Optimization for Sustainable Development Leo Liberti LIX, ´ Ecole Polytechnique, France MPRO — RODD – p. 1
Definitions MPRO — RODD – p. 2
What is Sustainable Development ? A paradigm MPRO — RODD – p. 3
What is Sustainable Development ? A paradigm A philosophy MPRO — RODD – p. 3
What is Sustainable Development ? A paradigm A philosophy A set of laws and regulations for manufacturing firms MPRO — RODD – p. 3
What is Sustainable Development ? A paradigm A philosophy A set of laws and regulations for manufacturing firms A moral obligation for all humans MPRO — RODD – p. 3
What is Sustainable Development ? A paradigm A philosophy A set of laws and regulations for manufacturing firms A moral obligation for all humans Producing with low CO 2 emissions MPRO — RODD – p. 3
What is Sustainable Development ? A paradigm A philosophy A set of laws and regulations for manufacturing firms A moral obligation for all humans Producing with low CO 2 emissions Only relying on “clean energy” MPRO — RODD – p. 3
What is Sustainable Development ? A paradigm A philosophy A set of laws and regulations for manufacturing firms A moral obligation for all humans Producing with low CO 2 emissions Only relying on “clean energy” Recycling waste MPRO — RODD – p. 3
What is Sustainable Development ? A paradigm A philosophy A set of laws and regulations for manufacturing firms A moral obligation for all humans Producing with low CO 2 emissions Only relying on “clean energy” Recycling waste Using public/clean transportation instead of private cars MPRO — RODD – p. 3
What is Sustainable Development ? A paradigm A philosophy A set of laws and regulations for manufacturing firms A moral obligation for all humans Producing with low CO 2 emissions Only relying on “clean energy” Recycling waste Using public/clean transportation instead of private cars Making sure hazardous material transportation is equitable MPRO — RODD – p. 3
What is Sustainable Development ? A paradigm A philosophy A set of laws and regulations for manufacturing firms A moral obligation for all humans Producing with low CO 2 emissions Only relying on “clean energy” Recycling waste Using public/clean transportation instead of private cars Making sure hazardous material transportation is equitable Development that can last forever MPRO — RODD – p. 3
What is Sustainable Development ? A paradigm A philosophy A set of laws and regulations for manufacturing firms A moral obligation for all humans Producing with low CO 2 emissions Only relying on “clean energy” Recycling waste Using public/clean transportation instead of private cars Making sure hazardous material transportation is equitable Development that can last forever “Décroissance” MPRO — RODD – p. 3
What is Sustainable Development ? A paradigm A philosophy A set of laws and regulations for manufacturing firms A moral obligation for all humans Producing with low CO 2 emissions Only relying on “clean energy” Recycling waste Using public/clean transportation instead of private cars Making sure hazardous material transportation is equitable Development that can last forever “Décroissance” Making sure the earth can survive MPRO — RODD – p. 3
What is Sustainable Development ? A paradigm A philosophy A set of laws and regulations for manufacturing firms A moral obligation for all humans Producing with low CO 2 emissions Only relying on “clean energy” Recycling waste Using public/clean transportation instead of private cars Making sure hazardous material transportation is equitable Development that can last forever “Décroissance” Making sure the earth can survive Preservation of biodiversity MPRO — RODD – p. 3
What is Sustainable Development ? A paradigm A philosophy A set of laws and regulations for manufacturing firms A moral obligation for all humans Producing with low CO 2 emissions Only relying on “clean energy” Recycling waste Using public/clean transportation instead of private cars Making sure hazardous material transportation is equitable Development that can last forever “Décroissance” Making sure the earth can survive Preservation of biodiversity Helping Africa MPRO — RODD – p. 3
The honest definition Optimization for Sustainable Development Set of applications of optimization techniques which also concern the environment MPRO — RODD – p. 4
Examples MPRO — RODD – p. 5
Scheduling nuclear plant outages Decide when to shut down nuclear plants subject to technical and demand constraints MPRO — RODD – p. 6
Smart buildings Buildings regulate their temperatures based on climate and smart energy usage Population-based optimization, evaluate fitness using EnergyPlus simulation manager MPRO — RODD – p. 7
Concentrator placement Smart grids ⇒ smart meters ⇒ concentrators Where do we place them? Several technical constraints MPRO — RODD – p. 8
Cost of equitability Hazmat transportation regulations often share the risk equitably among different administrative regions : this may cost lives MPRO — RODD – p. 9
Multifeature shortest paths Changing vehicles, optimizing time and CO 2 emissions, passing through given spots : used in road network routing devices MPRO — RODD – p. 10
A more precise definition MPRO — RODD – p. 11
Sustainability in time No single definition How do we propose to use optimization techniques for something that cannot even be defined precisely? Focus on one aspect “Development that can last forever” MPRO — RODD – p. 12
“Development”: working definition We define “development” as a set of processes that transform input into output input output process Input/output can be : mass, energy, information, work, time, value. . . These processes can sometimes be decomposed into complex networks of inter-related processes Conversely, processes can be combined to form networks in out in MPRO — RODD – p. 13
Transformation π hk v : quantity of k yielded per unit of h transformed by v ω k v : amount of k stored at v v process 1 unit of h π hk units of k v amount of k = ω k v MPRO — RODD – p. 14
Unsustainability MPRO — RODD – p. 15
Example Plant 1 draws products 1,2 from inputs 2,3,4,5, transforms 1,2 into 1 unit of 3 and 1 unit of 4 , pushed to outputs 6,7,8,9 2 3 4 5 1 1 2 2 ω = 1 1 π hk = 1 6 7 8 9 3 3 4 4 Decide flows on arcs MPRO — RODD – p. 16
Example Plant 1 draws products 1,2 from inputs 2,3,4,5, transforms 1,2 into 1 unit of 3 and 1 unit of 4 , pushed to outputs 6,7,8,9 2 3 4 5 1(1) 1(1) 1(2) 1(2) 1 1(1) 1(1) 1(2) 1(2) 6 7 8 9 Feasible solution with 8 units of flow MPRO — RODD – p. 16
Why is it unsustainable? Above solution is feasible Plant transforms one unit of 1,2 into 1 unit of 3 and 1 unit of 4 Input flow of 4 units of 1,2 produces eight units of 3,4 Only four units of 3,4 arrive at nodes 6,7,8,9 Four units wasted at plant We would like the model to warn us about this! MPRO — RODD – p. 17
Sustainability MPRO — RODD – p. 18
“Sustainable”: working definition Sustainable development : a process network G = ( V, A ) where transformed flow is conserved Forces to take into account every by-product of transformation process MPRO — RODD – p. 19
Flow conservation For v ∈ V let N − ( v ) = { u ∈ V | ( u, v ) ∈ A } and N + ( v ) = { u ∈ V | ( v, u ) ∈ A } Conservation of ordinary flow f : � � ∀ v ∈ V f uv − f vu = ω v u ∈ N − ( v ) u ∈ N + ( v ) Conservation of multicommodity flow f k : � � f k f k vu = ω k ∀ v ∈ V, k ∈ K uv − v u ∈ N − ( v ) u ∈ N + ( v ) Conservation of transformation flow ( transflow ) f k : � � − � π hk ω h f h f k vu = ω k ∀ v ∈ V, k ∈ K v + v uv v h ∈ K u ∈ N − ( v ) u ∈ N + ( v ) MPRO — RODD – p. 20
Transflow properties No process can create something from nothing: π kk ∀ v ∈ V, k ∈ K ≤ 1 v No process cycle can create something from nothing: ∀ m ∈ N , ( k i | i ≤ m ) ∈ K m , ( v i | i ≤ m ) ∈ V m ( v 1 = v m ∧ { ( v i , v i +1 ) | i < m } ⊆ A → π k 1 k 2 · · · π k m k 1 ≤ 1) v 1 v m Processes cannot destroy without transforming ( π kh ∀ v ∈ V, k, h ∈ K ≥ 0) v MPRO — RODD – p. 21
Transflow bounds Taking into account budget and limit constraints Limit constraints : no process v can exceed its given transformation limit λ k v � ω k f k uv ≤ λ k ∀ v ∈ V, k ∈ K v + v u ∈ N − ( v ) Budget constraints : transformation costs for commodity k at process node v are bounded above by budget B k v � γ k ω k f k ≤ B k ∀ v ∈ V, k ∈ K v + v uv v u ∈ N − ( v ) Often consider aggregated versions of these constraints MPRO — RODD – p. 22
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