A Hybrid Artificial Bee Colony Algorithm for Graph 3-Coloring

The Artificial Bee Colony (ABC) is the name of an optimization algorithm that was inspired by the intelligent behavior of a honey bee swarm. It is widely recognized as a quick, reliable, and efficient methods for solving optimization problems. This paper proposes a hybrid ABC (HABC) algorithm for graph 3-coloring, which is a well-known discrete optimization problem. The results of HABC are compared with results of the well-known graph coloring algorithms of today, i.e. the Tabucol and Hybrid Evolutionary algorithm (HEA) and results of the traditional evolutionary algorithm with SAW method (EA-SAW). Extensive experimentations has shown that the HABC matched the competitive results of the best graph coloring algorithms, and did better than the traditional heuristics EA-SAW when solving equi-partite, flat, and random generated medium-sized graphs

Computational Numerical Solution for Traveling Salesman Problem

This paper examined and analysed the desire of Traveling Salesman Problem (TSP) to find the cheapest way of visiting all given set of cities and returning to the starting point.     We presented a unique decomposition approach model for TSP in which the requirements and features of practical application in communication network, road transportation and supply chains are put into consideration.  We used a Mathematical Modeling solution with the application of Ant Colony Search Algorithm (ACSA) approach for result computation. In our approach, different Agents were created for difference purposes.   Information agent gathered information about best tour and detected the solution agent that arrived at a given point with information message containing details of where the solution agent has come from as well as best tour cost.  The place ant performs local pheromone decay on the relevant links.   This help to avoid random visit to irrelevant edges and allows the place ant to calculate the cost of tour of all place ants including the latest pheromone level on the links to each of the place ants. The solution agent uses available information to decide  which node to visit next and informs the place ant of  its decision to move to a given destination and update better tour  previously sampled while information about where to go next also obtained.       The place ant updates its pheromone value for that link using the equivalent of the algorithm for local pheromone update.    The cycle continues until solution agent arrives at its destination. The main advantage of our approach is that it permits the use of mixed integer programming and combinatorial optimization techniques to compute real optimal routing path, solving the problem in practice by returning actual shortest route with its numerical value and not the best effort result as provided by some previous models and analytical methods. The implementation was carried out using C# programming language.  Data used were generated and the performance evaluation of the model was carried out through simulation using Matlab 7.0.  The result shows that by considering all possible paths between a node as the source and another as the destination, all possible routes for a particular journey with shortest route in each case were generated. Keywords: Ant Colony, Combinatorial Optimization, Mixed Integer Programming, Pheromone, Search Algorithm and Traveling Salesman

Collective Intelligence for Optimal Power Flow Solution Using Ant Colony Optimization

This paper presents the performance ant collective intelligence efficiency for electrical network. Solutions for Optimal Power Flow (OPF) problem of a power system deliberate via an ant colony optimization metaheuristic method. The objective is to minimize the total fuel cost of thermal generating units and also conserve an acceptable system performance in terms of limits on generator real and reactive power outputs, bus voltages, shunt capacitors/reactors, transformers tap-setting and power flow of transmission lines. Simulation results on the IEEE 30-bus electrical network show that the ant colony optimization method converges quickly to the global optimum

Computational Numerical Solution for Traveling Salesman Problem

This paper examined and analyzed the desire of Traveling Salesman Problem (TSP) to find the cheapest way of visiting all given set of cities and returning to the starting point.     We presented a unique decomposition approach model for TSP in which the requirements and features of practical application in communication network, road transportation and supply chains are put into consideration.  We used a Mathematical Modeling solution with the application of Ant Colony Search Algorithm (ACSA) approach for result computation.  In our approach, different Agents were created for difference purposes.   Information agent gathered information about best tour and detected the solution agent that arrived at a given point with information message containing details of where the solution agent has come from as well as best tour cost.  The place ant performs local pheromone decay on the relevant links.   This help to avoid random visit to irrelevant edges and allows the place ant to calculate the cost of tour of all place ants including the latest pheromone level on the links to each of the place ants. The solution agent uses available information to decide  which node to visit next and informs the place ant of  its decision to move to a given destination and update better tour  previously sampled while information about where to go next also obtained.  The place ant updates its pheromone value for that link using the equivalent of the algorithm for local pheromone update.  The cycle continues until solution agent arrives at its destination. The main advantage of our approach is that it permits the use of mixed integer programming and combinatorial optimization techniques to compute real optimal routing path, solving the problem in practice by returning actual shortest route with its numerical value and not the best effort result as provided by some previous models and analytical methods. The implementation was carried out using C# programming language.  Data used were generated and the performance evaluation of the model was carried out through simulation using Matlab 7.0.  The result shows that by considering all possible paths between a node as the source and another as the destination, all possible routes for a particular journey with shortest route in each case were generated. Keywords: Ant Colony, Combinatorial Optimization, Mixed Integer Programming, Pheromone, Search Algorithm and Traveling Salesman

The Use of Persistent Explorer Artificial Ants to Solve the Car Sequencing Problem

Ant Colony Optimisation is a widely researched meta-heuristic which uses the behaviour and pheromone laying activities of foraging ants to find paths through graphs. Since the early 1990’s this approach has been applied to problems such as the Travelling Salesman Problem, Quadratic Assignment Problem and Car Sequencing Problem to name a few. The ACO is not without its problems it tends to find good local optima and not good global optima. To solve this problem modifications have been made to the original ACO such as the Max Min ant system. Other solutions involve combining it with Evolutionary Algorithms to improve results. These improvements focused on the pheromone structures. Inspired by other swarm intelligence algorithms this work attempts to develop a new type of ant to explore different problem paths and thus improve the algorithm. The exploring ant would persist throughout the running time of the algorithm and explore unused paths. The Car Sequencing problem was chosen as a method to test the Exploring Ants. An existing algorithm was modified to implement the explorers. The results show that for the car sequencing problem the exploring ants did not have any positive impact, as the paths they chose were always sub-optimal

Reactive approach for automating exploration and exploitation in ant colony optimization

Ant colony optimization (ACO) algorithms can be used to solve nondeterministic polynomial hard problems. Exploration and exploitation are the main mechanisms in controlling search within the ACO. Reactive search is an alternative technique to maintain the dynamism of the mechanics. However, ACO-based reactive search technique has three (3) problems. First, the memory model to record previous search regions did not completely transfer the neighborhood structures to the next iteration which leads to arbitrary restart and premature local search. Secondly, the exploration indicator is not robust due to the difference of magnitudes in distance matrices for the current population. Thirdly, the parameter control techniques that utilize exploration indicators in their feedback process do not consider the problem of indicator robustness. A reactive ant colony optimization (RACO) algorithm has been proposed to overcome the limitations of the reactive search. RACO consists of three main components. The first component is a reactive max-min ant system algorithm for recording the neighborhood structures. The second component is a statistical machine learning mechanism named ACOustic to produce a robust exploration indicator. The third component is the ACO-based adaptive parameter selection algorithm to solve the parameterization problem which relies on quality, exploration and unified criteria in assigning rewards to promising parameters. The performance of RACO is evaluated on traveling salesman and quadratic assignment problems and compared with eight metaheuristics techniques in terms of success rate, Wilcoxon signed-rank, Chi-square and relative percentage deviation. Experimental results showed that the performance of RACO is superior than the eight (8) metaheuristics techniques which confirmed that RACO can be used as a new direction for solving optimization problems. RACO can be used in providing a dynamic exploration and exploitation mechanism, setting a parameter value which allows an efficient search, describing the amount of exploration an ACO algorithm performs and detecting stagnation situations

Combinatorial Ant Optimization and the Flowshop Problem

Researchers have developed efficient techniques, meta-heuristics to solve many Combinatorial Optimization (CO) problems, e.g., Flow shop Scheduling Problem, Travelling Salesman Problem (TSP) since the early 60s of the last century. Ant Colony Optimization (ACO) and its variants were introduced by Dorigo et al. [DBS06] in the early 1990s which is a technique to solve CO problems. In this thesis, we used the ACO technique to find solutions to the classic Flow shop Scheduling Problem and proposed a novel method for solution improvement. Our solution is composed of two phases; in the first phase, we solved TSP using ACO technique which gave us an initial permutation or tour. We used the same trip as an initial solution for our problem and then improved it by using 2-opt exchanges which yielded in a promising result. Furthermore, we introduced another improvement technique which gave us a more promising result. We have compared our results with the best (optimal) and worst solution known till date. A comprehensive experimental study using existing dataset proves that our approach remarkably gives good results