The binary quadratic knapsack problem (QKP) aims at optimizing a cost function within single knapsack. Its applications and difficulty make it appealing for various industrial fields. In this paper we present an efficient strategy to solve the by modeling as Ising spin model using machine search its ground state which translates optimal solution of problem. Secondly, in order facilitate search,...

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...

A knapsack problem is to select a set of items that maximizes the total profit selected while keeping weight no less than capacity knapsack. As generalized form with multiple knapsacks, multi-knapsack (MKP) disjointed for each To solve MKP, we propose deep reinforcement learning (DRL) based approach, which takes as input available capacities profits and weights items, normalized unselected dete...

Many combinatorial problems involving weights can be formulated as a so-called ranged problem. That is, their input consists of a universe U , a (succinctly-represented) set family F ⊆ 2 , a weight function ω : U → {1, . . . , N}, and integers 0 ≤ l ≤ u ≤ ∞. Then the problem is to decide whether there is an X ∈ F such that l ≤ ∑ e∈X ω(e) ≤ u. Well-known examples of such problems include Knapsac...

Multiobjective Evolutionary Algorithms (MOEAs) are increasingly being used for effectively solving many real-world problems, and many empirical results are available. However, theoretical analysis is limited to a few simple toy functions. In this work, we select the well-known knapsack problem for the analysis. The multiobjective knapsack problem in its general form is NP-complete. Moreover, th...

it is shown in [1] that the optimal downlink radio resource allocation for non-realtime traffic in cellular cdma/tdma networks can be mapped to a multi-dimensional multiple-choice knapsack problem (mmkp) which is np-hard. in this correspondence we propose a heuristic algorithm with polynomial time complexity for this problem. numerical results indicate significant computational performance impr...

In 1963, K.P. Grotemeyer proved an interesting variant of the Gauss-Bonnet Theorem. Let M be an oriented closed surface in the Euclidean space R 3 with Euler characteristic χ(M), Gauss curvature G and unit normal vector field n. Grote-meyer's identity replaces the Gauss-Bonnet integrand G by the normal moment (a · n) 2 G, where a is a fixed unit vector: M (a · n) 2 Gdv = 2π 3 χ(M). We generaliz...

This paper describes a method of a cryptanalyst for a knapsack cipher. The deciphering method is based on the application of a heuristic random search hill-climbing algorithm, together with a genetic algorithm. It is shown that such an algorithm, implemented in Matlab environment, could be used to break a knapsack cipher. Some other aspects of the problem are discussed, too.

RSA Cryptosystem ElGamal Cryptosystem Messey Omura Cryptosystem Knapsack Cryptosystem Construction of Knapsack Cryptosystem Quadratic Residue Cryptosystem Hybrid Cryptosystem: Diffie Hellman’s key Exchange Digital Signatures A Classification of Digital Signature Schemes Digital Signature Schemes with Appendix Digital Signature Schemes with Message Recovery RSA Signature Scheme Feige– Fiat – Sha...

The Integer Knapsack Problem with Set-up Weights (IKPSW) is a generalization of the classical Integer Knapsack Problem (IKP), where each item type has a set-up weight that is added to the knapsack if any copies of the item type are in the knapsack solution. The k-item IKPSW (kIKPSW) is also considered, where a cardinality constraint imposes a value k on the total number of items in the knapsack...