Abstract In this paper, a new upper bound for the Multiple Knapsack Problem (MKP) is proposed, based on idea of relaxing MKP to Bounded Sequential Problem, i.e., multiple knapsack problem in which item sizes are divisible. Such relaxation, called sequential obtained by suitably replacing items instance with divisible sizes. Experimental results benchmark instances show that effective, terms qua...

(a) A policy of just playing item 3. This policy has depth 1. (b) A policy that plays item 2 first. If it is small, it plays item 1 whereas if it is large it plays item 3. After this, the final item is determined due to the fact that there are only 3 items in the problem. This policy has depth 2. Figure 4: Examples of policies in the simple 3 item, 2 sizes stochastic knapsack problem. Each blue...

We study the BKP hierarchy and prove the existence of an Adler– Shiota–van Moerbeke formula. This formula relates the action of the BW1+∞–algebra on tau–functions to the action of the “additional symmetries” on wave functions.