Tonči Carić

A Modelling and Optimization Framework for Real-World Vehicle Routing Problems

The globalisation of the economy leads to a rapidly growing exchange of goods on our planet. Limited commodities and transportation resources, high planning complexity and the increasing cost pressure through the strong competition between logistics service providers make it essential to use computer-aided systems for the planning of the transports. An important subtask in this context is the operational planning of trucks or other specialized transportation vehicles. These optimization tasks are called Vehicle Routing Problems (VRP). Over 1000 papers about a huge variety of Vehicle Routing Problems indicate the practical and theoretical importance of this NP-hard optimization problem. Therefore, many specific solvers for different Vehicle Routing Problems can be found in the literature. The drawback is that most of these solvers are high specialized and inflexible and it needs a lot of effort to adapt them to modified problems. Additionally, most real world problems are often much more complex than the idealized problems out of literature and they also change over time. To face this issue, we present an integrated modelling and optimization framework for solving complex and practical relevant Vehicle Routing Problems. The modular structure of the framework, a script based modelling language, a library of VRP related algorithms and a graphical user interface give the user both reusable components and high flexibility for rapid prototyping of complex Vehicle Routing Problems.

Travel time prediction using speed profiles for road network of Croatia

Prediction of travel time through the road network has a important part in traffic management systems and traveler information systems. Compared to the currently used constant speeds along the roads in Croatia, the speed profiles provide the information about time dependent speeds along the roads and increase the accuracy in travel time predictions. This way the overall costs of transportation can be reduced in both logistics and every day transportation. In this paper the processing of speed profiles for use in time dependent shortest path algorithm is performed which includes clustering, smoothing and first-in-first-out (FIFO) property analysis. The travel time predictions using different sets of speed profiles, dependent on cluster size and seasons, are compared to the real measured travel times. The results show the overall increase in accuracy of travel time prediction using speed profiles compared to constant speeds along the roads by at least 10 %.

Comparison of Calculated and Measured Travel Times with PND Prediction

Correct estimation of the travel time is a rather difficult task because it relies on many factors which act in an unpredictable way. To verify predicted travel time results obtained by calculation from historic data, we have tried to verify those results by measurement and comparison with industrial personal navigation devices available on the market. With the limited time and resources we were able to cover only a finite number of routes with different parameters. Comparison of results show that there are many factors which influence the travel time on short routes and results suffer from higher inaccuracy. On longer routes or on combination of more short routes results show much smaller deviation and are better comparable to the predicted ones.

Vehicle Routing Optimization Using Multiple Local Search Improvements

Combinatorial optimization problems on graphs arise in many practical applications. One of the most studied practical combinatorial optimization problem is the Vehicle Routing Problem (VRP). When coupled with modern in-car navigation and fleet management software, real world applications of VRP optimization result in significant cost savings. In this paper novel multiple improvements pivoting rule for Capacitated VRP (CVRP) is proposed. Its application significantly reduces computational time needed for CVRP optimization. A novel pivoting rule is implemented as part of the search step selection mechanism in the Iterated Local Search algorithm. Augmented iterated local search algorithm is tested on 4 large scale real-world problems in Croatia with up to 7,065 customers and 236 vehicles, and on standard CVRP benchmark sets. Real-world problem data was obtained from a large Croatian logistics company. Comparison of well known first and best pivoting rules with proposed novel multiple improvements pivoting rule regarding travel distance, number of search moves and computational time is given. Achieved computational speed-ups are up to 29 times compared to the first improvement pivoting rule and 9 times compared to the best improvement pivoting rule, without any substantial degradation in quality of the obtained solution.

Predicting waiting times at intersections

Traffic congestion that appears at intersections is the growing problem in urban areas of larger cities, as the capacity and efficiency of intersection affect the road network directly. This paper applies the method of the queuing theory for analyzing traffic conditions at intersections, especially waiting times. The flow of vehicles on the multi-lane road is described by Poisson process, while the intersection is modeled as server with/without group service. Using radar data collected at the intersection in the city of Zagreb, a queuing model is tested. The results show the application of queuing theory in study of traffic flows and waiting times on intersections.

Point-based estimation of calculated speed profiles for road segments

Route planning for freight and personal navigation in urban areas is rather difficult because optimal route is not only distance-but also time-dependent. This task often depends on varying traffic conditions which can be influenced by different factors. Optimal route planning is therefore dependent on the time of the day and of the day in the week for different urban areas. One of the usual solutions to this problem is calculation of speed profiles from GPS traces gathered from different vehicles. Speed profiles are calculated estimates of average speed which can be achieved on a specific road segment during one day. To calculate speed profiles we used gathered GPS data collected during five years and 4,000 vehicles, mostly in urban areas in Croatia. There are different approaches considering time and distance averaging, and final results depend of the chosen values. Actual speed estimation can be made using radar measurements which are point-based but can give a good estimate for the chosen segment. In this paper we compare measurements obtained using Frequency Modulated Continuous Wave (FMCW) radars with calculated speed profiles and present difference for the four road segments.

Optimizing charging station locations for fleet of electric vehicles using Multi-Source Weber Problem

The growth of demand for electric vehicles leads to the infrastructural problem of determining the locations for placing charging stations. Considering that the main drawback of electric vehicles is limited autonomy due to the limited capacity for storing energy, the solution can be found in optimal charging station locations. In this paper, we propose a model for optimizing charging station locations for electric vehicles based on the Multi-Source Weber Problem. The result is shown as minimization depending on the number of charging stations and related total travel distance. Floating car data collected in the urban area of the City of Zagreb is used to estimate the locations of charging demands for fleet of electric vehicles.