Testing the Performance of Bat-Algorithm for Permutation Flow Shop Scheduling Problems with Makespan Minimization

Bellabai, Jeen Robert; Leela, Brabin Nivas Murugadhas; Kennedy, Senthil Maharaj Ramesh

doi:10.1590/1678-4324-2022210840

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Article - Engineering, Technology and Techniques • Braz. arch. biol. technol. 65 • 2022 • https://doi.org/10.1590/1678-4324-2022210840 copy

Testing the Performance of Bat-Algorithm for Permutation Flow Shop Scheduling Problems with Makespan Minimization

Authorship SCIMAGO INSTITUTIONS RANKINGS

HIGHLIGHTS

BAT algorithm is presented to minimize makespan as objective for the permutation flowshop scheduling problem by modifying the process parameter.
In order to improve the initial quality & diversity, an NEH heuristics based constructive approach is given an initial solution.

Abstract

In this work, a BAT Algorithm is proposed to solve the permutation flow shop scheduling problem (PFSSP) with minimizing makespan criterion. In a PFSSP, there are n-jobs and m-machines with a proportional deterioration is considered in which all machines process the jobs in the same order, i.e., a permutation schedule. Every job comprises of a foreordained arrangement of assignment operations, each of which should be handled without intrusion for a given timeframe on a given machine. As of late, optimization algorithms such as ant colony optimization (ACO), simulated annealing (SA), artificial bee colony (ABC), genetic algorithm (GA), particle swarm optimization (PSO) and tabu search (TS) have assumed a significant role in solving PFSSPs. The popular NEH algorithm is considered as the parent algorithm to find the initial solution, and the makespan is minimized in two stages of simulation. The proposed algorithm is tested on 12 flow shop scheduling bench mark problems from OR Library. The proposed algorithm is validated with a well-chosen set of benchmark problems in the literature. Computational results indicate that the proposed bat algorithm is more efficient than the TLBO & HPSO algorithm.

Keywords:
Scheduling; Flow shop; BAT algorithm; Makespan; Benchmark Problem

TLBO for FSSP	Prob	WKS	BAT				TLBO [13]
TLBO for FSSP	Prob	WKS	Best	Max	Avg	APRD	Best	Max	Avg	APRD
20x5	Ta 001	1278	1278	1297	1284.9	0.5399	1278	1297	1287.2	0.7199
20x10	Ta 011	1582	1609	1683	1623.3	2.6106	1586	1618	1606	1.5171
20x20	Ta 021	2297	2323	2401	2355.4	2.5424	2325	2370	2344.7	2.0766
50x5	Ta 031	2724	2724	2730	2725.6	0.0587	2724	2741	2729.4	0.1982
50x10	Ta 041	2991	3119	3145	3110.6	3.8449	3120	3169	3141.4	5.0284
50x20	Ta 051	3771	4001	4101	4021.9	6.6534	3986	4095	4029.7	6.8602
100x5	Ta 061	5493	5493	5519	5496.4	0.0619	5493	5527	5499.4	0.1165
100x10	Ta 071	5770	5808	5846	5819.6	0.8596	5887	5997	5928.7	2.7504
100x20	Ta 081	6286	6485	6607	6527.2	3.8371	6549	6726	6617.8	5.2784
200x10	Ta 091	10868	10942	10942	10942	0.6809	10979	11079	11033	1.5182
200x20	Ta 101	11294	11600	11639	11622.5	2.9086	11855	12024	11940	5.7199
500x20	Ta 111	26189	26612	26652	26622.6	1.6557	27377	27565	27492	4.9754

Prob	PS (J^*M)	WKS	TLBO[13]			HPSO[18]			NPSO [19]			BAT
Prob	PS (J^*M)	WKS	Best	Max	Avg	Best	Max	Avg	Best	Max	Avg	Best	Max	Avg
Ta 001	20x5	1278	1278	1297	1287.2	1278	1278	1278	1278	1297	1279.9	1278	1297	1284.9
Ta 011	20x10	1582	1586	1618	1606	1582	1596	1587.3	1582	1639	1605.8	1609	1683	1623.3
Ta 021	20x20	2297	2325	2370	2344.7	2297	2315	2307	2297	2376	2334.9	2328	2401	2355.4
Ta 031	50x5	2724	2724	2741	2729.4	2724	2724	2724	2724	2729	2725	2724	2730	2725.6
Ta 041	50x10	2991	3120	3169	3141.4	3034	3063	3053.6	3034	3129	3086.9	3078	3145	3110.6
Ta 051	50x20	3771	3986	4095	4029.7	3923	3963	3944.6	3938	3989	3964.3	4001	4101	4021.9
Ta 061	100x5	5493	5493	5527	5499.4	5493	5493	5493	5493	5495	5493.2	5493	5519	5496.4
Ta 071	100x10	5770	5887	5997	5928.7	None	None	None	None	None	None	5808	5846	5819.6
Ta 081	100x20	6286	6549	6726	6617.8	None	None	None	None	None	None	6485	6607	6527.2
Ta 091	200x10	10868	10979	11079	11033	None	None	None	None	None	None	10942	10942	10942
Ta 101	200x20	11294	11855	12024	11940	None	None	None	None	None	None	11600	11639	11622.5
Ta 111	500x20	26189	27377	27565	27492	None	None	None	None	None	None	26612	26652	26622.6

Prob	PS(J^*M)	IG1[17]	IG2[17]	HDDE [11]	TLBO	BAT
Ta 001	20x5	0.39	0.46	1.49	0.72	0.54
Ta011	20x10	0.48	0.62	1.53	1.52	2.61
Ta 021	20x20	0.31	0.32	1.23	2.08	2.54
Ta 031	50x5	2.71	2.99	5.69	0.20	0.06
Ta 041	50x10	3.24	3.23	5.63	5.03	4.00
Ta 051	50x20	2.88	2.54	5.04	6.86	6.65
Ta 061	100x5	3.82	3.56	7.22	0.12	0.06
Ta 071	100x10	3.34	3.48	6.67	2.75	0.86
Ta 081	100x20	3.03	2.82	4.41	5.28	3.84
Ta 091	200x10	3.85	3.63	6.91	1.52	0.68
Ta 101	200x20	2.31	2.2	4.34	5.72	2.91
Ta 111	500x20	1.32	1.33	3.93	4.98	1.66
AREP		2.31	2.27	4.51	3.07	2.20

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[1] *Correspondence: jeenrobert@aaacet.ac.in; Tel.: +91-9488081212 (R.B.J.R.).