# A Stigmergy-Based Differential Evolution
## 1 Introduction  
Metaheuristics (MH) are computational algorithms inspired by biological phenomena that solve a great diversity of complex scientific and engineering problems, particularly optimization. Some key features of metaheuristics are: (1) robustness, (2) self-organization, (3) adaptation and (4) decentralized control [1]. Two of the most recognized branches in MH, which group several approaches, are Evolutionary Computation (EC) and Swarm Intelligence (SI) algorithms [2]. Even though different metaphors inspire them, all have a set of parameters that the user must tune in a manual, adaptive, or self-adaptive manner to help the algorithm's exploration/exploitation balance [3]. However, in several MH, the use of a global best candidate solution to direct the search process toward the real optimum is common. For instance, Harmony Search [4; 5; 6] utilizes several individuals from the harmony memory (HM) to improvise a new harmony, and this individual is incorporated into the HM only if it is better than the worst individual in the whole population. Differential Evolution [7] uses in most canonical variants [8] a weighted difference of at least two parents to generate a new individual, which interchanges information with the actual individual and becomes the trial solution. The selection step compares the trial individual's fitness against both the actual individual's fitness and the best individual found so far. Another metaheuristic approach is Particle Swarm Optimization [9], which considers the local best and the global best to make a velocity vector added to the actual individual togenerate a new individual, whose fitness is compared against the local best and the global best and, if necessary, replaces the global best. The canonical Fireworks algorithm [10; 11], whose population is composed of fireworks, modifies the individuals by consecutively applying the explosion, the Gaussian mutation, and the mapping operators. After such alterations, the new candidate solution's fitness is compared against the best individual so far, and the individual with better fitness value is kept in memory. Based on some plants' reproduction strategy, the authors in [12] proposed the Flower Pollination Algorithm (FPA). This metaheuristic uses the abiotic, biotic, and switch operators to either locally or globally modify the actual candidate solution. As in the previous algorithms, FPA keeps tracking the best global individual found at each iteration. Another algorithm is the Gravitational Search algorithm [13], in which the movements of the candidate solutions (called objects) consider their masses and accelerations to actualize their velocities and positions. As in other metaheuristics, the algorithm updates the global worst and the global best at each iteration. Other examples of metaheuristics that actualize the best solution found at each iteration are the Firefly Algorithm [14; 15], Cuckoo Search [16], Artificial Bee Colony optimization [17; 18] and Chicken Swarm optimization [19]. In order to solve high-dimensional problems and evaluate a large amount of data, it is necessary to improve the efficiency and execution times of evolutionary algorithms. Many authors consider parallel and distributed approaches of metaheuristic algorithms as alternatives to overcome the difficulties derived from the increase in data complexity. A recent review of parallel and distributed approaches for evolutionary algorithms is presented in [20]. In addition, much research reports metaheuristics translated to parallel languages, such as CUDA (Compute Unified Device Architecture) [21], which runs on parallel general-purpose graphic processing units (GPGPU). For example, a survey of GPU parallelization strategies for metaheuristics is conducted in [22]. The authors of [23] propose two approaches to parallelize the Gravitational Search algorithm using CUDA: one that modifies the whole population with a single kernel and another that utilizes multiple kernels to operate the complete population.