A General Cooperative Optimization Approach for Distributing Service Points in Mobility Applications

Thomas Jatschka,Tobias Rodemann,Günther R Raidl

doi:10.3390/a14080232

Abstract

This article presents a cooperative optimization approach (COA) for distributing service points for mobility applications, which generalizes and refines a previously proposed method. COA is an iterative framework for optimizing service point locations, combining an optimization component with user interaction on a large scale and a machine learning component that learns user needs and provides the objective function for the optimization. The previously proposed COA was designed for mobility applications in which single service points are sufficient for satisfying individual user demand. This framework is generalized here for applications in which the satisfaction of demand relies on the existence of two or more suitably located service stations, such as in the case of bike/car sharing systems. A new matrix factorization model is used as surrogate objective function for the optimization, allowing us to learn and exploit similar preferences among users w.r.t. service point locations. Based on this surrogate objective function, a mixed integer linear program is solved to generate an optimized solution to the problem w.r.t. the currently known user information. User interaction, refinement of the matrix factorization, and optimization are iterated. An experimental evaluation analyzes the performance of COA with special consideration of the number of user interactions required to find near optimal solutions. The algorithm is tested on artificial instances, as well as instances derived from real-world taxi data from Manhattan. Results show that the approach can effectively solve instances with hundreds of potential service point locations and thousands of users, while keeping the user interactions reasonably low. A bound on the number of user interactions required to obtain full knowledge of user preferences is derived, and results show that with 50% of performed user interactions the solutions generated by COA feature optimality gaps of only 1.45% on average.

Highlights

While there exists a vast amount of literature regarding setting up service points for mobility applications, such as vehicle sharing systems [1,2,3,4] or charging stations for electric vehicles [5,6,7,8], estimations of the existing demand distribution are usually obtained upfront by performing customer surveys, considering demographic data, information on the street network and public transport, and not that seldom including human intuition and political motives
The previously introduced Cooperative Optimization Algorithm was generalized to be applicable to more application scenarios and to larger instances with hundreds of potential service station locations and thousands of users
Results on artificial and real world inspired instances show how the solution quality improves as the amount of user feedback increases and that a near optimal solution is reached for most instances with a reasonably low amount of user interactions

Summary

Introduction

While there exists a vast amount of literature regarding setting up service points for mobility applications, such as vehicle sharing systems [1,2,3,4] or charging stations for electric vehicles [5,6,7,8], estimations of the existing demand distribution are usually obtained upfront by performing customer surveys, considering demographic data, information on the street network and public transport, and not that seldom including human intuition and political motives. Pagany et al [10] present a survey of 119 publications for locating charging stations for electric vehicles in which they discuss further problems with the above mentioned demand estimation methods

Objectives

Methods

Results

Conclusion