A comparison of multi-objective spatial dispersion models for managing critical assets in urban areas A comparison of multi-objective spatial dispersion

A comparison of multi-objective spatial dispersion

models for managing critical assets in urban areas

Advisor : Professor Frank Y. S. LinPresented by: Tuan-Chun ChenPresentation date: May 29 , 2012

Outline Introduction

Background on critical asset vulnerability

and protection

Multi-objective spatial modeling for siting

critical assets

Methods

Multi-objective models

Study area and data

Computational Results

Discussion and Conclusions



and protection


critical assets

Methods


Study area and data



IntroductionMajor disasters have prompted concern

about homeland security.

Prominent issue How to properly manage critical assets?◦ Critical assets are the key infrastructure

components crucial for the continuity of supplies, services, and communications.

◦ The need for developing strategies for effectively managing critical assets and their location. Especially in the case of possible human sabotage.

IntroductionPast researches :

◦ Methods for identifying critical infrastructure vulnerabilities and fortifying infrastructure networks.

◦ Models to minimize loss of both supply facilities and population demands in the context of natural disasters.

◦ Resilience-based research such as disaster relief management. ( objectives commonly involve locating and allocating emergency supplies for critical of vulnerable demands)

IntroductionThis paper focus on protect critical assets by

dispersing them from each other.◦ The p-dispersion model locates p critical facilities to

maximize the minimum distance separating and pair of vulnerability.

◦ Clustering of like facilities increases vulnerability to system failure.

Dispersing facilities protects them by lessening the chance that a single attack or disaster will disable two neighboring facilities simultaneously.

Problems !?

IntroductionPlanners and managers are unlikely to use

the p-dispersion model as the sole criteria fro planning a network for critical assets.◦ Deals only with distances between the facilities

themselves.

p-dispersion has been proposed as a secondary objective in a multi-objective model.◦ But it lacks a systematic exploration of the trade-

offs between dispersion and conflicting objectives (coverage, service efficiency, equity…etc)

IntroductionThe p-dispersion model is well-known to be

computationally difficult to solve for medium and large networks.

It is important to understand how fast multi-objective models solve when the p-dispersion model is combined with other objectives.

Introduction In this paper, Multi-objective spatial

dispersion models are developed and tested Explore and compare the spatial trade-offs and

other relevant objectives.

Integrate the p-dispersion problem with：◦ the maximal covering problem◦ the p-median problem◦ the p-center problem ◦ a variant of the p-maxian problem

IntroductionGoal：

◦ These models have potential to aid in the management and siting of critical assets.

◦ Comparing different multi-objective models’ resulting trade-off curves and computational efficiencies may help decision-makers using these models.



and protection


critical assets

Methods


Study area and data



Background on critical asset vulnerability and protectionCritical infrastructure vulnerability analysis is

not limited to connectivity of linkages. Indeed, Some of the most important components are nodes.

Locational properties of nodes are important aspects of vulnerability analysis .◦ An asset’s vulnerability is partly a function of its

possible exposure to harm.

Background on critical asset vulnerability and protectionMany researchers have developed methods

for protecting critical infrastructures, including allocating resources to critical assets.

There are two schools of thoughts in allocating resources to critical assets.◦ Allocating fortification resources to protect critical

assets against attack.◦ Allocating emergency response units in support of

critical assets resilience.

Background on critical asset vulnerability and protectionThe vast majority of studies developing

formal mathematical strategies for critical infrastructure protection ignore asset dispersion as a potential strategy for the protection of critical assets.

Yet, many researchers have identified dispersion to be an important aspect of increasing the security of critical assets.◦ Geographical concentration◦ Dense urban are more vulnerable to terrorist

attacks.

Background on critical asset vulnerability and protection

Geographical dispersion has been suggested as a strategy toward more resilient infrastructures.

But as a formal modeling strategy for protecting critical assets has not been afforded the attention it deserves.



and protection


critical assets

Methods


Study area and data



Multi-objective problems simultaneously optimize a set of objectives and provide a set of alternative solutions.

The most direct way of solving multi-objective problems is by using the weighting method. This allow for multiple objectives to be combined into a single objective.

The result of this problem is a set of Pareto-optimal solutions that form a Pareto-optimal trade-off curve.

Multi-objective spatial modeling for siting critical assets

Multi-objective models have been developed for siting facilities surrounding populations.◦ Risk sharing model (Ratick and White 1988)◦ Hybrid location model (Church, Gerrard, and Tsai

1998)◦ Spatial optimization model (Maliszewski and Horner

2010)

However, their model ignores inter-facility dispersion as an objective.


A fundamental spatial issue with managing critical assets

Concentration of resources in urban areas benefits society through agglomeration economies while simultaneously increasing the vulnerability of those resources due to over- concentration.

Thus, maximizing accessibility has been operationalized with :◦ the p-median model◦ the set-covering model ◦ the max covering model◦ the p-center problem


the p-median model minimizing weighted distance from nodes to their

closest facilities.

the set-covering model covering model for covering all nodes within a

specified distance standard with the minimum number of facilities.


the max covering model

maximizing demand coverage within a given distance by a specified number of facilities.

the p-center problem minimizing the maximum distance from any

population node to its closest facility.


Spacing of facilities can be accomplished in two general forms :

1. Minimum closeness can be incorporated as a pairwise constraint that requires the distance between any two facilities to be greater or equal to some user-specified critical distance.

Pros : do not alter the formulation of the objective function.

Cons: the distances between facilities are not determined through a model’s output, but by user-specified distance.


Multi-objective spatial modeling for siting critical assetsSpacing of facilities can be accomplished in

two general forms :

2. Modeled as its own objective where by there minimum inter-facility distance between any two facilities is maximized.

This type of objective can be formulated in discrete network space as the p-dispersion problem.

Despite many additional works in the facility dispersion literature, only a few published works have considered the p-dispersion problem with respect to accessibility objectives or other relevant objectives for siting critical assets

Thus, analyzing dispersion with other objectives relevant for placing critical assets would be useful.




and protection


critical assets

Methods


Study area and data



MethodsThis Research employs the p-dispersion

model, which maximizes the distances between facilities, in a multi-objective model in combination with several desirable-facility objectives.

The p-dispersion problem formulation :

(1)

Methods

(2)

(3)

(4)

MethodsCompare the trade-offs and computational

efficiencies of four different bi-objective models. ◦ the p-median model◦ the p-center problem◦ the max covering model◦ the p-maxian problem

MethodsThe p-median problem :

(5)

(6)

(7)

(8)

MethodsThe max covering problem :

(9)

(10)(11)

MethodsThe p-center problem :

(12)

(13)

Plus constraint (2), (4), (6)~(8)

MethodsThe p-maxian problem :

(14)

Subject to constraint (2), (4)

vj Number of potential targets



and protection


critical assets

Methods


Study area and data



Multi-objective modelsEach of the multi-objective models explored

are constructed using the weighting method of multi-objective programming.

The p-median and the p-dispersion

Subject to constraint (2), (4), (6)~(8)

(15)

Multi-objective modelsThe max covering problem and the p-

dispersion :

Subject to constraint (2), (4), (10)~(11)

(16)

Multi-objective modelsThe p-center problem and the p-dispersion :

Subject to constraint (2), (4), (6)~(8), and (13)

(17)

Multi-objective modelsA variant of the p-maxian problem and the p-

dispersion :

Subject to constraint (2), (4)

(17)



and protection


critical assets

Methods


Study area and data



Study area and dataThe study area for this research is the city of

Orlando Florida.

The data set consists of a network of 268 nodes representing census tract centroids. (taken from 2000 Census)

filtered from InfoUSA 2007 (using Standard industrial classification (SIC) code)

• Number of occupants > 25• Dollar assets and income > $1million• square footage > 10,000

Study area and data

Measure the separation between demands and potential facility sites by :

◦ Network distances

◦ Euclidean distances



and protection


critical assets

Methods


Study area and data



Computational ResultsParameters :

Algorithm : Branch and bound lower bound : D ≧ DLB

where D from the initial or previous run is set as DLB to prune unnecessary branches.

Weights (w) 0.01, 0.1, 0.2~1

Coverage (p) 5 (miles)

(a) p-median/p-dispersion

(b) Max-cover/p-dispersion

(c) p-center/p-dispersion

(d) p-maxian/p-dispersion



and protection


critical assets

Methods


Study area and data



Discussion and ConclusionsMulti-objective modeling can provide conspicuous

trade-off gains among conflicting spatial objectives, but very time consuming (at least NP-hard problem).

Single-objective models are perhaps too simplistic for actual siting situations, and computers are fast enough to solve multi-objective problems (but it can be a large in real world).

Therefore, it is important for policy maker or analysts to understand more about multi-objective spatial model for critical asset location management.

Discussion and ConclusionsSome multi-objective dispersion problems

provide more L-shape trade-offs than others.

In terms of computational performance, the p-center was the slowest.

In terms of trade-off gains between dispersion and competing, the max-cover had the most linear trade-off curve.

The trade-off curves for the p-median variant performed the best in terms of the trade-off curve, and also solved relatively fast.

Discussion and ConclusionsThis paper compared and assessed the

computational efficiencies of four different multi-objective models for spatially managing critical assets.

It also illustrated the potential use of several multi-multi-objective spatial models for the management of critical assets and has highlighted both the trade-offs of different conflicting goals.

Although multi-objective facility location models in the context of siting critical assets are computationally intensive, they are feasible with a reasonable number of candidate facility sites.

Discussion and ConclusionsThere are a number of opportunities for

future research :

◦ Look in more detail at ways of differentiating critical infrastructure facilities. (type of targets or supplies)

◦ Build in uncertainty regarding road network availability in the event of a disaster.

Thanks for your attention !!!

Documents

A comparison of multi-objective spatial dispersion models for managing critical assets in urban areas A comparison of multi-objective spatial dispersion