We consider the polyhedral structure of the precedence constrained knapsack (PCK) problem, also known as the partially ordered knapsack problem. A set of items N is given, along with a partial order, or set of precedence relationships, on the items, denoted by S ⊆ N × N. A precedence relationship (i, j) ∈ S exists if item i can be placed in the knapsack only if item j is in the knapsack. Each i...

Combinatorial evolution and forecasting of system requirements is examined. The morphological model is used for a hierarchical requirements system (i.e., system parts, design alternatives for the system parts, ordinal estimates for the alternatives). A set of system changes involves changes of the system structure, component alternatives and their estimates. The composition process of the forec...

We show a method for parallelizing top down dynamic programs in a straightforward way by a careful choice of a lock-free shared hash table implementation and randomization of the order in which the dynamic program computes its subproblems. This generic approach is applied to dynamic programs for knapsack, shortest paths, and RNA structure alignment, as well as to a state-of-the-art solution for...

This paper presents and analyzes cryptanalytic attacks on knapsack public key cryptosystems that are based on ideas from Diophantine approximation. Shamir’s attack on the basic Merkle-Hellman knapsack cryptosystem is shown to depend on the existence of ‘‘unusually good’’ simultaneous Diophantine approximations to a vector constructed from the public key. This aspect of Shamir’s attack carries o...

& is called a knapsack constraint. The special case of the MKP01 with %*!) is the classical knapsack problem (KP01), whose usual statement is the following. Given a knapsack of capacity and objects, each being associated a profit (gain) and a volume occupation, one wants to select + ( +, and + not fixed) objects such that the total profit is maximized and the capacity of the knapsack is not exc...

Participatory budgeting enables the allocation of public funds by collecting and aggregating individual preferences; it has already had a sizable real-world impact. But making the most of this new paradigm requires a rethinking of some of the basics of computational social choice, including the very way in which individuals express their preferences. We analytically compare four preference elic...

The strategic choice of parameters (crossover rate, mutation rate, population size, number of generations, among others) in an AG has a direct impact the success of evolutionary search. Therefore the definition of good values in the parameters of evolution can optimize the search process population, finding better solutions in shorter times. Thus a process of self-adaptation constitutes an impl...

Multiple-choice knapsack problem (MCKP) is a well-known NP-hard problem and it has a lot of applications in the real-world and theory. In this study, the Artificial chemical reaction optimization algorithm (ACROA) that uses integer string code is developed to solve MCKP. Four specific reaction operators are designed to implicate local and global search. A new penalty function that aims to force...

We will discuss knapsack problems that arise in certain computational number theory settings. A common theme is that the search space for the standard real relaxation is large; in a sense this translates to a poor choice of variables. Lattice reduction methods have been developed in the past few years to improve handling of such problems. We show explicitly how they may be applied to computatio...

Motivated by a food promotion problem, we introduce the Knapsack Problem for Perishable Items (KPPI) to address a dynamic problem of optimally filling a knapsack with items that disappear randomly. The KPPI naturally bridges the gap and elucidates the relation between the pspace-hard restless bandit problem and the np-hard knapsack problem. Our main result is a problem decomposition method resu...