This chapter explains the basics of simple linear regression. Showing different approaches to solve a prediction problem of this type. First, we explain the theory, then, it is solved by the algebraic method of least squares, checking the procedure and results through MATLAB. Finally, a basic example of the field of evolutionary computing is shown, using several evolutionary techniques such as PSO, DE, ABC, CS and the classical method of descending gradient. Which optimize the function to find the best coefficients for an estimated straight line. This is applied to a set of fatal traffic accident data in the U.S. states.

Agent-based modeling is a relatively new approach to model complex systems composed of agents whose behavior is described using simple rules. As a consequence of the agent interactions emerges a complex global behavioral pattern not explicitly programmed. In the last decade, an increasing number of metaheuristic techniques have been reported in the literature where authors claim their novelty and their abilities to perform as powerful optimization methods. Although these schemes emulate very different processes or systems, the rules used to model individual behavior are very similar. The idea behind the design of many metaheuristic methods is to configure a recycled set of rules that has demonstrated to be successful in previous approaches for producing new optimization schemes. Such common rules have been designed without considering the final global result obtained by the individual interactions. On the other hand, agent-based systems provide a solid theory and a set of consistent models that allow characterizing global behavioral patterns produced by the collective interaction of the individuals from a set of simple rules. Under this perspective, several agent-based concepts and models that generate very complex global search behaviors can be used to produce or improve efficient optimization algorithms. In this paper, a new metaheuristic algorithm based on agent systems principles is presented. The proposed method is based on the agent-based model known as “Heroes and Cowards”. This model involves a small set of rules to produce two emergent global patterns that can be considered in terms of the metaheuristic literature as exploration and exploitation stages. To evaluate its performance, the proposed algorithm has been tested in a set of representative benchmark functions, including multimodal, unimodal, and hybrid benchmark formulations. The competitive results demonstrate the promising association between both paradigms.

Recently, many dynamic optimization algorithms based on metaheuristic methods have been proposed. Although these schemes are highly efficient in determining a single global optimum, they fail in locating multiple optimal solutions. The central goal of dynamic multimodal optimization is to detect multiple optimal solutions for an optimization problem where its objective function is modified over time. Locating many optimal solutions (global and local) in a dynamic multimodal optimization problem is particularly crucial for several applications since the best solution could not always be the best implementable alternative due to various practical limitations. In spite of its importance, the problem of dynamic multimodal optimization through evolutionary principles has been scarcely considered in the literature. On the other hand, mean shift is a non-parametric and iterative process for detecting local maxima in a density function represented by a set of samples. Mean shift maintains interesting adaptive characteristics that allow it to find local maxima under dynamic environments. In this paper, the mean shift scheme is proposed to detect global and local optima in dynamic optimization problems. In the proposed method, the search strategy of the mean shift is modified to consider not only the density but also the fitness value of the candidate solutions. A competitive memory, along with a dynamic strategy, has also been added to accelerate the convergence process by using important information from previous environments. As a result, the proposed approach can effectively identify most of the global and local optima in dynamic environments. To demonstrate the performance of the proposed algorithm, a set of comparisons with other well-known dynamic optimization methods has been conducted. The study considers the benchmark generator of the CEC competition for dynamic optimization. The experimental results suggest a very competitive performance of the proposed scheme in terms of accuracy and robustness.