This paper addresses the problem of finding cutting planes for multi-stage stochastic integer programs.We give a general method for generating cutting planes for multi-stage stochastic integer programs basedon combining inequalities that are valid for the individual scenarios. We apply the method to generatecuts for a stochastic version of a dynamic knapsack problem and to stochasti...

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...

in this paper, a novel approach for multi response optimization is presented. in the proposed approach, response variables in treatments combination occur with a certain probability. moreover, we assume that each treatment has a network style. because of the probabilistic nature of treatment combination, the proposed approach can compute the efficiency of each treatment under the desirable reli...

We present an algorithm for the penalized multiple choice knapsack problem (PMCKP), a combination of the more common penalized knapsack problem (PKP) and multiple choice knapsack problem (MCKP). Our approach is to converts a PMCKP into a PKP using a previously known transformation between MCKP and KP, and then solve the PKP greedily. For PMCKPs with well-behaved penalty functions, our algorithm...

We model the problem of bidding in ad auctions as a penalized multiple choice knapsack problem (PMCKP), a combination of the multiple choice knapsack problem (MCKP) and the penalized knapsack problem (PKP) [1]. We present two versions of PMCKP, GlobalPMCKP and LocalPMCKP, together with a greedy algorithm that solves the linear relaxation of a GlobalPMCKP optimally. We also develop a greedy heur...

In the partially-ordered knapsack problem (POK) we are given a set N of items and a partial order ≺P on N. Each item has a size and an associated weight. The objective is to pack a set N ′ ⊆ N of maximum weight in a knapsack of bounded size. N ′ should be precedenceclosed, i.e., be a valid prefix of ≺P . POK is a natural generalization, for which very little is known, of the classical Knapsack ...

We consider the separable quadratic multi-knapsack problem (QMKP) which consists in maximizing a concave separable quadratic integer function subject to m linear capacity constraints. The aim of this paper is to develop an effective method to compute an upper bound for (QMKP) from a surrogate relaxation originally proposed in Djerdjour et al. (1988). The quality of three other upper bounds for...

One of the combinatorial optimization problems is Knapsack problem, which aims to maximize benefit objects whose weight not exceeding capacity knapsack. This paper introduces artificial bee colony algorithm select a subset project and represented by knapsack problem put best investment plan achieve highest profits within determined costs, this one applications financial field. The result from p...