# Problem Instances

Contents

- 1 Problem Instances
- 1.1 Particle Therapy Patient Scheduling
- 1.2 Districting and Routing Problem for Security Control
- 1.3 Network Design Problem with Relays
- 1.4 Rooted Delay-Constrained Minimum Spanning Tree Problems
- 1.5 Consensus Tree Problem
- 1.6 Periodic Vehicle Routing Problem with Time Windows
- 1.7 Periodic Vehicle Routing Problem and Periodic Traveling Salesman Problem
- 1.8 Vehicle Routing Problem with Compartments
- 1.9 Bi-level Vehicle Routing Problem
- 1.10 Balancing Bicycle Sharing System (BBSS) Problem
- 1.11 Mulitmodal Home-Healthcare Scheduling (MHS) Problem
- 1.12 Competitive Facility Location Problems
- 1.13 Multi Layer Hierarchical Ring Network Design Problem
- 1.14 Two Dimensional Pre-Marshalling Problem
- 1.15 Generalized Vehicle Routing Problem with Stochastic Demands
- 1.16 Virtual Network Mapping Problem

## Particle Therapy Patient Scheduling

Contact: Johannes Maschler, Martin Riedler, Günther Raidl

### Particle Therapy Patient Scheduling Problem (PTPSP)

Instances including a description of the used file format for the published results can be found here.

Updated instances and results can be found here.

### Simplified Intraday Particle Therapy Patient Scheduling Problem (SI-PTPSP)

The instances can be found here. For details on the instance format see the included README file.

The following publication considers these test instances:

1 result

## Districting and Routing Problem for Security Control

Contact: Benjamin Biesinger, Christian Kloimüllner

Instances for the published results can be found here.

## Network Design Problem with Relays

Contact: Markus Leitner, Ivana Ljubic, Martin Riedler, Mario Ruthmair

Instances including a description of the used file format can be found here. (Note: Instances 80N30C50L80F_B, 80N30C50L80F_B_p25, 80N30C50L50F_A, 80N30C50L50F_A_p25, 80N30C50L20F_A, and 80N30C50L20F_A_p25 differ from the ones used in our technical report; the results will be updated shortly)

Further instances from the literature can be found at https://sites.psu.edu/auk3/research/test-problems/.

## Rooted Delay-Constrained Minimum Spanning Tree Problems

Contact: Mario Ruthmair

- C++-Code for reading instance format
- complete instance graphs with 100, 200, 500, 1000 nodes and random integer edge costs and delays in [1,99]

## Consensus Tree Problem

Contact: Sandro Pirkwieser

- instances based on real data
- new artificially generated instances
- new artificially generated small instances

## Periodic Vehicle Routing Problem with Time Windows

Contact: Sandro Pirkwieser

We created instances based on Solomon's VRPTW instances with 100 customers:

- planning period of four days
- planning period of six days
- planning period of eight days

Of the newly created instances with a planning horizon of four days we generated smaller ones for the exact approaches:

- having 36 customers
- having 50 customers

## Periodic Vehicle Routing Problem and Periodic Traveling Salesman Problem

Contact: Sandro Pirkwieser

We created larger instances having 336 to 576 customers and a planning horizon of four or six days

## Vehicle Routing Problem with Compartments

Contact: Sandro Pirkwieser

- benchmark instances of Derigs et al. available here
- modified petrol benchmark instances of Derigs et al. exhibiting a harder packing subproblem

## Bi-level Vehicle Routing Problem

Contact: Günther R. Raidl, Bin Hu

## Balancing Bicycle Sharing System (BBSS) Problem

Contact: Christian Kloimüllner, Petrina Papazek

The homepage of the Balancing Bicylce Sharing System (BBSS) project can be found here.

Our instances are based on real data from Citybike Wien. We got information about 92 stations which contain fill levels at different time in the system, capacity of stations, geographic coordinates, and traveling times between stations.

We constructed instances which contain:

- capacity,
- initial fill level,
- target fill level of stations,
- traveling times, and
- (user) demand values for dynamic rebalancing.

Furthermore, our instances have different size of stations, namely, 10, 20, 30, 60, 90, 120, 180, 240, 300, 400, 500, 600 and 700. Thus, we got a set of artificial stations from our partner, the AIT (Austrian Institute of Technology), which extend the real data we got from Citybike Wien. In particular, we choose the stations for our instances randomly from a set of 92 real stations plus 664 artificial stations.

For the following set of instances we took a snapshot from the system of Citybike Wien to derive initial fill levels for the stations. Furthermore, we set the target value of stations to be 50% of their capacities. We used exactly one depot and also one travel time matrix and the demands for the stations are derived randomly for eight different time points.

- bench2: Benchmark instances based on data from Citybike Wien (used in [1-3, 6])

In EVOCOP-2013 results we list complete computational results based on bench 2 for comparing our auxilary algroithms for deriving loading operations described in [2013,4].

The next benchmark instances contain (user) demand values for the real stations which we got from our partner, the AIT. For the artificial stations we calculated random demand values according to a Beta distribution.

Moreover, we adopted the initial fill levels and target values. The initial fill levels for the artificial stations have been calculated the same way like we did it for the demands, i.e., such that the distribution of the fill levels for artificial stations is similar to that one of the real stations. The target values were set according to their demand. For stations with a high bike demand we set the target value to be 75% of the stations capacity, for stations with a high slot demand to 25% and if both, the bike- as well as the slot demand, are similar we set their target value to 50% of the capacity.

Additionally, we provided four different travel time matrices which show the traveling time at 4:30 am, 8:00 am, 12:00 pm, as well as 6:15 pm.

- bench3: Benchmark instances with advanced initial and target fill levels and time-varying travel times (used in [4,5])

Publications using these benchmark instances

6 results## Mulitmodal Home-Healthcare Scheduling (MHS) Problem

Contact: Günther R. Raidl, Matthias Prandtstetter

- Appendix to "Metaheuristics for Solving a Multimodal Home-Healthcare Scheduling Problem", submitted to Central European Journal of Operations Research
- Benchmark instances based on real world data

## Competitive Facility Location Problems

Contact: Benjamin Biesinger, Bin Hu, Günther R. Raidl

- Benchmark instances with 50 and 100 customers for the Leader-Follower Facility Location Problem with Proportional Customer Behavior
- Benchmark instances with 150 and 200 customers for the Discrete (r|p)-Centroid Problem (RPCP)
- Full result tables of "A Hybrid Genetic Algorithm with Solution Archive for the Discrete (r|p)-Centroid Problem", accepted by Journal of Heuristics

## Multi Layer Hierarchical Ring Network Design Problem

Contact: Christian Schauer, Günther R. Raidl

- Benchmark instances ranging from 22 to 439 nodes
- All results for the Multi-Commodity Flow Based Mixed Integer Linear Programming Approach

## Two Dimensional Pre-Marshalling Problem

Contact: Günther Raidl Benchmark instances for the Two Dimensional Pre-Marshalling Problem (2D-PMP) with 4,6,8,10,12,and 14 columns width, 4 stacks height and 50% and 75% fullness ratio. By combining these parameters we obtain a total of 6*1*2=12 categories of instances. Each category contains 50 instances. The instances were generated using the instance generator found at (https://sites.google.com/site/gciports/premarshalling-problem/bay-generator) provided by:

- Exposito-Izquierdo, C., Melian-Batista, B., Moreno-Vega, M.: Pre-marshalling problem: Heuristic solution method and instances generator. Expert Systems with Applications 39(9) (2012) 8337-8349

File names are encoded using the following key: instance_w_h_c_x.txt

- w - width
- h - height
- c - number of containers within bay (defined by fullness ratio)
- x - instance number within category

## Generalized Vehicle Routing Problem with Stochastic Demands

Contact: Benjamin Biesinger, Bin Hu, Günther R. Raidl

- Benchmark instances for the Generalized Vehicle Routing Problem with Stochastic Demands based on the instances for the GVRP (http://www.personal.soton.ac.uk/tb12v07/gvrp.html) using the same format. In the demand section the expected demand d for each cluster is listed along with a number x. This number determines the possible demand values which are given by D={d-ceil(x*d),...,d+ceil(x*d)} and each demand value has equal probability 1 / |D|.
- Full result tables of "A Variable Neighborhood Search for the Generalized Vehicle Routing Problem with Stochastic Demands", accepted by the EvoCOP 2015 coference.

## Virtual Network Mapping Problem

(Contact: Johannes Inführ, Günther Raidl)