A Novel Memetic Algorithm Based on Decomposition for Multiobjective Flexible Job Shop Scheduling Problem

Table 3

Comparison of three different aggregation functions on average IGD and HV values over 10 independent runs for all Kacem and BRdata instances.

Instance		IGD			HV
		MOMAD	MOMAD-WS	MOMAD-PBI	MOMAD	MOMAD-WS	MOMAD-PBI
ka	40000	0.1054	0.2108	0.1845	0.5910	0.5843	0.5860
ka	40000	0.1071	0.1252	0.1541	0.6574	0.6191	0.5917
ka	40000	0.0298	0.0400	0.0651	1.0594	1.0481	0.9762
ka	40000	0.1394	0.0767	0.1676	0.6802		0.6873
ka	40000	0.4002	0.4108	0.4405	0.3727	0.3474	0.2849
MK01	50000	0.0304	0.0254	0.0619^†	1.0316	1.0368	0.9975^†
MK02	50000	0.0415	0.0495	0.0972^†	0.9908	0.9772	0.9374^†
MK03	50000	0.0233	0.1251	0.2837^†	0.8296	0.7027	0.4929^†
MK04	50000	0.0340	0.0282	0.1128^†	1.1437	1.1455	1.0758^†
MK05	50000	0.0072	0.0057	0.1181^†	1.0576	1.0636	0.9120^†
MK06	60000	0.0473	0.0529^†	0.0993^†	0.9700	0.9610	0.8906^†
MK07	50000	0.0218	0.0313	0.1288^†	0.9906	0.9734^†	0.8484^†
MK08	50000	0.0000	0.0075	0.1943^†	0.5755	0.5705	0.3832^†
MK09	50000	0.0365	0.0396	0.1489^†	1.1893	1.1725^†	1.0642^†
MK10	70000	0.0391	0.0765^†	0.0597^†	1.1480	1.0751^†	1.0743^†

§ means the number of function evaluations; † means that the results are significantly outperformed by MOMAD; ‡ means that the results are significantly better than MOMAD.