## 1 Introduction  
Swarm intelligence techniques have gained popularity in recent decades because of their capacity to locate partially optimal solutions for combinatorial optimization problems. These have been applied in various areas, such as engineering, economics and industry, etc., and these problems benefit from the use of swarm intelligence techniques because they are usually very hard to solve accurately since there is no precise algorithm to solve them [1; 2]. Swarm intelligence techniques are approximate metaheuristics that include a wide range of smart algorithms normally inspired in natural processes, such as artificial honey bee (AHB), genetic algorithm (GA), cuckoo search (CS), and gravitational search algorithm (GSA) [3]. The imperialist competitive algorithm (ICA), was proposed in 2007 by [PERSON] and [PERSON]. ICA was originated on the idea of imperialism and in this process stronger countries try to colonize the weakest countries and make them part of their colonies [4]. This algorithm has been currently used in different industrial applications [5]. ICA was initially used in continuous optimization problems, but now it has been utilized on many complex optimization problems such as flowlines scheduling problems (FSP), traveling salesman problem (TSP), assembly line balancing problem (ALBP), and facility line design problem (FLP) [1]. In the recent literature, there are some articles where the imperialist competitive algorithm has been studied, such as the work on an imperialist competitive algorithm to optimize artificial neural networks for UCAV global path planning [6], where the competitive imperialist algorithm is used to train a neural network with which it is possible to reduce uncertainty and avoid falling into local minimum. Another paper is that of a hybrid imperialist competitive algorithm for minimizing make span in a multi-processor open shop [1]. In this case, a new linear programming model is proposed for programming problems of a multiprocessor store to minimize the make span, in which a hybrid imperialist competitive algorithm (ICA) with the genetic algorithm (GA) is used. Another work is the application of an imperialist competitive algorithm to the design of a linear induction motor [7]. In this paper, the competitive imperialist algorithm is used to design a low speed linear induction motor to improve efficiency with a high power factor. Finally, there is also a paper on the Imperialist Competitive Algorithm for Solving a Dynamic Cell Formation Problem with Production Planning [8]. This article uses the competitive imperialist algorithm to optimize the planning, production and reconfiguration costs in the cell formation with production planning. The imperialist competitive algorithm has been used in different applications and in different branches of engineering, but there are some aspects that can be explored to improve its performance, like the hybridization of the imperialist competitive algorithm with different metaheuristics, such as GA, PSO and other population based metaheuristics [3; 9; 10]. Since we can use the ICA algorithm as a starting point to create an initial solution or use the algorithm as a tool to promote exploration or exploitation. One aspect to be taken into account is to use the competitive imperialist algorithm in parallel to help accelerate the search and to achieve higher quality in the possible solutions. Another important alternative is to perform the adjustment of the ICA algorithm parameters to improve the algorithm efficiency as is the idea presented in this research. After analyzing the existing literature, it has been observed that until now there are no works where the dynamic adjustment of the parameters has been done using fuzzy logic and very few where the imperialist competitive algorithm for the minimization of mathematical functions has been used.