A Comparison of Tree Search Schemes for Decision Networks

Wallace B S Crowston

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4 (1. 8) 2. 2 (14. 3) 18. 5 2B (2. 7) 5. 3 (5. 8) 9. 4 (40. 8) 73. 2 2C (0. 8) 1. 4 (2. 0) 2. 4 (2. 2) 5. 6 2D (0. 8) 1. 0 (2. 2) 2. 4 (T97) 2E (0. 2) 0. 4 (1. 2) 1. 6 (81. 0) T95 All timies are in seconds. The times enclosed by parentheses are those required to find the optimal solution. The other times are those required to find and prove optima lity. Terminated.
T indicates that the solution was prematurely PARTITIONING ALGORITHM k k Define the cheapest alternative completion Q of p to be th...e set of decisions d. . , i = a(m), m = n + 1, . .
k '"" N with p such that S, C^ / ». Is minimum ^n m=n+I a(m)3 . , N feasible in conjunction • If *F °^ Pn' = Pn '-' ^n '^ equal to w of p, then Q is clearly the best completion of p, and all n "n n' - 16 - «■ i \ 1^ other completions of p need not be evaluated. The partitioning algorithm incorporates this consideration as follows: Partition the decision nodes of a problem into two sets: B, the Branch and Bound set; and Q, the cheapest alternative set.

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