E-dyNSGA-III: A Multi-Objective Algorithm for Handling Pareto Optimality over Time

Table 5

Minkowski distance values for DTLZ5(x,y) DMOPs.

Algorithm	Iterations	Objectives
		F1	F2	F3	F4	F5	F6	F7	F8	F9	F10
Pareto-PCA-NSGA-II	100 (DTLZ5(3,10))	0.9547	0.7652	0.6383	0.7295	0.4873	0.5084	0.6215	0.3187	0.8540	0.3694
	DTLZ5(5,10)	0.8032	0.9173	0.7492	0.7916	0.5826	0.5919	0.4395	0.6184	0.6831	0.5948
	200 (DTLZ5(3,10))	0.8126	0.8957	0.7316	0.6386	0.5194	0.5397	0.5817	0.6217	0.6683	0.5726
	DTLZ5(5,10)	0.8316	0.9107	0.7528	0.6637	0.5859	0.6183	0.7046	0.6173	0.6974	0.6163
	400 (DTLZ5(3,10))	0.8051	0.8584	0.7437	0.5846	0.4983	0.5273	0.5428	0.6104	0.5936	0.5284
	DTLZ5(5,10)	0.8104	0.8861	0.6901	0.5917	0.5620	0.6054	0.6939	0.5818	0.6411	0.5749
	600 (DTLZ5(3,10))	0.8152	0.7763	0.7195	0.5405	0.4592	0.5196	0.5097	0.5828	0.5754	0.5127
	DTLZ5(5,10)	0.7973	0.8150	0.6635	0.5235	0.5229	0.5936	0.6306	0.5572	0.6049	0.5207
	800 (DTLZ5(3,10))	0.7773	0.7102	0.6936	0.5603	0.4726	0.5903	0.5761	0.5614	0.5419	0.4816
	DTLZ5(5,10)	0.7618	0.7954	0.6395	0.5404	0.5190	0.6105	0.6054	0.5072	0.5810	0.5503
	900 (DTLZ5(3,10))	0.7183	0.6937	0.6294	0.6919	0.4330	0.5729	0.4609	0.5337	0.5172	0.4405
	DTLZ5(5,10)	0.6641	0.7294	0.5803	0.5906	0.5021	0.6308	0.5992	0.4826	0.5319	0.4904
	1000 (DTLZ5(3,10))	0.6992	0.6407	0.6390	0.5607	0.4118	0.6517	0.4349	0.5185	0.4728	0.4239
	DTLZ5(5,10)	0.6390	0.6973	0.7294	0.5621	0.5137	0.6116	0.5621	0.4319	0.5185	0.4705
Cloudde	100 (DTLZ5(3,10))	0.8954	0.7385	0.7106	0.7216	0.7036	0.7130	0.6942	0.6284	0.7705	0.6106
	DTLZ5(5,10)	0.7720	0.7251	0.7518	0.7735	0.6219	0.6142	0.5184	0.6285	0.6617	0.6169
	200 (DTLZ5(3,10))	0.8626	0.7152	0.6930	0.8215	0.6961	0.7218	0.7105	0.6170	0.7384	0.6048
	DTLZ5(5,10)	0.7385	0.6943	0.7305	0.7280	0.6105	0.5992	0.6998	0.5883	0.6595	0.5972
	400 (DTLZ5(3,10))	0.8428	0.7164	0.6647	0.8006	0.6764	0.7162	0.6996	0.5964	0.7159	0.5885
	DTLZ5(5,10)	0.7168	0.6979	0.7206	0.7303	0.6007	0.5730	0.6994	0.5693	0.6501	0.5726
	600 (DTLZ5(3,10))	0.8247	0.7071	0.6482	0.7836	0.6831	0.6947	0.6996	0.5817	0.6992	0.5742
	DTLZ5(5,10)	0.6915	0.6385	0.7115	0.6931	0.5980	0.5594	0.6999	0.5884	0.6372	0.5638
	800 (DTLZ5(3,10))	0.7193	0.7002	0.6298	0.7528	0.6406	0.7274	0.6986	0.5717	0.6850	0.5318
	DTLZ5(5,10)	0.7753	0.6273	0.7096	0.6429	0.6005	0.5496	0.6958	0.5796	0.6674	0.5490
	900 (DTLZ5(3,10))	0.6974	0.6996	0.6499	0.7327	0.6217	0.7106	0.6983	0.5596	0.6969	0.5642
	DTLZ5(5,10)	0.7514	0.6151	0.6941	0.6140	0.5555	0.5165	0.6989	0.6063	0.6486	0.5276
	1000 (DTLZ5(3,10))	0.6736	0.6721	0.6295	0.7164	0.6003	0.6637	0.6973	0.5496	0.6741	0.5412
	DTLZ5(5,10)	0.6990	0.5973	0.6686	0.5976	0.5374	0.5326	0.6984	0.5995	0.6271	0.5184
E-dyNSGA-III	100 (DTLZ5(3,10))	0.8991	0.6383	0.6283	0.7548	0.4552	0.4996	0.6385	0.5135	0.7954	0.3419
	DTLZ5(5,10)	0.9063	0.7396	0.7126	0.6076	0.6021	0.5591	0.4417	0.4157	0.6519	0.4886
	200 (DTLZ5(3,10))	0.6503	0.7292	0.7614	0.6166	0.4962	0.5288	0.6995	0.4007	0.6524	0.4527
	DTLZ5(5,10)	0.7294	0.6149	0.6337	0.6004	0.5916	0.5184	0.4406	0.5535	0.7642	0.5001
	400 (DTLZ5(3,10))	0.6638	0.7247	0.7308	0.6280	0.6135	0.5429	0.6735	0.4931	0.6384	0.4961
	DTLZ5(5,10)	0.7186	0.6846	0.6368	0.5908	0.5584	0.5230	0.5250	0.5409	0.6246	0.5814
	600 (DTLZ5(3,10))	0.6863	0.7164	0.7285	0.6008	0.6147	0.5226	0.6510	0.5037	0.6105	0.5010
	DTLZ5(5,10)	0.6930	0.6201	0.6365	0.7071	0.5527	0.5251	0.5307	0.5915	0.6025	0.5793
	800 (DTLZ5(3,10))	0.6681	0.6840	0.6810	0.5904	0.6003	0.5136	0.5509	0.5025	0.7205	0.4947
	DTLZ5(5,10)	0.6885	0.6380	0.6380	0.6912	0.5175	0.5248	0.5288	0.5841	0.5936	0.5375
	900 (DTLZ5(3,10))	0.6992	0.7003	0.6337	0.5604	0.5942	0.5287	0.5482	0.5698	0.4428	0.4719
	DTLZ5(5,10)	0.6127	0.6515	0.6447	0.6530	0.5114	0.5189	0.5995	0.5659	0.5730	0.5213
	1000 (DTLZ5(3,10))	0.6825	0.6990	0.6295	0.5561	0.5883	0.5162	0.5214	0.5378	0.4516	0.4436
	DTLZ5(5,10)	0.6295	0.6521	0.6417	0.6174	0.5119	0.5173	0.5583	0.5530	0.5682	0.4632