Using a modified invasive weed optimization algorithm for a personalized urban multi-criteria path optimization problem

doi:10.1016/j.jag.2012.03.004

International Journal of Applied Earth Observation and Geoinformation

Volume 18, August 2012, Pages 313-328

https://doi.org/10.1016/j.jag.2012.03.004 Get rights and content

Abstract

The personalized urban multi-criteria quasi-optimum path problem (PUMQPP) is a branch of multi-criteria shortest path problems (MSPPs) and it is classified as a NP-hard problem. To solve the PUMQPP, by considering dependent criteria in route selection, there is a need for approaches that achieve the best compromise of possible solutions/routes. Recently, invasive weed optimization (IWO) algorithm is introduced and used as a novel algorithm to solve many continuous optimization problems. In this study, the modified algorithm of IWO was designed, implemented, evaluated, and compared with the genetic algorithm (GA) to solve the PUMQPP in a directed urban transportation network. In comparison with the GA, the results have shown the significant superiority of the proposed modified IWO algorithm in exploring a discrete search-space of the urban transportation network. In this regard, the proposed modified IWO algorithm has reached better results in fitness function, quality metric and running-time values in comparison with those of the GA.

Highlights

▸ The original IWO algorithm was modified to solve the urban multi-criteria path optimization problem. ▸ A quality metric method was proposed for evaluating the results achieved by GA/modified-IWO algorithm. ▸ The proposed modified IWO algorithm has reached better results in comparison with those of the GA.

Introduction

The issue of finding the shortest/optimum path on networks is one of the most important network analyses, and it is necessary for calculating other network-analyses such as finding closest facility, finding service areas, vehicle routing problems, and multi-modal routing problems. Shortest path problems are categorized into two types including a single-criterion shortest path problems (SSPP) as well as multi-criteria shortest path problems (MSPP) (Mooney and Winstanley, 2006, Gandibleux et al., 2006, Hochmair, 2008).

In the MSPP, the shortest path problem solving regarding to two or more (in)dependent criteria as well as other additional constraints is the main goal. The MSPP is classified as a NP-hard problem, i.e., the quasi-optimum solution(s) must be accepted instead of the optimum one(s) (Gandibleux et al., 2006, Mooney and Winstanley, 2006). That is the reason why solving the MSPP is still so much important for both the researchers and the decision makers. So, attempts in approximating this quasi-optimum solution(s) will be continued for evaluating new MSPP approaches against previous significant ones.

The personalized urban multi-criteria quasi-optimum path problem (PUMQPP) is classified as both NP-hard and one of the branches of MSPP. In solving the PUMQPP, two or more dependent criteria are considered in a way minimizing a criterion (e.g., travel time) may cause to maximize the other(s) (e.g., travel length or travel degree of difficulty). In this case, finding the best compromising solution based on the importance-value (weight) of each criterion from the driver's point of view in the route selection is the main goal.

The issue of finding the personalized urban multi-criteria quasi-optimum path on urban transportation networks is one of the most complex network-analyses, and it can improve the way-finding services (McGinty and Smyth, 2000, Park et al., 2007, Sadeghi Niaraki and Kim, 2009, Nadi and Delavar, 2011). In recent years, although a number of researches have been undertaken in various personalized route planning and location-based services for improving way-finding services (Richter, 2009, Akasaka and Onisawa, 2008, Volkel and Weber, 2008, Park et al., 2007, Letchner et al., 2006, Zipf and Jost, 2006, Talaat and Abdulhai, 2006, Klippel and Winter, 2005, Rinner and Raubal, 2004, Winter, 2002), the previous researches designed in personalized multi-criteria route planning, which consider a driver's opinions in route selection (Sadeghi Niaraki and Kim, 2009, Nadi and Delavar, 2011) are still based on reducing these types of problems to a single-criterion shortest/optimum path problem (SSPP) by using a weighted linear-combination of all criteria for each edge of the network as an objective function. The studies done by Mooney and Winstanley (2006), Corne et al. (2003), and Pereira (2004) indicate this type of reduction is a radical simplification of a complex problem, and in reality the MSPP does not respond to this reduction satisfactorily.

In order to attain a way-finding service, which can solve the PUMQPP without simplifying it to a SSPP, we organized our current as well as our future studies in two main steps as follows:

1.
Before beginning a travel, the driver (as a client) selects his/her origin and destination as well as appropriate criteria via connecting to the specific web server. Then the driver introduces the percentage of importance-value (weight) of each selected criterion in his/her route selection.
2.
Based on the assigned importance-value of each criterion in route selection (step 1), the driver's multi-criteria quasi-optimum path is found in the server, and then is sent to the client/driver's device for further driving guidance before or during the travel to the destination. We assume that each client device has a GPS receiver, a data connection to the server via a GPRS network for example, and the computing and storing capabilities of a typical modern mobile phone.

The main goal of this research is to solve the personalized multi-criteria quasi-optimum path problem (PUMQPP) in an urban transportation network (step 2) without addressing the information and communication technology (ICT) network-service architectures.

Recently, the invasive weed optimization (IWO) algorithm has been used for solving various optimization problems like optimizing and tuning of a robust controller (Mehrabian and Lucas, 2006), optimal positioning of piezoelectric actuators (Mehrabian and Yousefi-Koma, 2007), developing a recommender system (Sepehri-Rad and Lucas, 2007), adaptive beamforming (Roshanaei et al., 2008), and DNA computing (Zhang et al., 2009). The IWO algorithm developed by Mehrabian and Lucas (2006) is a novel ecologically inspired algorithm. The IWO algorithm (Appendix A) simply simulates natural behavior of weeds in colonizing and finding suitable places for growth and reproduction.

In this research by using and modifying the IWO algorithm, some specific approaches are designed, implemented, and evaluated in comparison with the genetic algorithm (GA) for solving the PUMQPP. This research is designed in 3 main steps:

1.
Measuring each criterion value and calculating the fitness value of each route: In this study, specified approaches are proposed to measure each criterion value and the fitness value of every route respectively due to different ranges of each criterion and the necessity for considering the driver's route preferences to solve the PUMQPP.
2.
Developing the modified IWO algorithm: In this study, as the original IWO algorithm (Appendix A) is designed to solve continuous optimization problems (Mehrabian and Lucas, 2006, Zhang et al., 2009), it has been modified in order to solve the PUMQPP due to the discrete search-space of urban transportation networks.
3.
Proposing a quality metric: In this study, a quality metric is proposed to evaluate the best compromising solution achieved by the modified IWO algorithm in step 2.

This paper is organized in 9 sections. Section 2 illustrates the problem definition. Related works are exhibited in Section 3. Section 4 presents the specific approach, which is used to measure each route criterion as well as its fitness value. The modified IWO algorithm is presented in Section 5. A quality metric method for evaluating the best compromising solutions achieved by both the proposed genetic and modified IWO algorithms is described in Section 6. Section 7 contains the experiments. Section 8 discusses the theoretical and practical issues of the proposed modified IWO algorithm for solving the PUMQPP, and finally in Section 9, conclusions and the future work are considered.

Section snippets

Problem definition

Suppose the directed network G = (N,E). After eliminating all geometrical and topological errors (Ubeda and Egenhofer, 1997), G is defined in a way that $\forall e \in E and \forall i, j \in N : e (i, j) \to c (c_{i, j}^{1}, c_{i, j}^{2}, \dots, c_{i, j}^{M})$ . $c (c_{i, j}^{1}, c_{i, j}^{2}, \dots, c_{i, j}^{M})$ is a vector of dependent edge criteria-costs of size M. A vector of costs (c) can also be associated with the impedance needed to pass a j ∈ N of e(i, j) for a criterion (P for example). In this regard, the impedance value of j ∈ N is added to $c_{i, j}^{P}$ . The route description vector (

Related works

Deterministic algorithms and approximation schemes are available to solve a multi-criteria shortest path problem (MSPP) (Fernandez et al., 1999, Mandow and Perez de la Cruz, 2001, Skriver and Andersen, 2000, Martins et al., 1999, Martins and dos Santos, 1999, Hallam et al., 2001, Nepal and Park, 2003); unless they meet some problems such as the complexity of these approaches often prohibits their implementation in large urban route networks. They are limited to a few numbers of criteria, and

Measuring each route criterion and its fitness

By supposing a set of origin-destination pair, a driver can choose many possible routes. Each of these route-candidates has different values in their dependent criteria in a way minimizing a criterion (e.g., travel time) may cause to maximize the other(s) (e.g., travel length or travel degree of difficulty). Although the proposed method in this research is independent from the number of criteria, only three main dependent criteria are considered to solve the PUMQPP including ‘travel length’,

Modified IWO algorithm

The original invasive weed optimization (IWO) algorithm (Appendix A) can only optimize problems in which the elements of the solution are continuous real numbers, but it cannot be applied to discrete problems directly (Zhang et al., 2009) such as the personalized urban multi-criteria quasi-optimum path problem (PUMQPP). By proposing some specific methods for encoding and generating routes (weeds), calculating the fitness of each route (weed), as well as performing the spatial dispersal, we

Quality metric

Many quality indicators/metrics require knowledge of ideal solution(s) in order to measure how close the current approximation is to the optimal solution(s). In the personalized urban multi-criteria quasi-optimum path problem (PUMQPP), we suppose z* as the route description vector of the ideal solution R*, i.e., rdv(R*): $z^{*} = [\begin{array}{c} x_{1}^{*} & x_{2}^{*} & x_{3}^{*} \end{array}],$ where $x_{1}^{*}$ and $x_{2}^{*}$ are the shortest feasible travel-length and travel-time values between the origin and the destination achieved through employing an independent

Experiments

In order to evaluate the performance of the proposed modified IWO algorithm for solving the personalized urban multi-criteria quasi-optimum path problem (PUMQPP), the distance-to-ideal [Eq. (24)] is considered as a benchmark and the achieved results of the proposed modified IWO algorithm are compared with those of the proposed genetic algorithm (GA) (Appendix B). Experiments were performed using actual road maps of a central-part of Tehran transportation network at the scale of 1:2000. Tehran

Discussion

This study proposes and verifies approaches to solve the personalized urban multi-criteria quasi-optimum path problem (PUMQPP) for a driver by using the modified invasive weed optimization (IWO) algorithm before the driver begins his/her travel. The implemented proposed approaches have some specific characteristics. The first feature of these approaches is the possibility for developing the PUMQPP for any future researches to solve the other multi-criteria urban routing problems such as

Conclusions

In this paper, the original invasive weed optimization (IWO) algorithm was modified to solve the personalized urban multi-criteria quasi-optimum path problem (PUMQPP). The proposed modified IWO algorithm was designed with the capability of accepting unlimited route selection criteria with different ranges. In this regard, an approach was designed to measure each route criterion during the evolutionary process of the proposed modified IWO algorithm. Also, in the proposed modified IWO algorithm,

Acknowledgements

We would like to acknowledge Prof. Caro Lucas, the late joint-supervisor of this research for his brilliant opinions used. Also, the authors truly appreciate both Prof. Alfred Stein and anonymous journal referees for their insightful comments.

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Using a modified invasive weed optimization algorithm for a personalized urban multi-criteria path optimization problem

Abstract

Highlights

Introduction

Section snippets

Problem definition

Related works

Measuring each route criterion and its fitness

Modified IWO algorithm

Quality metric

Experiments

Discussion

Conclusions

Acknowledgements

Engineering Applications of Artificial Intelligence

Digital Signal Processing

Engineering Applications of Artificial Intelligence, December 2001

Aerospace Science and Technology

Ecological Informatics

International Journal of Applied Earth Observation and Geoinformation

Expert Systems with Applications

Annals of Nuclear Energy

Computers and Operations Research

Computers and Mathematics with Applications

Computers, Environment and Urban Systems

Advances in Evolutionary Algorithms: Theory Design and Practice

Personalized pedestrian navigation system with subjective preference based route selection

Algorithms and Theory of Computation Handbook

The good of the many out-weights the good of the one: evolutionary multi-objective optimization

The Newsletter of the IEEE Neural Networks Society

Computational Intelligence

Martins’ algorithm revisited for multi-objective shortest path problems with a Max–Min cost function

4OR: A Quarterly Journal of Operations Research

Genetic Algorithms and Engineering Optimization

Grouping of optimized pedestrian routes for multi-modal route planning: a comparison of two cities

GIS and genetic algorithms for HazMat route planning with security considerations

International Journal of Geographical Information Sc