## 4 Materials and Methods
### Methods for Solving Multi-Criteria Optimization Problems  
A common strategy for addressing multi-criteria optimization problems involves generating a set of Pareto-optimal solutions and selecting the most attractive option from this set. The success of this approach critically depends on the designer's ability to manage and interpret the Pareto set, particularly regarding its size and distribution [72]. Achieving Pareto-optimal solutions typically requires tuning various parameters. Classical methods, such as normal constraint, trade-off programming, and physical programming, have been developed to achieve this goal [73].  
However, traditional techniques often exhibit inefficiencies when tackling complex problems. They may fail to ensure Pareto optimality or cover the entire Pareto set. To overcome these challenges, evolutionary approaches are employed, which navigate the complexities of multi-criteria optimization by providing a global perspective of the solution space. These methods avoid local minima and offer multiple alternative solutions in a single optimization cycle.  
Despite these advantages, identifying satisfactory solutions that encompass the entire Pareto-optimal set is often impractical. The primary objectives of multi-criteria optimization are as follows:  
* Reduce the gap between the discovered non-dominated front and the true Pareto boundary.
* Provide a diverse set of solutions, ensuring a wide range of options.
* Maximize the positive effects derived from the non-dominated front, highlighting unattainable values for each criterion within the results.  
When employing evolutionary multi-criteria optimization algorithms, two significant challenges arise:  
1. Assigning fitness and selecting candidates to achieve a Pareto-optimal set.  
2. Population dispersion by introducing diversity-preserving operations to avoid early convergence and ensure an evenly spread non-dominated set.  
Unlike single-criteria optimization, where the objective and fitness functions align, multi-criteria optimization requires consideration of both dimensions. Evolutionary strategies addressing criteria independently, methods based on classic convolution, and Pareto dominance principles have emerged as distinct approaches.  
Instead of merging criteria into a single convolution function, some evolutionary algorithms alternate between criteria during the selection phase. For instance, [PERSON]. [31] suggested dividing the interim population into equal segments based on various criteria. Similarly, [PERSON]. [74] introduced a selection mechanism where individuals are compared using a specific or random criterion order. [PERSON]. [75] proposed a new program to enhance Pareto optimality by targeting optimal reduction.  
The concept of evaluating fitness based on Pareto dominance was pioneered by [76], who expanded this principle into new fitness assignment schemes rooted in Pareto dominance [77].  
Several additional methodologies address multi-criteria optimization using evolutionary techniques. These include parameter variation, pre-determination, population reinitialization, convolution, elitism, and diversity-enhancing \"niching\" methods. Examples of such approaches include fitness equalization, limited crossover, and isolation.  
In this study, one of the most renowned multi-criteria evolutionary algorithms, [PERSON]'s Multiobjective Genetic Algorithm (FFGA), is employed to address the multi-criteria optimization challenge of selecting an efficient ANN structure.