e+0(1.76e-1)	1.27e-1(4.21e-2)	9.65e-2(2.08e-2)
F12	(10,10)	1.20e+0(3.48e-1)	2.85e+0(1.17e-1)	7.94e-2(9.20e-3)	5.29e-2(7.60e-3)
dMOP3	(10,10)	5.07e-2(2.80e-3)	2.56e-2(6.00e-3)	2.26e-2(3.70e-3)	1.84e-2(2.00e-3)
ZJZ7	(10,10)	1.18e+0(2.07e-1)	2.56e-1(1.76e-2)	1.34e-1(3.32e-2)	1.10e-1(1.75e-2)
ZJZ8	(10,10)	4.99e-1(1.33e-1)	2.49e-1(8.80e-3)	1.30e-1(2.69e-2)	1.12e-1(2.61e-2)
JY10	(10,10)	1.27e+0(3.63e-1)	7.11e-1(4.07e-2)	3.10e-1(5.98e-2)	2.59e-1(8.45e-2)

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