Ant Colony Solving Multiple Constraints Problem: Vehicle Route Allocation

Abstract

Ant colonies are successfully used nowadays as multi-agent systems (MAS) to solve difficult optimization problems such as travelling salesman (TSP), quadratic assignment (QAP), vehicle routing (VRP), graph coloring and satisfiability problem. The objective of the research presented in this paper is to adapt an improved version of Ant Colony Optimisation (ACO) algorithm, mainly: the Elitist Ant System (EAS) algorithm in order to solve the Vehicle Route Allocation Problem (VRAP). After a brief introduction in the first section about MAS and their characteristics, the paper presents the rationale within the second section where ACO algorithm and its common extensions are described. In the approach (the third section) are explained the steps that must be followed in order to adapt EAS for solving the VRAP. The resulted algorithm is illustrated in the fourth section. Section five closes the paper presenting the conclusions and intentions.

The Smallest “Miner” of the Animal Kingdom and Its Importance for Raw Materials Exploitation

“…When all the ants (𝑛 ) have completed their routes, the value of the "pheromone" T is updated, based on the updated route Giter and the best solution so far 𝑠 , giving a higher value to the most efficient routes so that in the following simulation, they show a higher probability of following that route. A typical ACO algorithm consists of the following parameters that must be defined [90] A typical ACO algorithm (Table 1) was presented by Dorigo and Blum [89], where the initial value of the pheromones Ƭ for all possible paths is first determined, and the distances are calculated. Based on these values, the probability is calculated for each path so that the ant randomly chooses the path to follow.…”

“…When all the ants (𝑛 ) have completed their routes, the value of the "pheromone" T is updated, based on the updated route Giter and the best solution so far 𝑠 , giving a higher value to the most efficient routes so that in the following simulation, they show a higher probability of following that route. A typical ACO algorithm consists of the following parameters that must be defined [90] and the best solution so far s bs , giving a higher value to the most efficient routes so that in the following simulation, they show a higher probability of following that route. A typical ACO algorithm consists of the following parameters that must be defined [90]:…”

Synthetic Genes for Artificial Ants. Diversity in Ant Colony Optimization Algorithms

“…The authors successfully applied the ACO algorithms to solve difficult problems such as: vehicle route allocation (with multiple constraints) [13] [14] and optimal capacitor banks placement in power distribution networks [15] where the criterion of the mathematical optimization model was a nonlinear function based on costs and the model imposed equality constraints described by the network operating equations and inequality constraints required to maintain within admissible limits the parameters characterizing the system state.…”

“…for the vehicle route allocation problem [13] a local history parameter was used and H min , H max as global parameters).…”

An Efficient Solution for the VRP by Using a Hybrid Elite Ant System

“…Since the metaheuristic approaches are very efficient for escaping from local optimum, they are one of the best group algorithms for solving combinatorial optimization problems. Some of the most popular metaheuristics applied to the VRP are simulated annealing (SA) [11], genetic algorithm (GA) [12], tabu search (TS) [11], Computational Intelligence Approach [13], large neighborhood search [3], ant colony optimization (ACO) [14], hybrid ant colony optimization [15] and particle swarm optimization [16]. The VRP is intrinsically a multiple objective optimization problem (MOP) in nature that has received much attention because of its practical application in industrial and service problems [17].…”