# Simulated Annealing with Exploratory Sensing for Global Optimization
## 1 Introduction  
Metaheuristics work on finding fast and acceptable solutions for complex problems by trial and error methods. The problem complexity prevents pursuing every possible solution; therefore, the goal is to acquire a satisfactory and feasible solution within a suitable time. Theoretically, there is no guarantee to find the best solutions, and it is not recognized whether the algorithm will converge or not. Hence, design an efficient and practical algorithm that can mostly find a high-quality solution within a suitable time is crucial. In the past four decades, many applications and studies have applied Metaheuristics algorithms. tabu search (TS) [1], simulated annealing (SA) [2], genetic algorithms (GAs) [3], and other plentiful numbers of metaheuristics algorithms which have attracted much attention compared to each other. Generally, most of the well-known metaheuristics techniques are memory-less algorithms. Memory-less means that there is no idea about the history of previously found solutions. Thus, based on memory usage, metaheuristics can be classified into algorithms with memory and memory-less ones. The absence of memory in metaheuristics leads to the loss of the information gained in previous iterations. Thus, in many cases, this leads to re-visiting the already visited areasin the search region. It is clear that without a history/memory, a new search would be done in those areas with a chance of repeating the old solution. Thus, the time consumption cost will be high. On the other hand, using memory to build a history for \"some\" recent solutions in the already visited areas will save the computations' time. However, few pieces of metaheuristics research employed memory in their methods. Therefore, in the advanced metaheuristics, memory should be considered one of the fundamental elements of an efficient metaheuristic. In [4], a recent review of the memory usage and its effect on the performance of the main swarm intelligence metaheuristics. The investigation has been performed for memory, memory-less metaheuristics, and memory characteristics, especially in swarm intelligence metaheuristics. It has been investigated and shown that memory usage is essential to increase the effectiveness of metaheuristics by taking advantage of their previous successful histories. Simulated annealing (SA) is a well-known search algorithm used successfully in many search and optimization problems. Typically, the random walk of SA does not benefit from the memory of visited states, which can cause excessive random search and redundant behavior, especially with weak configurations of the SA. Moreover, unlike memory-based search algorithms such as tabu search, the search in SA is dependent on the choice of the initial settings to explore the search space and finding an acceptable solution. At the same time, there are limited indications of how much exploration has been carried out. Also, the lack of exploration eye can affect the quality of the final solutions and the termination time, which causes practitioners to use more extended cooling and substantial initial temperatures and increase the number of iterations, especially when the minimum cost is unknown. A few studies use different ways to overcome these issues. For example, in [5], a hybrid simulated annealing with solutions memory elements to solve university course timetable problems has been proposed. A memory-based methodology that redirects the search to return to unaccepted visited solutions when trapped in local minima has been used to escape from local minima. Authors in [6] proposed a hybrid algorithm that integrates different heuristics features, including using three types of memories, one long-term memory, two short-term memories, and an evolution-based diversification approach. In [7], a memory-based simulated annealing (MSA) algorithm is proposed for the fixed-outline floor planning of blocks. MSA implements a memory pool to keep some historical best solutions during the search.