Hybrid Algorithms for Fuzzy Reverse Supply Chain Network Design

Table 1

Combination of experimental parameters.

PSO	Population size	10	10	10	10	20	20	20	20
	Generations	500	500	1000	1000	500	500	1000	1000
	Max velocity	0.95	1.25	0.95	1.25	0.95	1.25	0.95	1.25
	Initial weight	1.25	2.15	1.25	2.15	1.25	2.15	1.25	2.15
	𝑐1, 𝑐2	2.05	2.05	2.05	2.05	2.05	2.05	2.05	2.05
	Avg. fitness	24462289	24461153	24460103	24458116	24459087	24460841	24458923	24457531
	Avg. execution time (sec.)	6.731	6.896	12.468	12.391	12.842	12.546	21.391	21.016
	Avg. convergence time (sec.)	4.766	4.275	8.791	8.437	7.986	8.311	17.694	16.972
GA	Population size	5	5	5	5	10	10	10	10
	Generations	500	500	1000	1000	500	500	1000	1000
	Crossover rate	0.75	0.8	0.75	0.8	0.75	0.8	0.75	0.8
	Mutation rate	0.08	0.07	0.08	0.07	0.08	0.07	0.08	0.07
	Avg. fitness	24465387	24464085	24462752	24461924	24463297	24463159	244603191	24459450
	Avg. execution time (sec.)	19.373	18.859	67.693	68.047	47.375	47.734	225.836	217.512
	Avg. convergence time (sec.)	17.716	16.827	62.549	62.764	44.507	44.642	219.675	211.741
PSO-GA	Population size	10	10	10	10	20	20	20	20
	Generations	500	500	1000	1000	500	500	1000	1000
	Max velocity	0.95	1.25	0.95	1.25	0.95	1.25	0.95	1.25
	Initial weight	1.25	2.15	1.25	2.15	1.25	2.15	1.25	2.15
	𝑐1, 𝑐2	2.05	2.05	2.05	2.05	2.05	2.05	2.05	2.05
	Mutation rate	0.08	0.07	0.08	0.07	0.08	0.07	0.08	0.07
	Avg. fitness	24790482	24692938	24662117	24579829	24507556	24453060	24697893	24662084
	Avg. execution time (sec.)	6.758	6.579	11.864	12.714	12.898	12.685	23.257	22.934
	Avg. convergence time (sec.)	3.147	3.038	5.342	6.182	6.379	5.824	12.681	12.507
GA-SA	Population size	5	5	5	5	10	10	10	10
	Generations	500	500	1000	1000	500	500	1000	1000
	Crossover rate	0.75	0.8	0.75	0.8	0.75	0.8	0.75	0.8
	Mutation rate	0.08	0.07	0.08	0.07	0.08	0.07	0.08	0.07
	Initial temperature	300	300	400	400	300	300	400	400
	Markov Chain Length	50	50	100	100	50	50	100	100
	Cooling rate	0.9	0.9	0.99	0.99	0.9	0.9	0.99	0.99
	Final temperature	1	1	5	5	1	1	5	5
	Avg. fitness	24459076	24458365	24458351	24458067	24457247	24456391	24457425	24457544
	Avg. execution time (sec.)	27.477	26.041	81.462	79.039	68.671	66.993	279.145	274.338
	Avg. convergence time (sec.)	22.374	20.768	74.744	73.412	63.467	62.522	265.074	263.862
PSO-SA	Population size	10	10	10	10	20	20	20	20
	Generations	500	500	1000	1000	500	500	1000	1000
	Max velocity	0.95	1.25	0.95	1.25	0.95	1.25	0.95	1.25
	Initial weight	1.25	2.15	1.25	2.15	1.25	2.15	1.25	2.15
	𝑐1, 𝑐2	2.05	2.05	2.05	2.05	2.05	2.05	2.05	2.05
	Initial temperature	300	300	400	400	300	300	400	400
	Markov Chain Length	50	50	100	100	50	50	100	100
	Cooling rate	0.9	0.9	0.99	0.99	0.9	0.9	0.99	0.99
	Final temperature	1	1	5	5	1	1	5	5
	Avg. fitness	24457588	24457887	24455842	24455147	24455895	24456068	24456457	24456778
	Avg. execution time (sec.)	14.073	13.422	26.087	25.971	26.479	25.706	38.926	37.433
	Avg. convergence time (sec.)	6.102	5.674	11.479	10.347	11.887	12.624	19.211	16.708