The existing algorithms for solving multi-objective optimization problems fall into three main categories: Decomposition-based, dominance-based, and indicator-based. Traditional multi-objective optimization problems mainly focus on objectives, treating decision variables as a total variable to solve the problem without considering the critical role of decision variables in objective optimization. As seen, a variety of decision variable grouping algorithms have been proposed. However, these algorithms are relatively broad for the changes of most decision variables in the evolution process and are time-consuming in the process of finding the Pareto frontier. To solve these problems, a multi-objective optimization algorithm for grouping decision variables based on extreme point Pareto frontier (MOEA-DV/EPF) is proposed. This algorithm adopts a preprocessing rule to solve the Pareto optimal solution set of extreme points generated by simultaneous evolution in various target directions, obtains the basic Pareto front surface to determine the convergence effect, and analyzes the convergence and distribution effects of decision variables. In the later stages of algorithm optimization, different mutation strategies are adopted according to the nature of the decision variables to speed up the rate of evolution to obtain excellent individuals, thus enhancing the performance of the algorithm. Evaluation validation of the test functions shows that this algorithm can solve the multi-objective optimization problem more efficiently.

Many-objective optimization problems (MaOPs) are challenging optimization problems in scientific research. Research has tended to focus on algorithms rather than algorithm frameworks. In this paper, we introduce a projection-based evolutionary algorithm, MOEA/PII. Applying the idea of dimension reduction and decomposition, it divides the objective space into projection plane and free dimension(s). The balance between convergence and diversity is maintained using a Bi-Elite queue. The MOEA/PII is not only an algorithm, but also an algorithm framework. We can choose a decomposition-based or dominance-based algorithm to be the free dimension algorithm. When it is an algorithm framework, it exhibits a better performance. We compare the performance of the algorithm and the algorithm with the MOEA/PII framework. The performance is evaluated by benchmark test instances DTLZ1-7 and WFG1-9 on 3, 5, 8, 10, and 15 objectives using IGD-metric and HV-metric. In addition, we investigated its superior performance on the wireless sensor networks deployment problem using C-metric. Moreover, determining objective domain for the objects of the wireless sensor networks deployment problem reduces the time and makes the solution set more responsive to user needs.