In this paper we develop a branch-and-bound algorithm for solving a particular integer quadratic multi-knapsack problem. The problem we study is defined as the maximization of a concave separable quadratic objective function over a convex set of linear constraints and bounded integer variables. Our exact solution method is based on the computation of an upper bound and also includes pre-procedu...

Problem Definition This problem deals with packing a maximum reward set of items into a knapsack of given capacity, when the item-sizes are random. The input is a collection of n items, where each item i ∈ [n] := {1, · · · , n} has reward r i ≥ 0 and size S i ≥ 0, and a knapsack capacity B ≥ 0. In the stochastic knapsack problem, all rewards are deterministic but the sizes are random. The rando...

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We consider a contextual version of multi-armed bandit problem with global knapsack constraints. In each round, the outcome of pulling an arm is a scalar reward and a resource consumption vector, both dependent on the context, and the global knapsack constraints require the total consumption for each resource to be below some pre-fixed budget. The learning agent competes with an arbitrary set o...

Multi-objective orienteering problems (MO-OPs) are classical multi-objective routing and have received much attention in recent decades. This study seeks to solve MO-OPs through a problem-decomposition framework, that is, an MO-OP is decomposed into knapsack problem (MOKP) traveling salesman (TSP). The MOKP TSP then solved by evolutionary algorithm (MOEA) deep reinforcement learning (DRL) metho...

scheduling for job shop is very important in both fields of production management and combinatorial op-timization. however, it is quite difficult to achieve an optimal solution to this problem with traditional opti-mization approaches owing to the high computational complexity. the combination of several optimization criteria induces additional complexity and new problems. in this paper, we pro...