k-best night vision devices by multi-criteria mixed...

1http://www.iict.bas.bg/acomin

10/15/2013

INSTITUTE OF INFORMATION AND COMMUNICATION TECHNOLOGIESBULGARIAN ACADEMY OF SCIENCE

Daniela Borissova, Ivan Mustakerov

K-best Night Vision Devices by Multi-Criteria Mixed-Integer

Optimization Modeling

ICME 2013: International Conference on Mathematical Engineering, Spain, Barcelona, 14-15 October 2013

AComIn: Advanced Computing for Innovation

10/15/20132

http://www.iict.bas.bg

INTRODUCTION

• Night vision devices (NVDs) offer significant benefits for night timeperformed tasks over unaided vision. They allow viewing in nighttime during numerous applications as military, security, rescueactions, navigation, hidden-object detection, wildlife observation,hunting, tourism, entertainment, etc.

• As a result of technological developments there exist a constantlygrowing number of different NVDs types and models with differentparameters. Therefore, the problem of proper device selectionconforming to given user requirements is actual.

• The performance evaluation and optimal selection of engineeringsystems have multi-level and multi-factor features. This definesessential difficulties that can be approached by multiple criteriadecision-making methods.


WASET - ICME 2013: International Conference on Mathematical Engineering, Spain, Barcelona, 14-15 October 2013

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• Most decision making problems deals with multiple objectives whichcannot be optimized simultaneously due to the inherentincommensurability and conflict between these objectives. Making atrade-offs between these objectives becomes a major subject to getthe best compromise solution.

• A variety of methodologies for solving multiple objective decision-making problems have been proposed. There are no better or worsetechniques, but some techniques better suit to particular decisionproblems than others do.

• The most popular multiple criteria decision-making methods includesuch models as scoring models, analytic hierarchy process, analyticnetwork process, ELECTRE, PROMETHEE, utility models, TOPSIS, andaxiomatic design.



INTRODUCTION

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• In contrast to these methods where pairwise comparisons and

deviation between the evaluations of two alternatives on a particular

criterion is considered, the proposed approach defines k-best devices

as a solution of a single multi-criteria optimization task.

• The basic idea is to reduce a given set of alternatives to k-best

accordingly the user point of view and taking into account given

relations and restrictions.

• The proposed optimization model allows determination of k-best

solutions for more rational and efficient decision-making. A

procedure for evaluation of deviation between ideal solution and

each of k-best devices is presented.



INTRODUCTION

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PROBLEM DESCRIPTION

• When choosing a NVD the user acts as a decision-maker (DM) andshould consider all the relevant parameters for the set of devices tochoose from. The preferred device should be that which comes closeto the decision maker’s objectives, which may often conflict. Theperformance of the NVDs depends on many parameters as: workingrange; field of view; objective focus range; battery life; weight; price.


working range

objective focus range

battery lifeweight

price

NVD performance

IIT

field of view


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PROBLEM DESCRIPTION

• The most essential NVDs parameter taken into account whenchoosing a particular device is its working range. A distinguish featureof working range is its dependency not only on the device modulesparameters, but also on the external surveillance conditions asambient light illumination, atmospheric transmittance, contrastbetween target and background, and not at last on the target area.


atmospheric transmittance

ambient light illumination

contrast between target and background

target area

NVD working range

IIT

field of view


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PROBLEM DESCRIPTION

• There are considerable advantages in making an explicit decision-

aiding framework ensuring that all concerns are identified and

addressed and the reasons behind a particular choice are made clear.

• The advantages of such structured approach are particularly apparent

where there are many alternative devices with numerous different

parameters values. Moreover, often user is interesting in more than

one alternative to make his final selection.

• To define k-best alternatives conforming to the given user

preferences toward NVDs parameters, a proper mathematical model

is developed.



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MULTI-CRITERIA MODEL FORMULATION OF K-BEST NVDS PROBLEM

• The purpose of multi-criteria problem is to support users in exploringsolutions that correspond best to their preferences, i.e. multi-criteriaapproach fits to the situations in which users are not able to define asingle goal function.

• On the other hand, mixed-integer optimization provides a powerfulframework for mathematically modeling of many optimizationproblems that involve discrete and continuous variables. Therefore,the NVDs performance is modeled as multi-criteria mixed-integeroptimization problem for determining of k-best selection of devicestaking into account NVDs parameters:

}Price Weight FR minimize}BL FOV R maximize

,,{,,{



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∑= Φ

=n

iii

iiiob

iob

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tai MSfDCAExR

1 min

*07.0 δττ

∑=

=n

iii xFOVFOV

1

∑=

=n

iii xBLBL

1

∑=

=n

iii xFRFR

1

∑=

=n

iii xWeightWeight

1

∑=

=n

iii xPricePrice

1

kxn

ii =∑

=1

1< k < n

subject to



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• The problem of evaluation of alternatives in terms of their distance tothe ideal solution can be seen as a “second-order” decision problem.After determining of k-best devices, if the user is interested toevaluate each of the chosen devices, the relative estimation betweenideal device and devices from the k-best set can be performed byfollowing the procedure:


determine the objective function value for an ideal device

determine the objective function values for each device within the k-best

determine the relative estimation for each device of k-best set compared to the ideal device


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NUMERICAL RESULTS AND DISCUSSION

• To illustrate the applicability of the proposed approach, realparameters data of 10 night vision goggles are used as input datashown in Table I.



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• The widely used approach for solving multi-objective optimizationproblems is to transform a multiple objective (vector) problem intosingle-objective (scalar) problems. Among decision methods,weighted-sum aggregation of preferences is the most common, as itis a direct specification of importance weights.

• The weighted sum method transforms multiple objectives into anaggregated scalar objective function by multiplying each objectivefunction by a weighting coefficient and summing up all contributorsto look for the Pareto solution.

maximize {w1R*(x) + w2 FOV*(x) + w3 BL*(x) + + w4FR*(x) + w5Weight*(x) + w6Price*(x)}

kxi

i =∑=

10

1

11

=∑=i

iwxi ∈ [0, 1]


0 ≤ wi ≤ 1

k ∈ [2, .., 9]


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• The proposed model defines k-best Pareto optimal solutionsconsidering the importance of each criteria expressed by DMpreferences. The applicability of the proposed approach isdemonstrated by four different sets of weighting coefficientsreflecting four different DM preferences about importance of criteriashown in Table II.



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• The solutions of task

(12) – (14) for

different sets of

weighting coefficients

considering all 10

devices of Table I for

k=3 and k=5 best

devices selections are

illustrated in Fig. 1.

Fig. 1. K-best NVDs selections for different DM preferences: a) for k = 3; b) for k = 5AComIn: Advanced Computing for Innovation


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• These k-best selections of devices could be the base from which theuser can make final choice decision. From the formal point of view,every Pareto-optimal solution is equally acceptable as the solution tothe multi-objective optimization problem. In practice, only onesolution has to be chosen as final decision. A procedure is proposedfor helping the DM in taking of his final decision, for defining how fareach of these k-best devices is from the “ideal” device:

• Step 1: Definition of an “ideal” device with “ideal” parameters i.e.device whose parameters have optimal (maximal/minimal) values.

• Step 2: Calculation of the objective function value for each of theselected k-best devices.

• Step 3: Subtract calculated value of objective function for each k-bestdevice from objective function value of “ideal” device and determinein percentage the relative distance of devices from “ideal” one.



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Fig. 2. Relative estimations of K-best NVDs for different DM preferences



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• The proximity of devices to the “ideal” depends on given DMpreferences (Fig. 2).

• Some of the devices in particular k-best selections are close to the“ideal” then others and could be considered as a good reasonablechoice. In case of DM-1, the device #1 is closest to the “ideal” anddevices #7 and #8 have almost same deviation from the “ideal”. Usingthe information of relative estimations for NVDs k-best, the DM couldmake the final choice in more informed and reasonable way.

• Four different scenarios for DM preferences are numerically tested to demonstrate the applicability of the proposed approach: 1) equivalent importance toward all defined device criteria; 2) emphasizing on working range, weight and price; 3) interesting in working range, field of view, weight and price;4) emphasizing on working range, focus range, weight and price.



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CONCLUSION

• The described NVD choice problem concerns devices optimalselection when a given number of alternatives have to be selectedfrom a finite set of alternatives with different parameters. Theproposed approach is based on solving of mixed integer nonlinearoptimization task. In contrast to the multi-criteria decision makingwhere the solution is single Pareto optimal choice from all of thefeasible alternatives, the proposed approach defines k-bestalternatives as a result of single run of the optimization task.

• The described approach for k-best choice by multi-criteria mixed-integer optimization modeling is suitable for other real-life problemsto support users in exploring solutions that correspond best to theirpreferences. Using such an approach would contribute to improvingthe quality of decisions by making the decision-making process morecomprehensible, efficient and rational.



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ACKNOWLEDGMENT

The research work reported in the paper is partly supported by the project AComIn – Advanced Computing for Innovation,

grant 316087, funded by the FP7 Capacity Programme(Research Potential of Convergence Regions)



k-best night vision devices by multi-criteria mixed...

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