Memetic algorithms and dynamic programming on vehicle routing problems in crisis situations

The Vehicle Routing Problem is a broad field of study and practice. In this article, we will introduce a general methodology to solve a Dial-a-Ride problem as proposed by Jean-François Cordeau in 2006, followed by a briefly presentation on its further development by Zhang et al. (Omega 54: 60–71, 2015. https://doi.org/10.1016/j.omega.2015.01.011), which involved the use of memetic algorithms to tackle the problem of transportation services regarding the moving of people or goods between locations. Memetic Algorithms are a type of optimization algorithms that have an evolutionary framework and include a list of local search components. Specifically, this kind of problems categorized as a multi-trip dial-a-ride problem, which involves designing multiple routes for each mode of transportation. Finally, an extensive presentation is made based on the principles of Dynamical Programming, which discretizes the optimization problems in stages and the techniques of Linear Programming. The main objective is to utilize real-time information from electronic platforms to determine the most optimal transportation plan at each step. This type of problem is complex due to two main factors: (a) the urgent need to transport people based on their triage scale, and (b) the immediate movement towards the final destination. Additionally, other significant issues need to be taken into account, such as (a) the presence of multiple start and destination points for transportation with varying distances and availabilities, (b) the destination points of one stage becoming the start points for the next stage, (c) limited resources at destination points, and (d) the requirement to achieve global optimization of the response time concerning emergencies and priorities. A comparison will take place regarding these three methodological approaches (general Dial-a-Ride, memetic algorithm, dynamic programming), providing the benefits and the drawbacks of each one and illustrated through a case study involving the timely transport of people.