Finding an energy efficient path for plug-in electric vehicles with speed optimization and travel time restrictions

Abstract

Transportation is one of the main factors when global total energy consumption is considered and is a significant contributor to emissions of harmful gases including carbon dioxide (CO2). Due to their lower tailpipe CO2 emissions compared to the vehicles with internal combustion engines, electric vehicles provide an opportunity to reduce environmental impacts of transportation. In this direction, a problem for plug-in electric vehicles (PEVs) is studied where the aim is to find an energy efficient path. Given an origin–destination pair over a directed network, this problem involves determining a path joining origin and destination, the speed of the PEV on each road segment, i.e., arc, along the path, the charging stations the PEV will stop by, and how much to recharge at each stop so as to minimize the total amount energy consumption. There are speed limits on each road segment, and PEV has to arrive at the destination on or before a given total time limit. For this problem, firstly, a mixed-integer second order cone programming formulation (MISOCP) is proposed. Secondly, to be able to solve larger size instances, a matheuristic is developed. Lastly, an iterated local search (ILS) algorithm is designed for this problem. Solution quality and computation times of the heuristics and the exact algorithm are compared on different instances. Differently from the literature, the speed values of the PEV on the arcs are considered as continuous decision variables in all proposed solution approaches. Moreover, consideration of the speed limits which can be legal limits or limits imposed by congestion makes our problem more realistic. The analysis of the results of the computational experiments gives the user an insight to select the proper solution approach based on the instance settings. MISOCP formulation becomes inadequate for larger instances. On the other hand, the heuristic solution approaches can solve such instances within reasonable computational times and therefore they have the potential to be integrated in some software to dynamically find energy efficient paths.