A Dynamic Programming based GA for 0-1 Modified Knapsack Problem

Abstract

The classical 0-1 knapsack problem is one of the more studied combinatorial optimization problem which belong to the NP class of algorithms. A number of its generalized forms have been addressed by various researchers using different designing techniques. In this paper, we design and analyze the Multiple Knapsack Problems (MKP) by using genetic algorithms. A modified Genetic Algorithm (mGA) is developed with the key focus on efficient encoding scheme for binary string representation and a competent dynamic programming based method for initial population generation. Furthermore transposition is applied in mGA instead of crossover for maintaining the population diversity. Performance analysis of the mGA, justifies our claims that the population incorporates adequate quality and diversity to reach a near optimal solution and transposition reduces the overall computation time.

Performance Study of Cultural Algorithms Based on Genetic Algorithm with Single and Multi Population for the MKP

“…This success is in part due to the unbiased nature of their operations, which can still perform well in situations with little or no domain knowledge (Reynolds, 1999). The basic EC framework consists of fairly simple steps like definition of encoding scheme, population generation method, objective function, selection strategy, crossover and mutation (Ahmed & Younas, 2011). In addition, the same procedures utilized by EC can be applied to diverse problems with relatively little reprogramming.…”

“…In the last few years, Genetic Algorithms (GAs) have been used to solve the NP-complete problems and have shown to be very well suited for solving larger Knapsack Problems (Fukunaga & Tazoe, 2009;Gunther, 1998;Sivaraj & Ravichandran, 2011). For larger knapsack problems, the efficiency of approximation algorithms is limited in both solution quality and computational www.intechopen.com cost (Ahmed & Younas, 2011). Spillman's experiment, which applies the GA to the knapsack problem, shows that the GA does not have a good performance in relatively small size problem, but works quite well in problems that include a huge number of elements (Spillman, 1995).…”

“…There are many packing problems where evolutionary methods have been applied. The simplest optimization problem and one of the most studied is the onedimensional (zero-one or 0-1) knapsack problem (Ahmed & Younas, 2011), which given a knapsack of a certain capacity, and a set of items, each one having a particular size and value, finds the set of items with maximum value which can be accommodated in the knapsack. Various real-world problems are of this type: for example, the allocation of communication channels to customers who are charged at different rates (Back et al, 1997).…”

“…During a study of 0-1 knapsack, a number of extensions and variants have been developed such as (Ahmed & Younas, 2011): Multiple Knapsack Problems (MKP), Multidimensional Knapsack Problems (MDKP), Multi Choice Knapsack Problems (MCKP) and Multiple Choice Multidimensional Knapsack Problems (MMKP). It is also important to consider other extensions such as (Chu & Beasley, 1998): Multiconstraint Knapsack Problem, and also the term "Multidimensional Zero-one Knapsack Problem".…”

“…Since the introduction of the Knapsack problems some algorithm techniques such as brute force, conventional algorithms, dynamic programming, greedy approach and approximation algorithm have been proposed (Ahmed & Younas, 2011).…”