Iteration split with Firefly Algorithm and Genetic Algorithm to Solve Multidimensional Knapsack Problems

Abstract

When we talk about optimization, we mean to get the best or the optimal solutions from some set of available substitutes for the problems. If constraints are introduced in the problem, the feasible range would change. As we venture further in optimization, different types of problems need different approaches. One very common problem is combinatorial optimization problems. Combinatorial optimization is a topic that consists of finding an optimal object from a finite set of objects. In simple terms, finding optimal solutions from some set of available datasets of a problem. Multi Knapsack Problem (MKP) is NP-hard combinational optimization problem better known as the multi-constraint knapsack problem. It is one of the extensively studied problems in the field as it has a variety of real world problems associated with it. In this paper, the Firefly algorithm is used with the Genetic algorithm to solve the Multidimensional Knapsack Problem (MKP). By using the properties of flashing behavior of fireflies together with genetic evolution, some benchmark problems are solved. The results are compared with some work from the literature.