June 2014 Alejandro Noriega Campero [email protected] Multiobjective system’s optimization for...

June 2014

Alejandro Noriega [email protected]

Multiobjective system’s optimization for policy design:

A case for electric distribution vehicles in Mexico City

The policy question

Stakeholder 1

System’s Status Quo

obj 1Stakeholder 2

obj 2

Stakeholder 3obj 3

Stakeholder 1

System’s Status B

obj 1Stakeholder 2

obj 2

Stakeholder 3obj 3

• Status quo configuration

• Status quo performance (obj 1, 2, 3, …)

• Status B configuration

• Status B performance (obj 1, 2, 3, …)

The policy question

Stakeholder 1


obj 1Stakeholder 2

obj 2

Stakeholder 3obj 3

Stakeholder 1

System’s Status B

obj 1Stakeholder 2

obj 2

Stakeholder 3obj 3




• Status B performance (obj 1, 2, 3, …)- Cost benefit analysis,

- negotiation, vote, etc.

The policy question

Stakeholder 1


obj 1Stakeholder 2

obj 2

Stakeholder 3obj 3

Stakeholder 1

?obj 1

Stakeholder 2obj 2

Stakeholder 3obj 3




• Status B performance (obj 1, 2, 3, …)- Cost benefit analysis

- Negotiation, vote, etc.

The policy question

Stakeholder 1


obj 1Stakeholder 2

obj 2

Stakeholder 3obj 3

Stakeholder 1

?obj 1

Stakeholder 2obj 2

Stakeholder 3obj 3

• Status quo configuration• Status quo performance (obj 1,

2, …)

• Status B configuration• Status B performance (obj 1,

2, …)

Design problem

Large design spaceLarge performance space

International development

The policy question – EV discussion

Electric Vehicles (EVs) in Mexico

LPG

An Economic Choice for Fleets

2011

• Indeed, policy and intervention hindered by an unclear system’s status B;

• stakeholders overwhelmed by complexity of an (infinite) multiplicity of possible status B’s

Stakeholders

Status B

?

manufacturers

state governments

fleet owners

The policy question

Stakeholder 1


obj 1Stakeholder 2

obj 2

Stakeholder 3obj 3

Stakeholder 1

?obj 1

Stakeholder 2obj 2

Stakeholder 3obj 3


2, …)


2, …)

Design problem


Design space explorationSystem optimization

Pareto multiobj. optimization

MDO

The policy question

Stakeholder 1


obj 1Stakeholder 2

obj 2

Stakeholder 3obj 3

Stakeholder 1

?obj 1

Stakeholder 2obj 2

Stakeholder 3obj 3


2, 3)


2, 3)

Design problem




MDO

• Elicit and focus policy analysis on the interesting set of system configurations, both design and performance spaces;

• which constitute the underlying structural system tradeoffs among objectives

Distribution EVs in Mexico City - questions

System’s Status Quo ?


2)


2)

Design problem



MDO

performance gap separating EV-containing fleets and system’s optima?

Optimal design of a distribution system, in terms of its economic performance?

• Vehicle design configurations, fleet composition, plant capacity, etc.

Is there a place for EVs in the optimal system designs? In what share?

System’s structural tradeoff between environmental and economic objectives?

• How does it vary at different levels of policy intervention?

• Pareto-optimal system configurations at each intervention/ tradeoff level?

System’s design optimization framework

Module A Module B

Module C

Inpu

t

Out

put

Simulation Model: distribution activity

Design spaceExploration

Search Algorithms

Multiobjective Optimization

Numerical Techniques

Heuristic Techniques (SA,GA)

1

2

n

x

x

x

Design Vector

1

2

z

J

J

J

Objective Vector

© Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox

Optimization Formulation – single objective

Obj 1: Economic performance Design Variables:

Factors # of levels Lower bound

Upper bound

plant tanks 250 kl 2 0 1

tanks 125 kl 2 0 1EV design1 Wheelbase 3 3.9 m 5.1 m

Battery cap. 9 80 KwH 120 KwH Power 3 1 3 Quantity 101 0 100

EV design2 Wheelbase 3 3.9 m 5.1 m Battery cap. 9 80 KwH 120 KwH Power 3 1 3 Quantity 101 0 100

EV design3 Wheelbase 3 3.9 m 5.1 m Battery cap. 9 80 KwH 120 KwH Power 3 1 3 Quantity 101 0 100

LPG vans Quantity 101 0 100Diesel trucks Quantity 101 0 100

Full factorial 2.1E+16

Obj 2: Environmental efficiency

𝑬𝑬=𝑤𝑒𝑙𝑙𝑡𝑜 h𝑤 𝑒𝑒𝑙𝑒𝑚𝑖𝑠𝑠𝑖𝑜𝑛𝑠(𝐶𝑂2𝑒𝑞)

product𝑑𝑖𝑠𝑡𝑟𝑖𝑏𝑢𝑡𝑒𝑑 (𝑘𝑔)

• Emissions along the supply chains per volume distributed

Optimization Formulation – single objective

Constraint Units Applicable to

Vehicle payload capacity

kgEVs, LPG vans,

diesel trucks

Vehicle loadable surface area capacity

m2EVs, LPG vans,

diesel trucks

Vehicle range capacity

km EVs

Plant output capacity kg plant

Constraints:Obj 1: Economic performance

Obj 2: Environmental efficiency

• Emissions along the supply chains per volume distributed


Module A Module B

Module C

Inpu

t

Out

put



Search Algorithms




1

2

n

x

x

x

Design Vector

1

2

z

J

J

J

Objective Vector


Simulation Model - LP Gas distribution

Module A Module B

Module C

Inpu

t

Out

put


1

2

n

x

x

x

Design Vector

1

2

z

J

J

J

Objective Vector

+10,000 fleet 80% mex. household energy Detailed data available

LP Gas Distribution

Simulation Model - LP Gas distribution

Vehicles

Inpu

t

Out

put


1

2

n

x

x

x

Design Vector

1

2

z

J

J

J

Objective Vector

Elaborated for Ministry of Energy

LPG state-regulated prices based on it

Economic and Plant Geospatial module Vehicles module

Plant

Geospatial

Economic(no inter-modular feedback)


Inpu

t

Out

put



Search Algorithms




1

2

n

x

x

x

Design Vector

1

2

z

J

J

J

Objective Vector


Vehicles

Plant

Geospatial

Economic

Scalarization

Approaches

Multiobjective Optimization – two paradigms

Pareto Approache

s

Vs.

• Avoid assumptions on stakeholder value functions

• Elicit the interesting set of system configurations, and underlying structural system tradeoffs among objectives

• Provide results to posterior human-in-the-loop decision making

Pareto optimal front

Optimization problem

Non-trivial optimization

• Discrete and categorical design variables

• Non-linear objectives

• Non-convex objectives

• Non-differentiable objectives

SearchAlgorithms

• Local search and evolutionary heuristics implemented; GA outperformed

• Parameter meta-optimization: mutation, crossover, etc.

• Design a Pareto-dominance fitness function

• Post optimality analysis and sensitivity analysis

Multiobjective Optimization – MOGA results

Insights:

• Negativity confirms tradeoff between NPV and environmental efficiency

• Convexity: marginal NPV cost per efficiency unit is significantly smaller at the left end

• A possible case for policy intervention

Pareto front approximation

Physical designs along pareto front

Multiobjective Optimization – MOGA

NPV

Environ. efficiency

NPV

Environ. efficiency

paretopoints



NPV

Environ. efficiency

NPV

Environ. efficiency

paretopoints

less FF trucks

more EVs

more battery

1st Phase

The policy question

Stakeholder 1


obj 1Stakeholder 2

obj 2

Stakeholder 3obj 3

Stakeholder 1

?obj 1

Stakeholder 2obj 2

Stakeholder 3obj 3


2, 3)


2, 3)

Design problem




MDO

• Elicit and focus policy analysis on the interesting set of system configurations (design and performance spaces);

• which constitute the underlying structural system tradeoffs among objectives, and the optimal system designs that yield them

Pareto front vs. LPG distributors optimum vs. Status Quo


Insight:• Status quo not optimal,

• If optimizing solely for NPV, as distributors do, status quo is quasi optimal

• The industry could reduce emissions in +30% without NPV losses

• Several transition costs not accounted in the model, e.g., tech. learning curves

Distributors optimum

Status Quo

Marginal and mean cost per CO2e ton emission reduction, along PF


a

b

a’

b’

Costs of CO2e emission mitigation:

• Marginal and mean costs increase significantly left to right

• Costs incorporate total LPG distributed during plant’s economic life of 15 years


Mean CO2e emission mitigation costs along the pareto front

($USD / CO2e ton)

Physical designs along PF


Mean CO2e emission mitigation costs along the pareto front($USD / CO2e ton)

Physical designs along PF

• Solar water heaters in low income households

100 USD/CO2t

NAMAs cost benchmark

59 USD/CO2t

• EVs introduction and incentive program in Colombia

• Feasible to substitute 50% of fossil fueled vehicles at 100 USD/CO2t

• Abating +40% of the industry’s CO2eq emissions

The policy question

Stakeholder 1


obj 1Stakeholder 2

obj 2

Stakeholder 3obj 3

Stakeholder 1

?obj 1

Stakeholder 2obj 2

Stakeholder 3obj 3


2, 3)


2, 3)

Design problem




MDO

• Elicit and focus policy analysis on the interesting set of system configurations (design and performance spaces);

• which constitute the underlying structural system tradeoffs among objectives, and the optimal system designs that yield them

May 2014

Alejandro Noriega [email protected]

Questions?

Modeling & Simulation – distribution

Plant module

Economic Module

Geospatial Module

Vehicle Module

Simulation

Model

Distribution of Liquefied Petroleum Gas (LPG) in Mexico City

LPG Distribution of LPG

Mexico City

+80% of household energy

in Mexico

+ 10,000 vehicle fleet

1.3 B USD industry annual sales

240 M USD in Mexico City

+20 million population

Modeling & Simulation – gas distribution industry

Modeling & Simulation

Vehicles Module

Inputs Outputs

• EV designs 1 - 3:

– Battery capacity

– Wheelbase

– Power

– Quantity in fleet

• EV designs 1 - 3:

– Payload constraint

– Surface area constraint

– Range constraint

– Vehicle cost

– Fuel efficiency


Vehicles Module

Modeling & Simulation – plant module

Plant module

Includes:

• Civil engineering

• Mechanical engineering

• Electrical engineering

• Legal and operational requirements

• Plant layout

Equipos de Gas, S.A. “Estimación de Planta para Gas LP ”. 2012

Outputs:

• Plant daily capacity

• Plant lifecycle costs


Economic Module

Energea S.A. “Estudio que determine los valores y niveles de las variables incluidas en la metodología utilizada para el cálculo de las tarifas máximas aplicables a la actividad de distribución de gas L.P.” 2012.

* State-regulated LPG prices set based

on this model


Geospatial Module and the vehicle routing problem

Multi-layer geospatial model

Road network

Demand

Pol. boundaries

Barriers

Elevation

Base images

Solve routing problems within city’s

transportation network


Geospatial Module and the vehicle routing problem

Multi-layer geospatial model Inputs Outputs

• Vehicles’ constraints : payload, surface and range

• Plant capacity

• Plant and demand geo-locations

• Product volume distributed (per vehicle)

• Kms traveled (per vehicle)

Road network

Demand

Pol. boundaries

Barriers

Elevation

Base images

Modeling & Simulation – inter-modular block diagram

Economic Mod

Dimensions & Layout

Engineering Systems

Range, efficiency,

capacity, power constraints

Vehicle Mix & Total LPG capacity

Geo-Clusters, routes

Vehicle sales, kms traveled,

CO2e emissions

revenue, free cashflow, NPV

Inputs to Model

Dimensions & Layout

Engineering Systems

Range, efficiency,

capacity, power Vehicle Mix &

Total LPG capacity

Geo-Clusters, routes

Vehicle sales, kms traveled,

CO2e emissions

revenue, free cashflow, NPV

Vehicles Geospatial ModuleIndustrial Plant

if( capacity mismatch)

No inter-modular feedback, just feedforward


Nested Vehicle Routing Problem (VRP),

Model complexity: np-complete, generalized TSP

Spatial clustering and surrogate model

Geospatial Module

Spatial clustering and within-cluster optimization

Optimization – Sensitivity analysis on best result

Sensitivity analysis

Insights:

• # of LPG tanks show the highest sensitivity and are set at their higher bounds

• Quantity of LPG vans and diesel trucks is highly sensitive as well, yet have found balance far from their bounds

Optimization – Sensitivity analysis on best result

Sensitivity analysis

• EV design variables

Optimization – Heuristics: Genetic Algorithm (GA)

Parameter optimization

50 100 150 200-1.153E+05

-1.152E+05

-1.151E+05

Average J(x*) for each Population Size Parameter Value

Population Size

Aver

age

J(x*)

($

'000

)

45 Genetic Algorithm runs, varying:

• Population size

• Population initial range

• Mutation and crossover probabilities

Variation exhibited by GA optima

Plant: 250kl tanksPlant: 125kl tanks

LPG van quantityDiesel truck quantity

EV overall fleet: wheelbaseEV overall fleet: batteryEV overall fleet: power

EV overall fleet: quantity

0.00 0.10 0.20 0.30 0.40 0.50 0.60

Standard Deviation Relative to Factor's Range Size (grouped variables)

Std / |domain|

What’s wrong with battery capacity variation?

• GA consistent (<5%) in quantities:

– of diesel trucks, of EVs, and of tanks on the industrial plant

• EV design variables show reasonable variation (<15%)

Insights

Optimization – Heuristics: Genetic Algorithm (GA)Variation -

Plant: 250kl tanksLPG van quantity

EV overall fleet: wheelbaseEV overall fleet: power

0.000.10

0.200.30

0.400.50

0.60

Standard Deviation Relative to Factor's Range Size (grouped variables)

Std / |dom...

What’s wrong with battery variation?

80 85 90 95 100 105 110 115 120 -

0.05

0.10

0.15

0.20

0.25

0.30

012345678

Ditribution of Battery Capacity in the Optimal Solutions

Ditribution of Battery Capacity in the Optimal SolutionsBattery Distribution in the Highest Optimal Solution

Battery Capacity (KwH)

% o

f veh

icle

s in

the

Opti

mal

Sol

ution

s

Num

ber

of v

ehic

les

in h

ighe

st o

ptim

al s

oluti

on's

flee

t

Insight:

• convergence to two types of complementary EV designs –

• one with higher battery capacity, for longer routes with sparser customers, and another with lower, for shorter routes with concentrated customers –

• Relevant for stakeholders: LPG distributors and vehicle manufacturers

Multiobjective Optimization – Environmental efficiency

J(x)2: CO2-e emissions per LPG

distributed

• Emissions along the supply chain:

CO2eq well-to-wheel emissions

𝐸𝐸=𝑤𝑒𝑙𝑙 𝑡𝑜 h𝑤 𝑒𝑒𝑙𝐶𝑂 2𝑒𝑞𝑒𝑚𝑖𝑠𝑠𝑖𝑜𝑛𝑠

𝐿𝑃𝐺𝑑𝑖𝑠𝑡𝑟𝑖𝑏𝑢𝑡𝑒𝑑

Diesel (l) LPG (kg) Electricity (Kwh)0

0.51

1.52

2.53

3.54

Chart 1.1: Well-to-wheel emissions per energy source

Tailpipe

Supply Chain

CO2e

q (k

gs)

Environmental sub-module implemented

1. Mutation and crossover parameters


2. Pareto fitness function

Pareto front approximation, variability and best parameters


Design of dominance function:• # of dominated• Uniqueness in PF

Parameter ranking measure:

• Elements from non-dominated front in meta non-dominated front

Best: - Mutation 2%- Crossover 100%



NPV

Environ. efficiency

NPV

Environ. efficiency

paretopoints

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June 2014 Alejandro Noriega Campero [email protected] Multiobjective system’s optimization for...

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