## 2 State-of-the-Art on Evolutionary Multi-Objective Optimization
### Dynamic Multi-Objective Optimization Methods  
Several Dynamic Multi-Objective Evolutionary Algorithms (DMOEAs) have been designed in the literature to solve DMOPs with time-varying objective, variables or constraints. A set of these are visible in Table 1. Five groups of DMOEAs are available in the literature to solve DMOPs: diversity-based techniques, memory-based approaches, prediction methods, parallel systems and transfer learning-based algorithms. The diversity-based approach [1] has shown the ability to solve dynamic problems with continuous and small time-varying parameters, and showed its limit when faced a severe environmental changes. Furthermore, the DMOPs have presented some periodical or recurrent changes, making storing the historical experience of solutions useful in preserving diversity. The dynamic non-dominated sorting genetic algorithm II (DNSGA-II) [1] is proposed to enhance the diversity of solutions when solving DMOPs. In DNSGA-II, a set of solutions was randomly selected for use as detectors and re-evaluated after each change. Then, if a change was detected, all selected solutions were re-initialized or hyper-mutated. Memory-based approaches use redundant representations of an evolutionary algorithm, using extra-memory components to detect future changes [11]. These approaches are very effective to solve DMOPs with periodically time-varying properties. However, such mechanisms slow the convergence and strengthen diversity in the EDO approaches. The main disadvantage of memory-based algorithms is the ineffectiveness of the redundant solutions stored in the archive. However, prediction-based methods tend to predict changes based-on limited patterns. Such a system can quickly detect the best global solution, but fail when the changes are stochastic, which increases the relative training error rates. The Steady-State and Generational Evolutionary Algorithm (SGEA) [11] was designed to effectively detect and react to the change in a steady-state manner. If a change is detected, a number of good solutions are re-used in the next processing step; then, a combination of previous and new solutions are used to approximate the new Pareto optimal front. The parallel approaches present an optimization process over multiple sub-swarms, which can handle the problem over a separate search space and are recommended for multi-modal problems, while being computationally expensive. A key challenge for these methods is finding an appropriate number of sub-swarms and their sizes. The Competitive-Cooperative Co-evolutionary Algorithm (dCOEA) in [12] aims to track the time-varying POP based on the decomposition of the optimization process. However, only the winners of each sub-population are used to manage the optimal solutions. The MOEA/D [13] is a decomposition-based approach, which aims to subdivide the population into several sub-populations and solve many sub-problems separately and simultaneously, making the MOEA/D system lower and more time-consuming. The prediction-based methods were developed based on machine-learning algorithms and can efficiently determine and optimize the initial population based on previous experience. However, the main limit is the insufficiency of useful knowledge at the beginning of the optimization process, and they are time-consuming. The population prediction strategy (PPS) [14] is a prediction-based method, which divides the non-dominated solutions into a centerpoint and a manifold; then, both are used to predict the future center point and manifold, respectively. When a change is detected based a population, re-initialization is operated. Transfer-learning-based techniques are reliable alternatives for DMOPs, based on the use of MOEA/D [13] as a baseline system. In 2020, the new memory-driven manifold transfer learning was proposed, based on the evolutionary algorithm (MMTL-MOEA/D) [15].