# Taxonomy of Scheduling Problems with Learning and Deterioration Effects
## 3 Results
### Solution Methods
#### 3.4.4 Metaheuristics  
Since metaheuristics have proved to be good methods to solve NP-hard combinatorial problems, this literature review identifies a wide variety of procedures to solve scheduling problems with learning and deteriorating effects. A set of 134 articles including metaheuristics show that they are used in 16% of works dealing with scheduling problems of a single machine, 41.4% of parallel machines, 44.3% of a flowshop and 81.8% of a hybrid flowshop. Furthermore, all the articles on job shop and flexible job shop scheduling problems use metaheuristics. The genetic algorithm (GA) is the most widely used metaheuristic for resolving this type of problem, followed by simulated annealing (SA) and tabu search (TS). Research on metaheuristic algorithms started around the 1950s, and new methods continue to appear frequently. Sophisticated approaches have emerged in recent years, and some of these new metaheuristics, such as artificial bee colony (ABC), invasive weed optimizer (IWO), grey wolf optimizer (GWO), whale optimization algorithm (WOA), league champions algorithms (LCA), and artificial-based-molecule chemical reaction optimization (ACRO), started to be applied in this field since 2019, and cat swarm optimization (CSO) was the first used in 2020. An overview of the evolution of metaheuristics can be found in the work of [PERSON] [98]. The use of hybrid metaheuristics has, moreover, recently also become very popular. Hybrid procedures are a combination of algorithms to take advantage of their individual characteristics and performances simultaneously. These approaches are presented in more than 40% of the short-listed papers that use metaheuristics. In this review, we found several authors who hybridize genetic algorithms with other methods such as tabu search [104; 105; 106], simulated annealing [107], variable neighborhood search [108; 109], kangaroo algorithm [110] and differential evolution [111]. Among other approaches, we found the particle swarm optimization hybridized with local search [38], a hybrid CS-JADE algorithm combining improved cuckoo search algorithms and self-adaptive differential evolution [38], a hybrid SC-VNS mixing society and civilization algorithm with variable neighborhood search [112], and a hybrid VNS-ASHLO algorithm incorporating variable neighborhood search and adaptive simplified human learning optimization [113]. Multi-criteria problems are usually solved using metaheuristics or hybrid metaheuristics, each with its special characteristics. The following are some of the approaches proposedby the authors: [PERSON] [114] to minimize makespan and total tardiness, [PERSON] et al. [45] to minimize total weighted tardiness and total energy consumption, and [PERSON] et al. [115] to minimize the weighted sum of makespan and total completion time, used a memetic multi-objective algorithm to obtain a set of solutions. First, the authors develop a non-dominated sorting method, and second, the authors appeal to the Pareto front. [PERSON] et al. [116] presented a multi-objective Hybrid Pigeon Inspired Optimization and Simulated Annealing Algorithm to minimize the makespan and the total energy consumption in a flexible job-shop scheduling problem considering deterioration effects. In the same way, to minimize the makespan and total tardiness in a hybrid flowshop, [PERSON] et al. [117] developed algorithms by hybridizing water flow-like algorithms (WFA) with non-dominated sorting and ranking concepts. [PERSON] [39] developed a novel metaheuristic called levy flight embedded particle swarm optimization (LFEPSO) to solve a multi-objective problem (minimizing the makespan and machine hiring cost). [PERSON] et al. [118] proposed a novel hybrid Pareto artificial bee colony algorithm (HPABC), in which the advantage of using the Pareto front was to prioritize the obtained solutions, minimizing the makespan and the total weight tardiness simultaneously. Some methods referred to in the literature are based on genetic algorithms, such as those by [PERSON] [119], [PERSON] et al.