Problem statement:The aim of this research is to investigate the Traveling Salesman Problems with Multi-Relations (TSPMR) in which each of the vertices has several edges and different weights. The study concerns the weights fluctuated by time in which the problem has more complexity than general TSP problem. However, this type of problem closes to the real-world situation in engineering aspect. Approach: The new genetic algorithm was developed specially for the TSPMR. With the new genetic algorithm, the new coding system is a mixer between the integer numbers (represents the vertices) and the binary (represents the edges). The experiments were done to investigate the suitable input variables, which are a population size, generation, crossover rate and mutation rate. Results: The suitable generation between 300 and 400, the suitable crossover rate between 20 and 60% and the suitable mutation rate between 30 and 80%. Conclusion: The new developed method in this research is found to efficiently solve the problem with less than 100 vertices, which can reduce 50% of the transportation cost. In case of 100 -1,000 vertices problem, the transportation cost is reduced approximately by 20%. If the vertices are more than 1,000, the transportation cost can be reduced less than 20%. For the large size of problem as 30,000 vertices, the transportation cost is reduced for 6.07%.

Problem statement:This study deals with the pickup and delivery traveling salesman problem with traffic conditions (PDTSPTW), an extension of the pickup and delivery traveling salesman problem (PDTSP) where each customer to be served is associated with two quantities of product to be collected and delivered. Almost PDTSP problems uses distance between each point of customers as Euclidean Distance and are not concerned with other parameters to find minimal cost. Approach: The PDTSPTC concerns more parameters, such as street network and vehicle speed, which results it closer to the real world condition. The study also proposes the developed genetic algorithm called "Hybrid Encoding Genetic Algorithm (HEGA)". The concept is to combine binary encoding and integer encoding together, causing the in complexity of the algorithm structure and the ease of implementation. Results: the HEGA can save the travel cost about 26-57%. It is obviously seen that HEGA in the PDTSPTC test problems result the fast convergence that is about 12-43% and in all, the computational time is under 6 seconds. Conclusion: The HEGA performs quite well when testing a test problem. Computation times are small in all case. The PDTSPTC is closer to real-world conditions than PDTSP. This problem can be applied in logistics immediately if the distance of streets, traffic conditions (average vehicle speed in each street) and vehicle conditions (fuel consumption rate and vehicle capacity) are known.