Two Chaotic Patterns of Dynamic Risk Definition for Solving Hazardous Materials Routing Problem

Table 2

Best and secondary optimal paths and their lengths from Ardabil (node 33) to Sanandaj (node 67).

Chaos equation	(Cost, risk)	Solution ranking	Ranked most probable path	Length (KM)
Logistic map	(0, 1)	Best optimal	33 34 37 38 39 40 42 44 45 50 51 52 53 59 60 65 85 67	783	74
		Secondary optimal	33 34 37 38 39 40 42 44 45 50 51 52 53 58 61 64 85 67	657	63
	(0.3, 0.7)	Best optimal	33 34 37 38 39 40 42 44 45 50 51 52 53 58 61 64 85 67	657	116
		Secondary optimal	33 34 37 38 39 40 42 44 45 50 51 52 53 59 60 65 85 67	783	97
	(0.5, 0.5)	Best optimal	33 34 37 38 39 40 42 44 45 50 51 52 53 58 61 64 85 67	657	185
		Secondary optimal	33 34 37 38 39 40 42 44 45 50 51 52 53 59 60 65 85 67	783	93
	(0.7, 0.3)	Best optimal	33 34 37 38 39 40 42 44 45 50 51 52 53 58 61 64 85 67	657	318
		Secondary optimal	33 34 37 38 39 40 42 44 45 50 51 52 53 59 60 65 85 67	783	35
	(1, 0)	Best optimal	33 34 37 38 39 40 42 44 45 50 51 52 53 58 61 64 85 67	657	365
		Secondary optimal	No path
	Best solution		(33 34 37 38 39 40 42 44 45 50 51 52 53 58 61 64 85 67)	644
Route to chaos	(0, 1)	Best optimal	33 34 37 38 39 40 42 44 45 50 46 83 47 82 48 75 72 65 85 67	1023	99
		Secondary optimal	33 34 37 38 39 40 42 44 45 50 51 52 53 59 60 65 85 67	783	83
	(0.3, 0.7)	Best optimal	33 34 37 38 39 40 42 44 45 50 51 52 53 59 60 65 85 67	783	162
		Secondary optimal	33 34 37 38 39 40 42 44 45 50 46 83 47 82 48 75 72 65 85 67	1023	60
	(0.5, 0.5)	Best optimal	33 34 37 38 39 40 42 44 45 50 51 52 53 59 60 65 85 67	783	207
		Secondary optimal	33 34 37 38 39 40 42 44 45 50 46 83 47 82 48 75 72 65 85 67	1023	78
	(0.7, 0.3)	Best optimal	33 34 37 38 39 40 42 44 45 50 51 52 53 59 60 65 85 67	783	348
		Secondary optimal	33 34 37 38 39 40 42 44 45 50 46 83 47 82 48 75 72 65 85 67	1023	11
	(1, 0)	Best optimal	33 34 37 38 39 40 42 44 45 50 51 52 53 59 60 65 85 67	783	365
		Secondary optimal	No path
	Best solution		(33 34 37 38 39 40 42 44 45 50 51 52 53 59 60 65 85 67)	783

Cost, risk) priority set is ordered by left to right.
Frequency is regarding 365 iterations.