Bi-Criteria Multiple Knapsack Problem with Grouped Items

Abstract

The multiple knapsack problem with grouped items aims to maximize rewards by assigning groups of items among multiple knapsacks, considering knapsack capacities. Either all items in a group are assigned or none at all. We propose algorithms which guarantee that rewards are not less than the optimal solution, with a bound on exceeded knapsack capacities. To obtain capacityfeasible solutions, we propose a binary-search heuristic combined with these algorithms. We test the performance of the algorithms and heuristics in an extensive set of experiments on randomly generated instances and show they are efficient and effective, i.e., they run reasonably fast and generate good quality solutions.

Unifying Futures and Spot Market: Overbooking-Enabled Resource Trading in Mobile Edge Networks

“…Differential pricing rule considers a more general case where the seller charges different nonmembers with different prices, where problem F 2 in discussed. Specifically, (26a) in F 2 refers to a knapsack problem with grouped items [47], for which the dynamic programming can also be applied, similar with (27a); while (26b) in F 2 represents a non-convex problem under any given g n , for which the solution of obtaining the optimal offloading rate is given by Appendix D. Specifically, each non-member with task execution requirement decides an optimal offloading rate based on each price, while the seller determines the trading vector by changing non-members with different prices, associated the relevant offloading rates, to maximize its utility. Pseudocode for solving F 2 is detailed by Algorithm 3, where X * , G * , and Λ * indicates the final trading decision vector, price vector, and offloading rate vector, respectively.…”