# A Dynamic Parameter Tuning Strategy for Decomposition-Based Multi-Objective Evolutionary Algorithms
## 1 Introduction  
Many real-life problems involve conflicting and interdependent objectives. The challenge is to optimize multiple objectives simultaneously within a given region, which is known as a multi-objective optimization problem. Multi-objective optimization problems are very important and highly researched in real life, such as in engineering applications, including coil spring design problems for commercial three-wheeled vehicles [1], solar photovoltaic forecasting [2], wind energy forecasting and research issues [3], air pollution forecasting issues [4], aerodynamic design issues [5], etc. [PERSON] and [PERSON] defined the multi-objective optimization problem as shown in Equation (1) [6]:  
The decision space is represented by \(\Omega_{\mathrm{x}}\subseteq\mathrm{R}^{n}\), while \(n_{h}\), \(n_{g}\) represent the number of equations and inequalities, respectively. The number of objectives is denoted by m, and \(F(x):\Omega_{x}\to R^{M}\) is the objective function vector used to solve for x. Therefore, a multi-objective optimization problem typically yields a set of optimal solutions, known as the Pareto optimal solution set. In 1896, the scholar [PERSON] introduced the concept of the Pareto optimal solution. A domination is defined as follows: \(\forall\mathrm{f}_{\mathrm{f}}(\mathrm{x}_{i})\leq\mathrm{f}_{t}(\mathrm{x}_{ j})\) and \(\exists\mathrm{f}_{t}(\mathrm{x}_{i})<\mathrm{f}_{t}(\mathrm{x}_{j})\), \(\mathrm{j}=1,2\,\ldots,\mathrm{m}\), \(x_{i}\) dominates \(x_{j}\), denoted \(x_{i}<x_{j}\), and is referred to as Pareto domination. A solution is considered Pareto optimal if it is not dominated by any other solutions. The set of objective values corresponding to each solution in the Pareto solution set is known as the Pareto frontier [7]. [PERSON] and [PERSON] proposed the MOEA/D algorithm for decomposition-based multi-objective optimization in 2007 [8]. The approach adopted involves decomposition to address multi-objective problems. This is achieved by converting a multi-objective problem into multiple single-objective sub-problems that can be solved individually, and utilizing a neighborhood search strategy and weight vectors to ensure global convergenceand diversity. Compared to other multi-objective optimization algorithms, such as the dominance-based multi-objective optimization algorithm (NSGA-II), MOEA/D has several advantages: the MOEA/D algorithm uses a decomposition strategy for solving, so it can effectively deal with high-dimensional problems [9; 10; 11]; approximation of Pareto optimal solutions by collaborative solving among subproblems [12; 13]; and using a single reference point to guide solution generation reduces the number of depth evaluations and improves the efficiency of the algorithm by only evaluating the solution in the vicinity of the reference point in each problem [14; 15; 16]. \[\left\{ \begin{array}{rl}min&F(x)=\left(f_{1}(x),f_{2}(x),\ldots,f_{m}(x) \right)^{T}\\ s.t.&h_{i}(x)=0,\quad i=1,\ldots,n_{h}\\ &g_{i}(x)\geq 0,\quad i=1,\ldots,n_{g}\\ &x\in\Omega_{x}\end{array} \right. \tag{1}\]  
MOEA/D commonly uses three decomposition methods: the weighted sum method, the Tchebycheff approach, and the penalty-based boundary intersection method (PBI). The algorithm's performance is affected by the number of weight vectors used in the weight summation approach [17], too few to adequately explore the various regions of the Pareto front, and too many, leading to an increase in terms of the algorithm's computational complexity. Also, when the distribution of the weight vectors is not uniform [18], it may lead to the weight vectors being too dense or sparse in some regions, which affects the search ability of the algorithm. The Chebyshev aggregation approach has a large dependence on the weight vector [19], and the determination of the weights between the objective functions needs to be performed [20]. Also, when there are fewer objectives, the distribution of optimal solutions obtained by the Chebyshev aggregation approach is more scattered [21].