We study an extension of the precedence constrained knapsack problem where the knapsack can be filled in multiple periods. This problem is known in the mining industry as the open-pit mine production scheduling problem. We present a new algorithm for solving the LP relaxation of this problem and an LP-based heuristic to obtain feasible solutions. Computational experiments show that we can solve...

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 Multiple Knapsack problem (MKP) is a hard combinatorial optimization problem with large application, which embraces many practical problems from different domains, like cargo loading, cutting stock, bin-packing, financial and other management, etc. It also arise as a subproblem in several more complex problems like vehicle routing problem and the algorithms to solve these problems will bene...

Motivated by a real world application, we study the multiple knapsack problem with assignment restrictions (MKAR): We are given a set of items N = f1; : : : ; ng and a set of knapsacks M = f1; : : : ;mg. Each item j 2 N has a positive real weight wj and each knapsack i 2 M has a positive real capacity ci associated with it. In addition, for each item j 2 N a set Aj M of knapsacks that can hold ...

In this paper, we present a new methodology to adapt any kind of lattice reduction algorithms to deal with the modular knapsack problem. In general, the modular knapsack problem can be solved using a lattice reduction algorithm, when its density is low. The complexity of lattice reduction algorithms to solve those problems is upper-bounded in the function of the lattice dimension and the maximu...

The most e¢cient algorithms for solving single criterion {0,1}-knapsack problems are based on the core concept and the core problem. However, those concepts remain unnoticed in the multiple criteria case. In this paper we bring them to this topic. A large amount of e¢cient solutions are considered for analysing the importance of the core itself and the core problem. The results show that the pr...

Problem statement: Knapsack problem is a typical NP complete problem. During last few decades, Knapsack problem has been studied through different approaches, according to the theoretical development of combinatorial optimization. Approach: In this study, modified evolutionary algorithm was presented for 0/1 knapsack problem. Results: A new objective_func_evaluation operator was proposed which ...

We are concerned with a variation of the standard 0–1 knapsack problem, where the values of items differ under possible S scenarios. By applying the ‘pegging test’ the ordinary knapsack problem can be reduced, often significantly, in size; but this is not directly applicable to our problem. We introduce a kind of surrogate relaxation to derive upper and lower bounds quickly, and show that, with...

In this paper, an interesting and easy method to solve the multi-dimensional  knapsack problem is presented. Although it belongs to the combinatorial optimization, but the proposed method belongs to the decision making field in mathematics. In order to, initially efficiency values for every item is calculated then items are ranked by using Multiple Criteria Decision Making (MCDA).  Finally, ite...