Many combinatorial optimization problems are known to be NP-complete. A common point of view is that finding fast algorithms for such problems using polynomial number of processors is unlikely. However facts of this kind usually are established for "worst" case situations and in practice many instances of NP-complete problems are successfully solved in polynomial time by such traditional combin...

I cannot help but start this review with an analogy between the knapsack problem and the traveling salesman problem (TSP), the two most studied problems of combinatorial optimization. Both problems are easy to explain even to a stranger, both are hard to solve. Each of these problems is important in its own right as well as due to numerous applications. Each of the two problems forms an excelle...

The classic knapsack and related problems have natural generalizations to arbitrary (non-commutative) groups, collectively called knapsacktype problems in groups. We study the effect of free and direct products on their time complexity. We show that free products in certain sense preserve time complexity of knapsack-type problems, while direct products may amplify it. Our methods allow to obtai...

The ordinary genetic algorithm may be thought of as conducting a single market in which solutions compete for success, as measured by the fitness funtion. We introduce a two-market genetic algorithm, consisting of two phases, each of which is an ordinary single-market genetic algorithm. The twomarket genetic algorithm has a natural interpretation as a method of solving constrained optimization ...

Solving some mathematical problems such as NP-complete problems by conventional silicon-based computers is problematic and takes so long time. DNA computing is an alternative method of computing which uses DNA molecules for computing purposes. DNA computers have massive degrees of parallel processing capability. The massive parallel processing characteristic of DNA computers is of particular in...

Mathematical models of biogeography inspired the development of the biogeography-based optimization algorithm. In this article we propose a binary version of biogeography-based optimization (BBO) for the Knapsack Problem. Two new mutation operators are proposed to extend the biogeography-based optimization algorithm to binary optimization problems. We also demonstrate the performance of the res...

Ralph Gomory has recently aroused interest in a special type of knapsack problem in which the constraint coefficients and constant term are elements of a finite additive group. The significance of this problem lies in the fact that it is closely related to the general integer linear programming problem, resulting by removing the nonnegativity restrictions on those variables in the general probl...

Knapsack problems are important NP-Complete combinatorial optimization problems. Although nearly all the classical instances can be solved in pseudo-polynomial time nowadays, yet there are a variety of test problems which are hard to solve for the existing algorithms. In this paper we propose a new approach based upon binary particle swarm optimization algorithm (BPSO) to find solutions of thes...