The multiple-choice multi-period knapsack problem sits in the interface of multiple choice programming and knapsack problems. Previous studies of this problem had attempted to find its optimal solution through the branch-and-bound procedure using special-ordered-sets. In this paper, we propose another solution approach based on the dynamic programming to locate its optimal solution through the ...

In this article, the beam search approach is extended to multicriteria combinatorial optimization, with particular emphasis on its application to bicriteria { 0,1} knapsack problems. The beam search uses several definitions of upper bounds of knapsack solutions as well as a new selection procedure based on -indicator that allows to discard uninteresting solutions. An in-depth experimental analy...

In this paper, we address the temporal knapsack problem (TKP), a generalization of classical problem, where selected items enter and leave at fixed dates. We model TKP with dynamic program exponential size, which is solved using method called Successive Sublimation Dynamic Programming (SSDP). This starts by relaxing set constraints from initial iteratively reintroduces them when needed. show th...

The optimization of Multidimensional Knapsacks with Family-Split Penalties has been introduced in the literature as a variant more classical Knapsack and Multi-Knapsack problems. This problem deals set items partitioned families, when single item is picked to maximize utility, then all its family must be picked. Items from same can assigned different knapsacks, this situation split penalties ar...

We build facets of the quadratic 0-1 knapsack polytope following two different approaches. The quadratic 0-1 knapsack polytope is included in the Boolean quadric polytope introduced by Padberg [12] for unconstrained 0-1 quadratic problem. So in a first approach, we ask the question which are the facets of the Boolean quadric polytope that are still facets of the quadratic 0-1 knapsack polytope....

Knapsack public-key encryption schemes are based on the knapsack problem, which is NP-complete. Merkle-Hellman knapsack encryption scheme was the first concrete realization of a public-key encryption scheme. As its secure basis is superincreasing knapsack problem, it has been demonstrated to be insecure. Many variations have subsequently been proposed, whose knapsack vector density are less tha...

Since no competitive online algorithms exist for general knapsack problems, we consider online variants of knapsack problems with two assumptions: (i) the weight of each item is very small compared to the knapsack capacity; (ii) the value-to-weight ratio of each item is lower and upper bounded by two positive constants L and U . We design a deterministic threshold-based algorithm for the online...

This paper describes an artificial immune system approach (AIS) to modeling phenomenon characterized by uncertainty, and real-time decision-making. The proposed AIS represents combination of optimization techniques and neural networks. The AIS develops antibodies (the best control strategies) for different antigens (different "scenarios"). This task is performed using some of the optimization o...

In this paper we introduce the knapsack problem for perishable inventories concerning the optimal dynamic allocation of a collection of products to a limited knapsack. The motivation for designing such a problem comes from retail revenue management, where different products often have an associated lifetime during which they can only be sold, and the managers can regularly select some products ...