Optimizing Route Planning via the Weighted Sum Method and Multi-Criteria Decision-Making - Guanquan Zhu; Minyi Ye; Xinqi Yu; Junhao Liu; Mingju Wang; Zihang Luo; Haomin Liang; Yubin Zhong (Mathematics)
Choosing the optimal path in planning is a complex task due to the numerous options and constraints; this is known as the trip design problem (TTDP). This study aims to achieve path optimization through the weighted sum method and multi-criteria decision analysis. Firstly, this paper proposes a weighted sum optimization method using a comprehensive evaluation model to address TTDP, a complex multi-objective optimization problem. The goal of the research is to balance experience, cost, and efficiency by using the Analytic Hierarchy Process (AHP) and Entropy Weight Method (EWM) to assign subjective and objective weights to indicators such as ratings, duration, and costs. These weights are optimized using the Lagrange multiplier method and integrated into the Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) model. Additionally, a weighted sum optimization method within the Traveling Salesman Problem (TSP) framework is used to maximize ratings while minimizing costs and distances. Secondly, this study compares seven heuristic algorithms—the genetic algorithm (GA), particle swarm optimization (PSO), the tabu search (TS), genetic-particle swarm optimization (GA-PSO), the gray wolf optimizer (GWO), and ant colony optimization (ACO)—to solve the TOPSIS model, with GA-PSO performing the best. The study then introduces the Lagrange multiplier method to the algorithms, improving the solution quality of all seven heuristic algorithms, with an average solution quality improvement of 112.5% (from 0.16 to 0.34). The PSO algorithm achieves the best solution quality. Based on this, the study introduces a new variant of PSO, namely PSO with Laplace disturbance (PSO-LD), which incorporates a dynamic adaptive Laplace perturbation term to enhance global search capabilities, improving stability and convergence speed. The experimental results show that PSO-LD outperforms the baseline PSO and other algorithms, achieving higher solution quality and faster convergence speed. The Wilcoxon signed-rank test confirms significant statistical differences among the algorithms. This study provides an effective method for experience-oriented path optimization and offers insights into algorithm selection for complex TTDP problems.