📡 Radio Link Frequency Assignment Problem (RLFAP)

The Radio Link Frequency Assignment Problem is a Constraint Satisfaction Problem (CSP) which consists of assigning frequencies to a set of radio links defined between pairs of sites in order to avoid interferences.
Extensive description of the problem can be found here.

Search methods used:

• Backtracking with Forward Checking (FC)
• Backtracking with Maintaining Arc Consistency (MAC)
• Forward Checking with Conflict directed BackJumping hybrid (FC-CBJ)
• Min Conflicts

Use of heuristics:

In order to speed up the search, I am using a conflict directed variable ordering heuristic such as is the dom/wdeg heuristic. Due to the difficulty of the instances, the search time takes several hours, but, with the help of dom/wdeg heuristic the search time takes only a few seconds. The heuristic it is used in all of the above methods while searching.
Reference to the related paper about dom/wdeg heuristic below.

Experimental results:

Method: Forward Checking (FC) with dom/wdeg heuristic

Instance	Result	Time(s)	Assignments	Constraint checks
11	SAT	~9	13855	2829739
2-f24	SAT	~0.05	254	22384
2-f25	UNSAT	~41	198551	37282795
3-f10	SAT	~1.1	4304	777626
3-f11	UNSAT	~49	210370	38962375
8-f10	SAT	~630	2512599	325083064
8-f11	UNSAT	~204	638778	86488684
14-f27	SAT	~36	99915	5052782
14-f28	UNSAT	~180	318864	19178933
6-w2	UNSAT	~0.05	250	46258
7-w1-f4	SAT	~0.2	2308	106877

Method: Maintaining Arc Consistency (MAC with AC3) with dom/wdeg heuristic

Instance	Result	Time(s)	Assignments	Constraint checks
11	SAT	~11	4560	9261742
2-f24	SAT	~0.1	228	165964
2-f25	UNSAT	~145	52330	100095447
3-f10	SAT	~2	852	1269090
3-f11	UNSAT	~36	8292	25501966
8-f10	SAT	~46	14149	30407876
8-f11	UNSAT	~6	1979	4608720
14-f27	SAT	~18	15389	4337430
14-f28	UNSAT	~22	8874	8185280
6-w2	UNSAT	~0.08	44	93186
7-w1-f4	SAT	~0.2	442	277559

Method: FC-CBJ hybrid with dom/wdeg heuristic

Instance	Result	Time(s)	Assignments	Constraint checks
11	SAT	~4	5576	1185589
2-f24	SAT	~0.5	250	22287
2-f25	UNSAT	~11	44875	8899233
3-f10	SAT	~0.8	2697	480205
3-f11	UNSAT	~25	85283	15145162
8-f10	SAT	~130	334057	48612625
8-f11	UNSAT	~30	64408	9435454
14-f27	SAT	~25	50859	2615605
14-f28	UNSAT	~20	29178	2012526
6-w2	UNSAT	~0.05	250	46258
7-w1-f4	SAT	~0.3	2120	96116

Method: Min Conflicts with maximum steps = 1000 (average of 5 executions)

Instance	Result	Time(s)	Assignments	Constraint checks	Constraints violated
11	UNSAT	~6.3	1680	9529708	10
2-f24	UNSAT	~1.8	1200	3022859	12
2-f25	UNSAT	~1.7	1200	2963507	18
3-f10	UNSAT	~3.9	1400	6183665	39
3-f11	UNSAT	~3.8	1400	6147748	42
8-f10	UNSAT	~5.9	1680	8005154	215
8-f11	UNSAT	~6.4	1680	7995665	262
14-f27	UNSAT	~7	1916	9540495	338
14-f28	UNSAT	~6.9	1916	9524215	439
6-w2	UNSAT	~1.1	1200	1641059	82
7-w1-f4	UNSAT	~1.2	1400	1499578	64

Usage

  $ python3 rlfap.py <instance> <method>

i.e., for the instance "11" run each of the methods (FC/MAC/FC-CBJ/Min-Conflicts) as follows:

  $ python3 rlfap.py 11 FC              
  $ python3 rlfap.py 11 MAC             
  $ python3 rlfap.py 11 FC-CBJ          
  $ python3 rlfap.py 11 Min-Conflicts  

CODE CITATION

I use csp.py, search.py & utils.py from https://github.com/aimacode/aima-python.

REFERENCES

Boussemart, F., Hemery, F., Lecoutre, C., & Sais, L. (2004). Boosting systematic search by weighting constraints. In ECAI (Vol. 16, pp. 146-150) (http://www.frontiersinai.com/ecai/ecai2004/ecai04/pdf/p0146.pdf)