Imperialist Competitive Algorithm with Variable Parameters to Determine the Global Minimum of Functions with Several Arguments
We have implemented an Imperialist Competitive Algorithm (ICA) to a determine the global minimum for nine functions. Some of these represent benchmarks of the problem, while others have expressions that we have defined. For a start, we used three of these functions to determine a set of optimal parameters for the ICA. Then we studied the way in which the behaviour of the ICA is affected by these parameters in order to solve the problem put forth for the nine functions. Finally, we studied the behaviour of the ICA as affected by variable parameters for the most difficult of the nine functions. In our algorithm, the values of some of the parameters change dynamically. The results indicate a better behaviour of the solutions provided by this method. 1 The Imperialist Competitive Algorithm: Structure and Parameters At the "IEEE Congress on Evolutionary Computation" held on September 27 28, in 2007, Esmaeil Atashpaz Gargari and Carlos Lucas presented a paper describing a new type of evolutionary algorithm inspired by history [1] Called the "Imperialist Competitive Algorithm" (ICA) it is modelled on the political and historical events from the 17th, 18th and 19th centuries. The ICA belongs to the category of meta heuristic algorithms based on sets of candidate solutions called "populations" (along with genetic algorithms, algorithms of the "swarm of particles" type, GSA gravitational search algorithms, etc. The standard structure of an ICA as presented in [1] is the following: 1. Generating an initial set of countries; 2. Initializing the imperialist countries; 3. Occupying the colonies; 4. Assimilating the colonies; 5. If a colony has better results than the imperialist country then a. Interchanging the colony with the imperialist country 6. The imperialist competition: a. Computing the results of the empires b. Occupying the weakest colony of the weakest empire by another empire c. If the weakest empire has no colonies left then i. Removing this empire