In this paper, we propose the assignment problem of resources humans’ methodology by using the multiple knapsack approach to formulate the studied problem, and solve it by using the genetic algorithm for obtaining the optimal assignment of the new qualified employees that ensures the maximization the productivity by introducing constraints corresponding to the cost of each posts, and capacity o...

In this paper, we study the set of 0−1 integer solutions to a single knapsack constraint and a set of non-overlapping cardinality constraints (MCKP). This set is a generalization of the traditional 0− 1 knapsack polytope and the 0− 1 knapsack polytope with generalized upper bounds. We derive strong valid inequalities for the convex hull of its feasible solutions by lifting the generalized cover...

Valid inequalities for 0-1 knapsack polytopes often prove useful when tackling hard 0-1 Linear Programming problems. To use such inequalities effectively, one needs separation algorithms for them, i.e., routines for detecting when they are violated. We show that the separation problems for the so-called extended cover and weight inequalities can be solved exactly in O(nb) time and O((n+ amax)b)...

Many combinatorial optimization problems such as the bin packing and multiple knapsack problems involve assigning a set of discrete objects to multiple containers. These problems can be used to model task and resource allocation problems in multi-agent systems and distributed systems, and can also be found as subproblems of scheduling problems. We propose bin completion, a branch-and-bound stra...

In their paper [22], Myasnikov, Nikolaev, and Ushakov started the investigation of classical discrete integer optimization problems in general non-commutative groups. Among other problems, they introduced for a finitely generated (f.g.) group G the knapsack problem and the subset sum problem. The input for the knapsack problem is a sequence of group elements g1, . . . , gk, g ∈ G and it is aske...

In this note, we analyze a bilevel interdiction problem, where the follower’s program is a parametrized continuous knapsack. Based on the structure of the problem and an inverse optimization strategy, we propose for its solution an algorithm with worst-case complexity O(n). Keywords— Bilevel programming, Continuous knapsack problem, Polynomial time. 1 Model Recently, a number of papers have bee...

During the last decades, much research has been conducted on deriving classes of valid inequalities for mixed integer knapsack sets, which we call knapsack cuts. Bixby et al. (The sharpest cut: the impact of Manfred Padberg and his work. MPS/SIAM Series on Optimization, pp. 309–326, 2004) empirically observe that, within the context of branch-and-cut algorithms to solve mixed integer programmin...

The moth search algorithm (MS) is a relatively new metaheuristic optimization which mimics the phototaxis and Lévy flights of moths. Being an NP-hard problem, 0–1 multidimensional knapsack problem (MKP) classical multi-constraint complicated combinatorial with numerous applications. In this paper, we present hybrid learning MS (HLMS) by incorporating two mechanisms, global-best harmony (GHS) Ba...

The knapsack problem is a classic optimisation problem that has been recently extended in the setting of groups. Its study reveals to be interesting since it provides many different behaviours, depending on the considered class of groups. In this paper we deal with groups generated by Mealy automata—a class that is often used to study group-theoretical conjectures—and prove that the knapsack pr...

In this paper, we solve 0-1 knapsack problem using genetic algorithm. The knapsack problem is also called the NP (non deterministic polynomial) problem. We have to maximize the profit value that can be put in to a knapsack under the confinement of its weight. Solve the knapsack problem and also show its possible and effectiveness crowd an example. The Genetic Algorithm uses corrupted renewal an...