# HyperDE: An Adaptive Hyper-Heuristic for Global Optimization
## 1 Introduction
### State of the Art  
Currently, there are a plethora of approaches, namely heuristics, that are able to search the problem space for optimal solutions. An extensive list of heuristics can be found in [1]. We enumerate a few that are considered representative by being the most cited: Particle Swarm Optimization (PSO) [2], Simulated Annealing (SA) [3], Ant Colony Optimization (ACO) [4], Artificial Bee Colony (ABC) [5], Harmony Search (HS) [6], Gravitational Search Algorithm (GSA) [7], Firefly Algorithm (FA) [8]; many others have original traits. These methods intelligently evaluate the solution space, attempting to predict where the best solution is located, considering the past discovered solutions. A partial exploration is desired because the real world problems are complex; an exhaustive exploration is not feasible due to time and computational constraints. This being said, it is not guaranteed that the heuristic has found the global optima at the end of the search. The stochastic methods that are considered in this paper are enumerated below. Firstly, inspired by the theory of evolution, we have the basic Differential Evolution (DE) [9] algorithm along with two variants: the adaptive success-history based named SHADE [10] together with L-SHADE [11], which has additionally a linear population size reduction strategy. Inspired by the behavior of groups of individuals found in nature, such as animals and insects, there are various swarm optimization algorithms: Sparrow Search Algorithm (SSA) [12], Bald Eagle Search (BES) [13], Whale Optimization Algorithm (WOA) [14], Harris Hawks Optimization (HHO) [15], and Hunger Games Search (HGS) [16]. The conceptual contribution and the underlying metaphor of some of these algorithms may be questionable [17], but many of them have good practical behavior. Inspired by concepts from mathematics, we have Chaos Game Optimization (CGO) [18], while Slime Mold Algorithm (SMA) [19] can be considered a bio-inspired search algorithm. Most of the techniques listed above are not far from the state-of-the-art; other methods are not so recent but are well established. What is to be taken into consideration is that DE together with SHADE and LSHADE are considered the key contenders in our methodology validation, the other algorithms being less relevant. Each enumerated method performs in a different manner, excelling at solving a particular subset of problems while not being appropriate for solving some other problems. Many of the available heuristics have hyper-parameters whose values affect the performance of the search, therefore being able to tailor the algorithm to the given problem. It often happens that the methods fail to converge to the global optima, remaining stuck in a locally optimal solution instead and struggling to find a balance between exploration and exploitation. Regarding the development of hyper-heuristics, the field of study is relatively new, with an increase in publications on this subject over the last three-four years [20]. There are several methods available, such as approaches based on genetic programming [21], graph-based [22], VNS-based [23], ant-based [24], tabu search-based [25], greedy selection-based [26], GA-based [27], simulated annealing-based [28], and reinforcement learning-based [29]. Those are several relevant examples that initiated the domain in various directions. More recent hyper-heuristics that merit attention could be a simulated-annealing-based hyper-heuristic [30], a reinforcement learning-based hyper-heuristic [31], a genetic programming hyper-heuristic approach [32], a Bayesian-based hyper-heuristic approach [33] and a very appealing, highly general approach for continuous problems [34]. None of the above resembles our proposed method; as revealed in [20], most of the hyper-heuristics are designed to be applied in different domains, problems such as scheduling, timetabling, constraint satisfaction, routing policies, not continuous problems as in our study.