Solving Partial Differential Equations Using a New Differential Evolution Algorithm

Table 1

Fitness and RMSE.

Case	Algorithm	Fitness	RMSE
PDE1	DE/ran/1/bin	9.4210×10^−2	1.0269×10^−2
	DE/ran/1/exp	4.6360×10^−4	7.2340×10^−4
	DE/current-to-best/2/bin	1.9190×10^−1	1.6346×10^−2
	DE/current-to-best/2/exp	1.5922×10^1	5.6488×10^−1
	DE-New	4.6345×10^−4	7.2560×10^−4
	Result from [24]	—	6.3700×10^−3
PDE2	DE/ran/1/bin	1.2251×10^−1	1.0285×10^−2
	DE/ran/1/exp	1.1404×10^−4	2.6039×10^−4
	DE/current-to-best/2/bin	7.3667×10^−1	2.8889×10^−2
	DE/current-to-best/2/exp	2.6998×10^1	7.4573×10^−1
	DE-New	1.1351×10^−4	2.4529×10^−4
	Result from [24]	—	1.1600×10^−3
PDE3	DE/ran/1/bin	1.0013×10^−1	1.0973×10^−2
	DE/ran/1/exp	4.1618×10^−6	4.2589×10^−5
	DE/current-to-best/2/bin	1.3256×10^−1	1.2053×10^−2
	DE/current-to-best/2/exp	9.5633	1.4867×10^−1
	DE-New	6.0052×10^−8	9.4888×10^−6
	Result from [24]	—	5.9000×10^−3
PDE4	DE/ran/1/bin	9.1112×10^−2	7.5679×10^−3
	DE/ran/1/exp	3.0683×10^−3	6.6047×10^−3
	DE/current-to-best/2/bin	5.2632×10^−1	2.1121×10^−2
	DE/current-to-best/2/exp	6.6558	1.1495×10^−1
	DE-New	3.0661×10^−3	6.6054×10^−3
	Result from [24]	—	1.2300×10^−3
PDE5	DE/ran/1/bin	1.0649	3.6933×10^−2
	DE/ran/1/exp	8.2231×10^−1	3.7063×10^−2
	DE/current-to-best/2/bin	5.1483	6.8413×10^−2
	DE/current-to-best/2/exp	7.4642×10^1	1.0544
	DE-New	8.2224×10^−1	3.7243×10^−2
	Result from [24]	—	9.0600×10^−4
PDE6	DE/ran/1/bin	7.3267×10^−1	3.7452×10^−1
	DE/ran/1/exp	4.3440×10^−1	3.7732×10^−1
	DE/current-to-best/2/bin	4.6867	3.6634×10^−1
	DE/current-to-best/2/exp	6.2369×10^1	6.5142×10^−1
	DE-New	4.3435×10^−1	3.8225×10^−1
	Result from [24]	—	1.7900×10^−2