We study the problem of maximizing a monotone submodular function subject to Multiple Knapsack constraint. The input is set I items, each has non-negative weight, and bins arbitrary capacities. Also, we are given submodular, f over subsets items. objective find packing subset items A⊆I in such that f(A) maximized. Our main result an almost optimal polynomial time (1−e−1−ε)-approximation algorit...

We introduce and study a discrete multi-period extension of the classical knapsack problem, dubbed generalized incremental knapsack. In this setting, we are given set n items, each associated with non-negative weight, T time periods non-decreasing capacities $$W_1 \le \dots W_T$$ . When item i is inserted at t, gain profit $$p_{it}$$ ; however, remains in for all subsequent periods. The goal to...

This article addresses the problem of converting a single-objective combinatorial into multi-objective one using Pareto front approach. Although existing algorithms can identify optimal solution in space, they fail to satisfy constraints while achieving performance. To address this issue, we propose artificial bee colony optimization algorithm with classical theme called fitness sharing. approa...