*4.1. Optimization Methods*

Optimization methods that can be applicable to Smart Grid must comply with the requirements of real-time performance, consideration of technical requirements and actual production situation of various production capacities, while mitigating difficulties of weak convergence and local pinning [12,48]. The observed works in the literature distinguish five optimization-method groups [12,54]:


Analytical methods require the definition of algebraic expressions basis of which can the optimization process be analyzed. Such approach will result with a well-developed mathematical model of the observed system. That model can be used in together with measurement data, but it is very demanding, almost impossible, to use it for more complex systems and challenges [12,26]. The advantage of the analytical approach is manifested through the usage of the model in conjunction with measured values and external input data. The common opinion in the literature is how optimization procedures can be divided into methods that result in precise solutions and methods that result in good-enough optimal Pareto solutions [55–58]. An overview and grouping of optimization methods is shown in Figure 2.

This paper observes best practices and methods that according to the authors can be used for real-world use cases. The usability is tried and proved by modeling and simulation in software engineering environment. This paper deals with the groups from Figure 2 and gives an overview of what has been tried, what has been repeated and what can be applied to real-world systems.

**Figure 2.** Optimization methods for Smart Grid applications.

A meta-heuristic approach is an iterative optimization process that can be assigned as a guidance for subordinate heuristics [59]. The heuristic process is beneficial for solving optimization problems in cases where a precise and accurate solution is not unique, when the set of acceptable solutions exist and when the precision of all solutions does not necessarily have to be absolute but good enough to be pragmatic enough [60]. Heuristic algorithms can be specifically developed to solve a particular problem or universally applicable with the common search criteria. In any case, heuristic algorithms can be used in a search for a specific set of possible solutions and finding out the best solution in the set. Meta-heuristic methods represent advanced procedures in which the heuristic process is further enhanced in every iteration of the solution search and most often apply universally applicable heuristic procedures [61]. The way of refining heuristic process with each iteration can be defined as a separate heuristic process and therefore such complex methods are called meta-heuristics. If the meta-heuristic optimization is complemented with the precise calculation results of individual solutions, it becomes possible to state that general strategies are specifically applicable, and the results are accurate and precise, thus using best of both worlds. For most meta-heuristic methods, it is necessary to properly represent the problem, procedures and operators within the legitimacy of performing the

heuristics and to partially limit the scope of the solution. Metaheuristic methods that are significantly proven and applicable in solving various problems are local search, tabu search, simulated annealing, genetic algorithm (GA) and ant-colony algorithm [54,60–62].

Computational intelligence approach includes dedicated tools and intelligent procedures for solving certain types of problems that do not necessarily need to be optimization problems. Recognized examples of the methods based on the computational intelligence are fuzzy logic, artificial neural networks, rough sets theory, expert systems and probabilistic agents [63] and application of these methods is often necessary for the purpose of making decisions about individual values, sorting and numeric marking according to certain rules. The wider conception of computational intelligence comprises all heuristic and meta-heuristic optimization procedures and the boundary of the specific category where particular approach belongs to is often unclear.

Methods based on evolutionary principles are powerful optimization procedures most often used in optimization problems where is necessary to consider the fulfillment of two or more objectives. A common feature of optimization methods based on evolutionary principles is the existence of one or more decision-making procedures, the so-called evaluation according to fitness function [56]. Using iterative optimization process based on these methods it is possible to direct the search for solutions in each subsequent iteration to the area where the previous iteration achieved the best solution. Considering the above principle, it is possible to conclude that these methods are like meta-heuristic procedures, which additionally confirms the ambiguous boundary and complexity of the categorization of certain methods.

Hybrid methods combine two or more processes to a single optimization process. The most common hybrid methods are synthesis of the optimization process and computer intelligence decision-making procedures [60]. All optimization methods may encounter certain performance problems in finding the best global solution, low convergence, and long calculation time if they are not properly adapted to the observed problem [9].
