## 5 Evaluation and Simulation Results
* Household 1: The cost savings are substantial, particularly during the summer months, when P2P trading significantly reduces costs;
* Household 2: Consistent cost savings are shown throughout the year, with notable reductions during the autumn months;  
Figure 3: (**a**) cost comparison and savings for household 1, (**b**) cost comparison and savings for household 2, (**c**) cost comparison and savings for household 3, highlighting the impact of P2P trading in reducing costs, achieving savings, and generating benefits from surplus energy trading. * Household 3: Variable cost savings are demonstrated, with the highest benefits observed in October and March. The Pareto front analysis was conducted using MOEA/D, which evaluated a total of 100 points across 50 generations. Figure 4 presents the 3D Pareto front, highlighting the optimal trade-off points. In this 3D representation, the algorithm aims to find the optimal balance between cost, benefit, and utilization for P2P energy trading. Each point on the Pareto front indicates a possible solution, where the axes represent the cost (f1), benefit (f2), and utilization (f3). The points on this front are non-dominated solutions, meaning no other solutions in the space perform better in all three objectives simultaneously. The algorithm evaluates solutions iteratively, improving them via crossover, mutation, and neighborhood search. The weight vectors and the decomposition approach of MOEA/D allow for exploring various trade-offs between the objectives. The evaluation history shows that each generation consistently evaluated 100 points, reflecting a stable and systematic approach to the optimization process. The resulting Pareto front coordinates indicate a range of solutions, each representing different trade-offs between the three objectives. Most points on the Pareto front maintain a high benefit-to-cost ratio with near-perfect utilization values. For example, several points, with a cost of KRW 102,339.649, a benefit of KRW 77,584.546, and a utilization rate of 100%, consistently appeared across different generations, indicating stable and reliable solutions. However, the optimal solutions derived from the Pareto front provide clear insights into the most balanced outcomes for households. One solution, with a cost of KRW 32,205.0, a benefit of KRW 32,205.0, and a utilization rate of approximately 57.5%, highlights a scenario where cost minimization, benefit maximization, and utilization are balanced. Other optimal solutions, such as those balancing cost and benefit or cost and utilization, underscore the flexibility of the P2P trading model. These solutions reflect the potential for substantial economic benefits while maintaining efficient energy use, allowing decision-makers to explore and select the most suitable balance for their energy strategy. Figure 4: Pareto Front for three objectives (MOEA/D). To validate the effectiveness of the proposed MOEA/D-based multi-objective optimization framework, a comparative analysis with the Non-dominated Sorting Genetic Algorithm II (NSGA-II), a widely recognized evolutionary algorithm in multi-objective optimization, is conducted Figure 5. The performance is evaluated based on three objectives: cost minimization, benefit maximization, and energy utilization. NSGA-II results in a cost of KRW 51,754.5, a benefit of KRW 44,853.9, and an energy utilization rate of 49.86%. While NSGA-II produced higher benefit values, MOEA/D demonstrated better performance in cost minimization and energy utilization, highlighting its suitability for applications emphasizing these objectives.