1. Making Choices using Structure at the Instance Level within a Case Based Reasoning Framework Cormac Gebruers*, Alessio Guerri †, Brahim Hnich* & Michela Milano † * Cork Constraint Computation Centre, University College Cork. † DEIS, University of Bologna.

2. Overview Motivation Objectives Case Study: The Bid Evaluation Problem Case Based Reasoning CBR Indications Further Work

3. Motivation Sometimes its easy to choose between a CP or an IP algorithm. In many domains, the choice is not so simple. Choice is problem instance dependent. How do we decide? Using Structure at the Instance Level?

4. Objectives A methodology to predict whether to use a CP or IP algorithm for problem instances; Algorithm portfolio selection. Methodology must be –low knowledge from the end users perspective We would also like –Cheap to compute –Keep most effort off-line

5. Case Study The Bid Evaluation Problem Choice whether to use CP or IP is not clear. Two sub-problems –‘IP’ subproblem: Winner Determination Problem –‘CP’ subproblem: Temporal Feasability

6. Winner Determination Problem Winner Determination Problem (WDP): –From a set of bids, choose a subset that covers a set of required tasks, subject to lowest cost or maximum revenue. –e.g. Oil/Gas Field Construction… Oil company tender for a set of construction jobs & accept optimal lowest cost set of bids that covers all construction jobs. WDP is np-hard. IP represents the technology of Choice to solve it.

7. Temporal Feasibility Time windows and temporal constraints introduced into the WDP → BEP Interactions within problem makes CP/IP Choice unclear Extending our previous example… –Oil company tender for a set of construction jobs & accept optimal lowest cost set of bids that satisfy delivery date and construction sequencing constraints.

8. Algorithms for BEP IP based Algorithm: –IP Model –Complete Branch and Bound based on Linear Relaxation (LR) of the problem without temporal constraints. CP based Algorithm: –CP Model –Limited Discrepancy Search –Fail First variable selection heuristic. –The value selection heuristic chooses the minimum price-for-task value next. Hybrid CP/IP Algorithm (HCP): –based largely on a CP model & CP algorithm. –Value Ordering Heuristic decided using IP

9. Case Based Reasoning We explore how well CBR can decide between IP algorithm and HCP algorithm for the BEP. If 2 instances are ‘similar’ then the same algorithm should apply to both. CBR makes a prediction by comparing a new instance to a store of examples for which the correct choice is known.

10. CBR System

11. Similarity Two decisions: –Choice of problem representation R –Choice of similarity measure f sim In the proceedings, the similarity measure given is inaccurate. The correct formula takes the following form:

12. A Key Challenge Find a cheap problem representation R, and a cheap similarity measure f sim that predicts whether to use CP, IP or CP/IP based algorithms.

13. Indications

14. Performance of several quite different approaches suggests that Structure at the Instance Level exists and can be exploited All approaches significantly outperform both “Use-Best” and “Weighted Random” Using quite basic problem representations and cheap similarity measures, we achieve acceptable prediction levels

15. Future Work In-depth analysis of data obtained. Further domains, richer algorithmic decisions Consider dynamic algorithm choice during execution. CBR; intelligent candidate feature and similarity measure identification