Maximally Distant Codes Allocation Using Chemical Reaction Optimization and Ant Colony Optimization Algorithms

Abstract

Error correcting codes, also known as error controlling codes, are set of codes with redundancy that allows detecting errors. This is quite useful in transmitting data over a noisy channel or when retrieving data from a storage with possible physical defects. The idea is to use a set of code words that are maximally distant from each other, hence reducing the chance of changing a valid codeword to another valid codeword by flipping bits. The problem can be viewed as picking m codes out of 2ⁿ available n-bit combinations, such that the aggregate hamming distance among those codewords is maximized. Due to the large solution spaces of such problems, greedy algorithms are sometimes used to generate quick and dirty solutions. However, modern evolutionary search algorithms like genetic algorithms, swarm particles, gravitational search and others, offer good alternatives, yielding near optimal solutions in exchange for some time. Chemical Reaction Optimization (CRO) has emerged as a new evolutionary algorithm to solve complex optimization problems. This algorithm mimics the molecular interactions towards finding a minimal energy state, which corresponds to an optimal solution for the problem in hand. In this research, we proposed a solution for the maximally distant codes allocation problem, through a binary knapsack mapping and compared the performance with the well established Ant Colony Optimization (ACO) algorithm, which is inspired by the ant’s capability to find the shortest path between the nest and source of food. The binary knapsack mapping was used in the two algorithms. Test results showed that the CRO outperformed the ACO in every metric given any time budget.