We extend the classical 0-1 knapsack problem by introducing disjunctive constraints for pairs of items which are not allowed to be packed together into the knapsack. These constraints are represented by edges of a conflict graph whose vertices correspond to the items of the knapsack problem. Similar conditions were treated in the literature for bin packing and scheduling problems. For the knaps...

The knapsack problem is believed to be one of the “easier” N P -hard problems. Not only can it be solved in pseudo-polynomial time, but also decades of algorithmic improvements have made it possible to solve nearly all standard instances from the literature. The purpose of this paper is to give an overview of all recent exact solution approaches, and to show that the knapsack problem still is h...

Cuckoo search (CS) is one of the most recent population-based meta-heuristics. CS algorithm is based on the cuckoo’s behaviour and the mechanism of Lévy flights. Unfortunately, the standard CS algorithm is proposed only for continuous optimisation problems. In this paper, we propose a discrete binary cuckoo search (BCS) algorithm in order to deal with binary optimisation problems. To get binary...

In this paper a new Genetic Algorithm based on a heuristic operator and Centre of Mass selection operator (CMGA) is designed for the unbounded knapsack problem(UKP), which is NP-Hard combinatorial optimization problem. The proposed genetic algorithm is based on a heuristic operator, which utilizes problem specific knowledge. This center of mass operator when combined with other Genetic Operator...

Variety and diversity of population are essential for convergence to global optimal in genetic algorithm. In this study, the concepts of fitness distribution, expected and cumulative fitness distribution, reproduction rate and loss of diversity are defined for a sexual selection mechanism, and their performance of this type of selection mechanism is studied theoretically. Then a genetic algorit...

The mean eld theory (MFT) approach to knapsack problems is extended to multiple knapsacks and generalized assignment problems with Potts mean eld equations governing the dynamics. Numerical tests against \state of the art" conventional algorithms shows good performance for the mean eld approach. The inherently parallelism of the MFT equations makes them suitable for direct implementations in mi...

Binary optimization problems are in the most case the NP-hard problems that call to satisfy an objective function with or without constraints. Various optimization problems can be formulated in binary expression whither they can be resolved in easier way. Optimization literature supplies a large number of approaches to find solutions to binary hard problems. However, most population-based algor...

This paper presents a detailed treatment of genetic algorithms with decomposition procedures as developed for large scale multidimensional 0-1 knapsack problems with block angular structures. Through the introduction of a triple string representation and the corresponding decoding algorithm, it is shown that a potential solution satisfying not only block constraints but also coupling constraint...