Advanced Modeling of Industrial Optimization Problems
1. Advanced Modeling of Industrial
Optimization Problems:
Beyond Algebraic & Algorithmic Modeling Languages
J.D. Kelly & A. Vazacopoulos
Industrial Algorithms
jdkelly@industrialgorithms.ca & alkis@industrialgorithms.com
September 10, 2012
2. UOPSS: Modeling the Objects
● UOPSS = Unit-Operation-Port-State Superstructure.
● Unit-operations are the structural objects combining
"physical" units with "procedural" operations (eg.
Equipment x Activities or Machine x Job).
● Port-states are the structural points where
resources, etc. are consumed & produced.
● UOPS superstructure models the hyper-network of
UOPS to PSUO connectivity.
● UOPSS objects define the "keys" of the problem or
model.
4. UOPSS: Modeling the Objects
● UOPSS is designed for batch, continuous and
dimensional process industries and has the
following types & sub-types:
● ProcessB, ProcessC, ProcessD, Perimeter,
Pool, Pipeline, Pileline, Parcel & Port (In/Out).
● Blender, Splicer, Splitter, Separator, Reactor,
Fractionator & Blackbox for Processes.
● Stock, Utility, Utensil, Time & Task for Ports.
5. QLQP: Modeling the Attributes
● QLQP = Quantity-Logic-Quality Phenomena.
● Phenomenological is different from/orthogonal to
hierarchical, structural, spatial & temporal dimensions.
● Quanties = rates, flows, holdups, yields, durations,
● Logic = setups, startups, switchovers, shutdowns,
sequences, slots,
● Qualities = densities, components, properties,
conditions, coefficients,
● Logistics is the combination of Quanity & Logic
(MILP) and Quality is the combination of Quantity &
Quality (NLP).
6. QLQP: Modeling the Attributes
U O U O U O O U Attributes
Attributes Phenomenological Attributes of
Quantity, Logic and Quality
P S P S Attributes P S S P
8. Advanced Modeling
● Philosophy = "Configure v. Code".
● Allows the modeler or user the ability to focus on
the important aspects of the industrial optimization
problem (IOP) instead of its algebra & algorithms.
● Most of the variables and constraints found in an
IOP can be generalized or formalized using
UOPSS objects and QLQP attributes.
● We currently have over 125 different variable-types &
over 185 different constraint-types including over 100
sets/lists & 150 parameters (and counting ...).
9. Advanced Modeling System: IMPRESS
● IMPRESS = Industrial Modeling & Presolving
System.
● Problems are configured either interfacing with a
flat-file language (IML = Industrial Modeling
Language) or interactively using a programming
language such as Python, Java, C#, C++, C or
Fortran (IMI = Industrial Modeling Interchange).
● We currently have bindings to several linear and
nonlinear programming solvers such as COINMP,
GLPK, LPSOLVE, SCIP, XPRESS, XPRESS-SLP,
CONOPT, IPOPT, KNITRO, NOVA & SLPQP.
10. Advanced Modeling System: IMPRESS
● IMPRESS uses the following resources or entities
to formulate or model the IOP:
– SETS & LISTS = integer- & string-keyed to store integers.
– CATALOGS = integer-keyed to store strings.
– PARAMETERS = integer-keyed to store reals.
– VARIABLES = integer-keyed to store complexes (Re/Im).
– CONSTRAINTS = integer-keyed to store complexes.
– DERIVATIVES = 2 integer & 1 real parallel vectors.
– EXPRESSIONS = 1 integer & 1 real parallel vectors.
– FORMULAS = integer-keyed to store 1 integer & 1 complex
parallel vectors.
11. Key Differences with AML's
● AML's use sorted database table technology to store
and manipulate sparse data.
● IMPRESS also stores the sparse data in a database
table format (i.e., coordinate, triplets, ordered-pairs, non-
zeros, etc.) but manipulates the data using a proprietary
referencing technique for spot or random-access.
● AML's manage the time-period dimension like any
other key, index or cursor in the sparse data table.
● IMPRESS inherently manages the time-period dimension
as a separate appendable-array or vector which is
manipulated using whole-array or vectorized processing
(much faster as the number of time-periods increases).
12. Key Differences with AML's
● AML's always export each nonlinear constraint
instance as a prefix/postfix (RPN) tokenized
expression in byte-code.
● IMPRESS also does this for nonlinear solvers such as
XPRESS-SLP & LINDO-SLP but can also be embedded
directly into function callbacks required by CONOPT,
IPOPT, KNITRO, NOVA & SLPQP in machine-code
(requires substantially less memory).
● Some AML's perform their own mostly linear
presolving calculations (AMPL & AIMMS).
● IMPRESS performs LP primal presolving as well as
nonlinear presolving such as detecting if nonlinearly
declared constraints are linear after presolve.
13. Important Features
● Digitization Engine:
● All time-varying data such as orders, transactions or
events are entered in continuous-time where they are
either discretized (uniform) or distributed (non-
uniform) into time-periods over the time-horizon.
– This also includes a compression & continuosization on the
solution data to remove temporal redundancy.
● Differentiation Engine:
● All 1st-order partial derivatives are either supplied
analytically or computed numerically of analytical
quality using complex-step differencing & graph-
colouring. * The modeler or user is not responsible
for providing derivatives.
14. Important Features
● Documentation Engine:
● All constraints are externalized into a "human-
readable" form as well as all other entities such as
sets, lists, parameters, variables & formulas have
annotations available.
● Diagnostic Engine (Work-in-Progress ...):
● Experience says that over 95% of IOP's have
infeasibilities that occur in the linear part of the model
where these can be quickly identified in LP primal
presolve. The rest require artificial or what we call
excursion variables in both the integer and nonlinear
parts of the model and are generated automatically.
15. Important Features
● Demarcation Engine (Openings, Wet-Plant Problem):
● Optimizing into the future is the goal but respecting the
past & present is vital to properly achieving this i.e., the
"demarcation" between the past & future time-lines.
Addressing the previous activities currently occurring in
the problem must be respected as we look-ahead into the
future.
For example, if a unit-operation has a minimum run-length
of 10-hours & if it started 2-hours in the past then there is
a minimum of 8-hours left i.e., it can be shutdown after 8-
hours into the future.
– It also includes respesting future operations when at a certain
future time a known event is to occur (predictive- or preventative-
maintenance).
16. System Architecture: SIIMPL
● SIIMPL = Server, Interfacer, Interacter, Modeler,
Presolver Libraries.
● There are five DLL components in IMPRESS:
● Server = data modeling & presolving routines.
● Interfacer = parsing for the language.
● Interacter = inserting, updating & viewing routines for
the interchange.
● Modeler = formulating of the variables, constraints,
derivatives & expressions including
"dependent" sets, lists & parameters.
● Presolver = bindings for 3rd-party solving-systems.
17. Types of Optimization & Estimation
● IMPRESS is designed both for industrial decision-
making & data-mining problems deployed off-line,
in-line & on-line such as:
● Planning & Scheduling Optimization (active).
● Data Reconciliation & Regression Estimation (passive).
● Real-Time Control & Optimization (active).
● Monitoring, Tracking & Tracing (passive).
– The terms active & passive imply the "degree of causality".
Active models must be "causal" (cause & effect amongst
variables) & passive models may or may not be causal (no
cause & effect required) also known as "observational".
18. Types of Optimization & Estimation
● IMPRESS directly manages the integration of
planning & scheduling decision-making by exploiting
its hierarchical nature:
● Planning decisions are implemented as either lower &
upper hard bounds (min 1-norm excursions) or as target
soft bounds (min 2-norm deviations) in the scheduling.
● IMPRESS can also model "hybrid" planning &
scheduling problems i.e., a mix of planning &
scheduling constraints in the same model/horizon:
● Both "big" & "small" time-buckets or periods are included
in the problem by allowing one or more operations on the
same unit for the same time-period (single or multi-use).
19. Types of Optimization & Estimation
● IMPRESS inherently manages the integration of the
logistics & quality QLQ phenomena in either
planning or scheduling problems:
● Logistics has quality proxy'd and Quality has logic fixed
but quanties are free/finite. This is a "truncated"
Bender's Decomposition heuristic to avoid MINLP but is
very effective in practice and is a natural mechanism to
manage complexity.
● IMPRESS includes estimatibility diagnostics:
● Observability, redundancy and variability estimates are
calculated as a postsolve for all measured (reconciled)
and unmeasured (regressed) variables using novel
sparse matrix techniques (no GJ, QR or SVD required).
20. Complexity Management
● IMPRESS is intended to assist with the ubiquitous
issue of "complexity management" in IOP's.
● Managing uncertainty & hierarchy are somewhat
addressed but managing complexity is difficult:
– how to balance accuracy, tractability & operability when
modeling & implementing the solution.
● What looks like uncertainty & hierarchy management
issues may be the inability to model the IOP's
complexity ...
– Perceived supply & demand uncertainty maybe the inability of
the upstream producer & downstream consumer to manage
their production or manufacturing as well as intermediate
transportation or distribution.
21. Poor Man's Parallelism
● MPP = Multi-Problem Parallelism.
● MPP does not require IMPRESS to be multi-
threaded unless the solver is multi-threaded (parallel
Barrier or B&B) but allows multiple processes to be
run concurrently managed by the operating-system.
● IMPRESS has a low memory footprint allowing
many problems to be run simultaneously on multi-
core, shared-memory computers with different
starting-values, settings and/or solvers.
● Due to the nonlinear and nonconvex nature of these
problems local solutions can and will occur so extra runs
can be beneficial to potentially find better solutions.
22. MILP Example - SeqDepSwo
● SeqDepSwo = Sequence-dependent switchovers
w/ "repetitive-maintenance" (setup).
– This instance can be considered as the "Prize-Collecting
Traveling-Salesman Problem" (PCTSP).
– This formulation is from Kelly & Zyngier, "An Improved MILP
Modeling of Sequence-Dependent Switchovers for Discrete-
Time Scheduling Problems",I&ECR, 46, 4964-4973, (2007).
● Horizon duration = 30-days, period duration = 1-day.
● Production-line rate (semi-continuous) = 18-tons/day.
● Ten-materials (3..5-day run-lengths), 3-families (3-3-4),
1-cleanout task (1-day run-length, rate = 2-tons/day).
● Demands of 0..72-tons w/ release,due-dates = 0,30-days
w/ prices of $+1/ton & cleanout costs of $-1/ton.
23. MILP Example - SeqDepSwo
● Maximum profit = $540 = $1/ton * 18-tons/day * 30-days
● Provably optimal profit = $502 = 1 * 18 * 28 + -1 * 2 * 1
– Schedules 3rd family and either the 1st or 2nd family in any
sequence (3rd then 1st or 2nd OR 1st or 2nd then 3rd) with one
cleanout instance & one idle day.
Idle
Python 2.7 w/ Matplotlib 1.1.0
Cleanout
24. MILP Example - SeqDepSwo
Python 2.3 w/ Dia 0.97.2 Creates a *.UPS file
which can be used in
both IML & IMI
UOPSS Stencil Sheet
Cleanout
25. MILP Example - SeqDepSwo
● Python 2.7 w/ ctypes w/ IMPRESS-IMI:
from ctypes import *
# Number of materials (including maintenance) and families.
nmaterials = 10+1
nfamilies = 3
# Include IMPRESS constants and callbacks.
execfile("IMPRSimi.py")
# Set the problem path and name.
problem = c_char_p(b"C:/IndustrialAlgorithms/Problems/seqdepswo")
# Root the problem (initializes).
rtnstat = imis.IMPRSroot(problem)
# Reserve the problem memory.
rtnstat = imis.IMPRSreserve(problem,IMPRSall) Past & Future
# Receive the chronological data. Time Horizon Duration &
Time-Period Duration
dthp = c_double(-1.)
dthf = c_double(30.)
dtp = c_double(1.0)
rtnstat = imii.IMPRSreceiveT(byref(dthp),byref(dthf),byref(dtp))
26. MILP Example - SeqDepSwo
● Python 2.7 w/ ctypes w/ IMPRESS-IMI:
# Receive the construction data.
for i in range(nmaterials):
if i < nmaterials-1:
j = i+1
else:
j = -1
... add Sj UO and UOPS
“PL” is a
uname = c_char_p(b"PL") Continuous-Process
oname = c_char_p(str(j))
utype = c_char_p(b"processc")
usubtype = c_char_p(b"")
uuse = c_char_p(b"")
rtnstat = imii.IMPRSreceiveUO(uname,oname,utype,usubtype,uuse,IMPRSkeep)
pname = c_char_p(b"IN")
One inlet &
sname = c_char_p(str(j)) one outlet port
ptype = c_char_p(b"in")
psubtype = c_char_p(b"")
puse = c_char_p(b"")
rtnstat = imii.IMPRSreceiveUOPS(uname,oname,pname,sname,ptype,psubtype,puse,IMPRSkeep) “Keep” or “Erase”
pname = c_char_p(b"OUT")
sname = c_char_p(str(j))
ptype = c_char_p(b"out")
rtnstat = imii.IMPRSreceiveUOPS(uname,oname,pname,sname,ptype,psubtype,puse,IMPRSkeep)
... add Dj UO and UOPS
36. Coding New Variables & Constraints
● Although IMPRESS is not an AML, coding or
creating your own variables, constraints, derivatives
& expressions as well as sets, lists, parameters &
formulas is possible.
● Coding/creating a variable: Type = Continuous, Binary, etc.
– vregister(number,name,dimension,type)
– vreceive(index,value) Objective Function Weights
– vrestrain(index,lower,upper,weight)
● Coding/creating a constraint (f(x)+...+A*x+b ~ 0):
– cregister(number,name,dimension,type)
Defines Sparsity-Pattern
– creceive(index,value)
– dratio(cindex,vindices,derivatives optional) Defines Expression
– erelate(cindex,ntokens,instructions,values)
37. Challenges
● Understanding how to configure IOP's to improve
business performance (economics, efficiency, etc.).
● Understanding how to configure IOP's for
tracatability (good solutions in reasonable-time).
● Troubleshooting IOP's for inconsistent & incorrect
results (not infeasible but not expected either).
● Incrementing & iterating the IOP from solution to
solution (manually or automatically) to improve its
solution accuracy & reality.
● Improving the formulation of the IOP's model to help
in the above (tighter, smaller, faster, smarter, ...)
