# A Two-Archive Many-Objective Optimization Algorithm Based on D-Domination and Decomposition
###### Abstract  
Decomposition-based evolutionary algorithms are popular with solving multi-objective optimization problems. It uses weight vectors and aggregate functions to keep the convergence and diversity. However, it is hard to balance diversity and convergence in high-dimensional objective space. In order to discriminate solutions and equilibrate the convergence and diversity in high-dimensional objective space, a two-archive many-objective optimization algorithm based on D-dominance and decomposition (Two Arch-D) is proposed. In Two Arch-D, the method of D-dominance and adaptive strategy adjusting parameter are used to apply selection pressure on the population to identify better solutions. Then, it uses the two archives' strategy to equilibrate convergence and diversity, and after classifying solutions in convergence archive, the improved Tchebycheff function is used to evaluate the solution set and retain the better solutions. For the diversity archive, the diversity is maintained by making any two solutions as far apart and different as possible. Finally, the Two Arch-D is compared with other four multi-objective evolutionary algorithms on 45 many-objective test problems (including 5, 10 and 15 objectives). Good performance of the algorithm is verified by the description and analysis of the experimental results. m 202215392215392153921539215392153  
With the development of optimization technology, the many-objective optimization algorithm is used to solve many-objective optimization problems [9; 10; 11]. The larger the number of objectives, the greater the proportion of nondominated solutions in the candidate solutions, which worsens the selection pressure of PF. Maintaining population diversity in high-dimensional objective space is also a challenging task [12]. For these problems, scholars have proposed that many algorithms can be divided into the following three types according to the different methods. The first is indicator-based algorithms, e.g., an optimization algorithm [13] based on a new enhanced inverted generation distance indicator is proposed, which automatically adjusts the reference points according to the new indicator contribution. A many-objective optimization algorithm [14] based on IGD indicator and nadir estimation is proposed. IGD is used to select solutions with convergence and diversity. They use indicators to evaluate the convergence and diversity of solutions and guide the search process, the final solution set depends mainly on the indicator characteristics included, such as hypervolume (HV) indicator [15], R2 indicator [16], \(I_{e^{+}}\) indicator [17] and the inverted generational distance (IGD). HV is one of the commonly used indicators [18; 19], but it requires a large amount of calculation, which is generally exponential. Evaluating IGD requires the real Pareto front, which is unknown in real-life problems. The second category is based on the Pareto dominance relationship, e.g., NSGA-II/SDR [20], GrEA [21], VaEA [22] and B-NAGA-III [23], which uses improved Pareto domination to select solutions. The larger the number of objectives, the larger the number of dominant solutions [24]. The method based on Pareto dominance mainly relies on diversity measurement to distinguish solutions, so the population will lose the selection pressure and cannot ensure diversity. To address these issues, more efforts should be made to design diversity maintenance mechanisms to ensure diversity. The third is based on decomposition. The main idea is to transform a MaOP into a set of subproblems by decomposition method and optimize the subproblems in a collaborative way using evolutionary search. The most representative algorithm is the MOEA/D proposed in 2007 [25]. Many similar algorithms have since emerged, such as MOEA/DD [26], MOEA/AD [10], MOEA/D-SOM [27], MOEA/D-AM2M [28], hpaEA [29] and ar-MOEA [30], etc. These algorithms have gained wide popularity due to their good performance.