Adaptive Constructive Interval Disjunction
Bertrand Neveu,Gilles Trombettoni +1 more
- 04 Nov 2013
- pp 900-906
TL;DR: On a representative sample of instances, ACID appears to be the best approach in solving and optimization, and has been added to the default strategies of the Ibex interval solver.
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Abstract: An operator called CID and an efficient variant 3BCID wereproposed in 2007. For numerical CSPs handled by interval methods, these operators compute a partial consistency equivalent to Partition-1-AC for discrete CSPs. The two main parameters of CID are the number of times the main CID procedure is called and the maximum number ofsub-intervals treated by the procedure. The 3BCID operator is state-of-the-art in numerical CSP solving, but not in constrained global optimization. This paper proposes an adaptive variant of 3BCID. The number of variables handled is auto-adapted during the search, the other parameters are fixed and robust to modifications. On a representative sample of instances, ACID appears to be the best approach in solving and optimization, and has been added to the default strategies of the Ibex interval solver.
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Figures
Table III OPTIMIZATION PROBLEMS: ACID1 RESULTS 
Figure 1. Task of the var3BCID procedure. The parameter s3b is set to 10 and scid is set to 1. 
Table I CONTINUOUS CSP SOLVING: ACID1 RESULTS. FOR EACH PROBLEM, WE PRESENT ITS NUMBER OF VARIABLES AND THE RESULTS OBTAINED BY ACID1: THE CPU TIME, THE NUMBER OF BRANCHING NODES IN THE SEARCH TREE, THE AVERAGE NUMBER OF VARCIDED VARIABLES (TUNED BY ACID1 DYNAMICALLY). WE ALSO REPORT THE BEST AND THE WORST METHODS AMONG ACID1, HC4, 3BCID-fp, AND 3BCID-n, THE CPU TIME RATIO OF ACID1 OVER THE BEST METHOD AND OVER THE WORST METHOD. 
Table IV OPTIMIZATION PROBLEMS: GAIN RATIO IN SOLVING TIME: TIME ACID1/TIME XXX 
Table II NCSP: SOLVING TIME GAIN RATIOS. WE REPORT THE NUMBER OF PROBLEMS SOLVED BEFORE 3600 S AND BEFORE 10,000 S, AND DIFFERENT STATISTICS ON THE CPU TIME GAIN RATIO OF ACID1 OVER EACH COMPETITOR Ci (ONE PER COLUMN): THE AVERAGE, MAXIMUM, MINIMUM AND STANDARD DEVIATION VALUES OF THIS RATIO acid1 time
Citations
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Constructive interval disjunction
Gilles Trombettoni,Gilles Chabert +1 more
- 23 Sep 2007
TL;DR: Two new filtering operators for numerical CSPs (systems with constraints over the reals) based on constructive disjunction, as well as a new splitting heuristic, which compares advantageously to the 3B operator while being simpler to implement.
•Proceedings Article
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Christian Bessiere,Romuald Debruyne +1 more
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