Journal of Advanced Transportation

Volume 2019, Article ID 5874085, 18 pages

https://doi.org/10.1155/2019/5874085

## Multiobjective Calibration Framework for Pedestrian Simulation Models: A study on the Effect of Movement Base Cases, Metrics, and Density Levels

Correspondence should be addressed to Martijn Sparnaaij; ln.tfledut@jiaanraps.m

Received 31 January 2019; Revised 15 April 2019; Accepted 28 May 2019; Published 3 July 2019

Guest Editor: Milad Haghani

Copyright © 2019 Martijn Sparnaaij et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

Ideally, a multitude of steps has to be taken before a commercial implementation of a pedestrian model is used in practice. Calibration, the main goal of which is to increase the accuracy of the predictions by determining the set of values for the model parameters that allows for the best replication of reality, has an important role in this process. Yet, up to recently, calibration has received relatively little attention within the field of pedestrian modelling. Most studies focus only on one specific movement base case and/or use a single metric. It is questionable how generally applicable a pedestrian simulation model is that has been calibrated using a limited set of movement base cases and one metric. The objective of this research is twofold, namely, to (1) determine the effect of the choice of movement base cases, metrics, and density levels on the calibration results and (2) to develop a multiple-objective calibration approach to determine the aforementioned effects. In this paper a multiple-objective calibration scheme is presented for pedestrian simulation models, in which multiple normalized metrics (i.e., flow, spatial distribution, effort, and travel time) are combined by means of weighted sum method that accounts for the stochastic nature of the model. Based on the analysis of the calibration results, it can be concluded that (1) it is necessary to use multiple movement base cases when calibrating a model to capture all relevant behaviours, (2) the level of density influences the calibration results, and (3) the choice of metric or combinations of metrics influence the results severely.

#### 1. Introduction

The creation and implementation of a commercial pedestrian simulation will, ideally, consist of multiple steps. One of those steps is calibrating the model whereby the goal is to increase the accuracy of the model predictions by obtaining the parameter set that results in the best replication of reality. As such, calibration is an important step.

Yet, up to recently, calibration has received relatively little attention within the field of pedestrian modelling [1, 2]; this is mainly attributed to the lack of data [1, 3–5] especially at high densities. Despite this issue, there are many studies in which authors calibrate a pedestrian model (e.g., [6–10]) usually by using a fundamental diagram [11] or trajectories. However, as multiple authors mention, the calibration attempts in these studies are limited and mostly focus on only one or a few aspects [1, 4, 5, 11, 12]. Most studies focus on one specific movement base case (e.g., a bidirectional flow in a straight corridor), use only one metric, or do not look at various population compositions.

It is questionable how generally applicable a pedestrian simulation model is that has been calibrated using a limited set of movement base cases. Campanella, Hoogendoorn, and Daamen [13] and Duives [14] show that using different flow situations leads to different optimal parameter values. That is, both studies identify that for general usage (i.e., using a single model for many different applications) one needs to calibrate a pedestrian simulation model using multiple movement bases to capture all relevant behaviours. The effect of using different metrics during the calibration has been investigated by Duives [14] in relation to pedestrian dynamics and among others [15–17] in relation to vehicular traffic. These studies illustrate that different combinations of metrics clearly lead to different calibration results. Wolinski et al. [18] also calibrate a number of models using different metrics. Though they do not show the effect of using different metrics on the resulting optimal parameter set, the results show clearly that the model fit to the data depends on the metric used. Furthermore, Hänseler, Bierlaire, Farooq, and Mühlematter [19] also note differences between the optimal parameter sets obtained using different metrics or a combination of them when calibrating their macroscopic model.

To overcome the problem of obtaining different results when using different movement base cases and/or metrics, three multiple-objective calibration frameworks have been proposed in recent years which try to take a more inclusive approach. Wolinski et al. [18] propose a framework which can potentially incorporate multiple objectives. However, during their benchmarking tests they only apply combinations of one movement base case and one metric. Campanella et al. [13] show how a microscopic model can be calibrated using multiple movement base cases and how this compares to calibrating the model with only one movement base case. This study still only uses one metric during the calibration. The work by Duives [14] uses multiple movement base cases with multiple metrics and furthermore includes different combinations of weights in the objective function and is thus the most extensive of the three. However, except for the spatial distribution metric, the study does not show the results for the other individual metrics. Hence, it is not possible to exactly determine the effect the different individual metrics have on the resulting optimal parameter set.

So, even though these works illustrate that the choice of the combinations of movement bases and metrics will influence the optimal parameter set obtained during calibration, all three studies have their limitations. For example, they do not explicitly examine the effect of the level of density which might be a relevant factor given that work by Campanella et al. [13] shows that poorness of data can affect calibration results and work by [20] also shows some differences in the obtained parameter sets for a low and high density case of a bidirectional flow. Furthermore, the effects of using different metrics are also still poorly understood. And, as work by Campanella, Hoogendoorn, and Daamen [21] shows that using multiple objectives during the calibration will lead to a better validation score for general usage, it is clear that increased insights into which objectives to use during calibration can improve model validity.

Given these observations the objective of this research is twofold. Firstly, the objective is to determine the effect of the choice of movement base cases, metrics, and density levels on the calibration results. Secondly, the objective is to develop a multiple-objective calibration method for pedestrian simulation models to determine the aforementioned effects, taking into account the stochastic nature common to many microscopic pedestrian models.

This study aims to add value to the current body of literature by means of a more extensive study of the impact of calibration framework setup on the validity of a pedestrian simulation model. This extension provides, among other things, novel insights into the effect of the level of density of the movement base case and more detailed insights into the effect of using a range of metrics in the calibration process. Furthermore, this study features a different type of model (i.e., vision-based model [22]) than the previous most extensive studies (i.e., [13, 14]), which both calibrated NOMAD. Thus, this study also illustrates the replicability of their results and the conclusions of those previous studies.

The rest of the paper is organized as follows. Section 2 briefly describes the microscopic pedestrian simulation model. Section 3 shortly introduces the methodology of the sensitivity analysis and presents the results of the analysis. In Section 4 the calibration methodology is elaborated upon. This is followed by the presentation of the results of calibrating the model using a single objective in Section 5. Section 6 presents the results of the multiobjective calibration. Finally, this paper closes of with a discussion of the results, conclusions, and the implications of this work for practice.

#### 2. Brief Introduction to Pedestrian Dynamics

This section introduces pedestrian dynamics (PD), a microscopic pedestrian simulation model developed by INCONTROL Simulation Solutions. It offers a user the ability to model the movement behaviour of pedestrians at all three behavioural levels (strategic, tactical, and operational). Though, in this research pedestrians only have one activity, namely, to walk from their origin to their destination via a single route, and hence there is no need to model the activity choice, the activity scheduling or the route choice. The model featuring the operational walking dynamics is discussed in more detail underneath.

The operational behaviour of the INCONTROL model consists of two parts, i.e., route following and collision avoidance, which together determine the acceleration of a pedestrian at every time step. PD determines the acceleration of a pedestrian by the combination of ‘social forces’ and a desired velocity component. The pedestrian itself is represented by a circle with a radius . At every time step the acceleration of a pedestrian is determined as follows:where and are, respectively, the desired and current velocity of pedestrian . and are the physical forces that occur on contact with another pedestrian or a static obstacle. And lastly, is the relaxation time. Furthermore, in case the speed of the pedestrian drops below a certain threshold (i.e., the minimal desired speed parameter) the pedestrian does not move until the next time step when the resulting speed is higher than the threshold.

The desired velocity is determined according to the method proposed by Moussaïd et al. [22]. The method uses a vision-based approach to avoid collisions. This approach combines the collision avoidance with the preferred speed and the desired destination to determine the desired velocity. The desired velocity is determined by means of two heuristics, namely,(1)A pedestrian chooses the direction that results in the most direct path to its desired destination given the presence of both static and dynamic obstacles.(2)A pedestrian chooses the speed that, in case there is an obstacle in the preferred direction, results in the lowest time-to-collision whereby this time is always larger than .

The pedestrian only takes into account obstacles that are within its field of vision (), which is determined by the current orientation of the pedestrian, the viewing angle , and the viewing distance . The desired direction is determined by minimizing (2).where is the distance to the closest expected obstacle in the direction of , which is equal to if there are no obstacles within the viewing range. is the angle towards the desired destination. The desired speed is given by where is the preferred speed of the pedestrian and is the distance between the pedestrian and the first expected collision in the desired direction. is determined as follows:where is the distance to the first expected collision in the desired direction of pedestrian and the personal distance of pedestrian . The personal distance is the distance a pedestrian wants to keep between itself and another pedestrian.

There are two important notes regarding the implementation of this method in PD, namely: Regardless of the settings for the viewing angle and viewing distance, the model will only take into account the four closest pedestrians (who are within the field of vision) when determining the desired velocity. Not all parameters can be adapted by the user; the parameters governing the physical forces (i.e., and ) are, namely, not user-adaptable.

The desired destination of each pedestrian is determined using the Indicative Route Method proposed by Karamouzas, Geraerts, and Overmars [23]. This desired destination is influenced by two (user-adaptable) parameters which are the “Preferred clearance”, which influences the minimal distance a pedestrian wants to keep between its desired destination and a static obstacle, and the “Side preference update factor”, which influences the strength of the desired destination location changes given the current position of the pedestrian and the current deviation from the originally planned path.

As is the case for many pedestrian models, PD is stochastic by nature (i.e., two simulations with exactly the same parameters and input but with different seeds result in different outcomes). In this study there are three main causes for this stochasticity, namely, the preferred speed, the initial destination point, and the exact point of origin. The first contributes to the stochasticity due to the fact that every pedestrian is randomly assigned a preferred speed from a given distribution. The latter two causes of stochasticity are points whose location influences the desired destination and whose exact position is a randomly determined location within a respective origin or destination area. The fact that the model is stochastic by nature has to be taken into account during the calibration and is discussed in more detail in the next section.

#### 3. Sensitivity Analysis

A sensitivity analysis is performed to determine to which particular parameters the model is sensitive. This section describes the methodology of the sensitivity analysis and presents the results of this analysis. The results of the sensitivity analysis are used to determine which parameters should be incorporated in the calibration process, as recalibrating all model parameters is not feasible within the time frame of this study. How the results are used to determine the calibration search space and why it is not feasible to include all parameters is explained in more detail in Section 4.5, Search Space Definition.

##### 3.1. Methodology of the Sensitivity Analysis

The goal of the sensitivity analysis is to determine which of the 7 model parameters of the INCONTROL model (see Table 1) that influence the operational behaviour most affect the model’s results. The authors expect that the sensitivity depends on the scenario. Thus, the analysis is performed for all seven scenarios used in the calibration. These scenarios are as follows: A high density bidirectional flow, a high density corner flow, a high density t-junction flow, a bottleneck flow and low density variants of the bidirectional, corner, and t-junction flows. For a detailed description of the scenarios, see Section 4.1.