The Multi-Objective Distinct Candidates Optimization

Approach

Rasmus K. Ursem, PhDOptimization specialist

Stuctural and Fluid Mechanics, R&T Grundfos Management A/S

Peter Dueholm Justesen, MsCPhD student

Dept. of Computer ScienceUniversity of Aarhus

A novel view promoting better use of “true” multi-objective optimization methods in

industry

Disciplines at Grundfos using optimization – MODCO is a distill of challenges in these MO problems

Fluid mechanics•Parts in contact

with the water (Inner surfaces)

Hardware•Electronics for steering algorithm

Motor control•Steering algorithm

of the motor

Motor design•Geometry of

motor parts

Structural mechanics•Strength of parts so they can withstand forces

Production•Assembly robots

Storage•Minimal invetory

Summary of observations• Nearly all problems are multi-objective with constraints.• Most problems are many-objective with 5-10 objectives and 10-20

constraints.• Some problems have 35-50 objectives and 50-80 constraints.• Some problems are multi-disciplinary – problematic if simulators are

interdependent. • Most problems are discrete, but with ordered parameter values (rounded

reals). • Highly different solutions may have nearly the same performance on many

objectives.• Not all objectives are in conflict.

Motivation for MO in industry• HUGE savings are possible – in 2009 I helped save approx 40 mio. €.• Complexity is beyond what a human can comprehend and design manually.• Automation of tedious tasks allow the engineer to work at a higher level of

abstraction.

Demotivator for research… Weighted sum is clearly the best approach – so far.

General Motivation for the MODCO approach – Incorporating Preferences in MO

1) A priori

3) A posteriori

2) Progressive/interactive

•DM lacks problem understanding.•Several reruns necessary.•Often only narrow region covered.•Overloading DM with work.•Noninteractive systems are often domain-specific (expert systems).

•Too many solutions to properly post-process.

•DM focus on objective space.

[Deb, 2001]

Industrial Motivation for the MODCO Approach – Better Utilization of “True” MO Methods (I)Post-processing hundreds of Pareto-optimal solutions is

infeasible• Too expensive to construct and test all prototypes.

– Each printed prototype costs around 5000 €.– Assembly and test costs around 1000 €.

• Too time-consuming to conduct detailed simulations.– Full simulation may take 1-2 working days to execute.

• Problem setup covers a part of the full design/investigation.– Solution need to be put into a larger context.– Additional evaluation is needed to determine potential.– Lack of models may call for other evaluation techniques.

Need for an algorithm returning a low number of solutions.

Industrial Motivation for the MODCO Approach – Better Utilization of “True” MO Methods (II)Physical realization of a single solution• Simulators are inaccurate.

– A confidence level of ±5% invalidates comparison of nearly identical solutions differing by e.g. 0.1%.

• Prototyping methods are inaccurate.– Rough walls and inaccuracies create differences

between simulated and tested designs.

• Mass production methods change the solution.– Intentional changes: Small adoptions to make

solution produceable in mass manufacturing.– Unintentional changes: Welding seams,

tolerances, casting knobs, etc.

Power losses vs. Price for 3700, 4500, 4800 rpm

11.00

12.00

13.00

14.00

15.00

16.00

17.00

9.00 9.50 10.00 10.50 11.00 11.50 12.00 12.50 13.00

Power losses [W]

Price

[DKK

]

3700 RPM

±5% ±1

%

Need for an algorithm keeping a minimal distance.

Industrial Motivation for the MODCO Approach – Better Utilization of “True” MO Methods (III)Decision making among large sets of solutions• Hard to translate loose formulations into weights or other preference

methods. – DM says “We would like to compare 3-5 clearly different designs”.– Domain expert says “I know many different designs

exists with nearly identical performance.”

• DMs’ favor solutions in knee regions.– Projects are not willing to “pay” a lot for a small

improvement.

• DM often needs to inspect and compare solutions in detail.– Visualization of solutions is often necessary.– Comparison of many solutions (5+) is often impossible.– Comparing few solutions would allow DM to use

implicit knowledge and preferences.Need for controllable level of distinctiveness, knee search, and few

solutions.

Distill Observations from Industry and add MO Multiobjective Distinct Candidates OptimizationFive features of the ideal MODCO algorithm1. Return Pareto-optimal solutions.

– Obvious need for any MO-algorithm.

2. User-defined maximal number of solutions.– User should define how many solutions he wants to post-process.

3. User-defined distinctiveness of the returned solutions.– User defines how different the solutions should be in objective and design

space.

4. User-defined accuracy of simulators.– Algorithm should not return solutions that are overlapping wrt. accuracy.

5. Return solutions in knee regions or according to user-defined preferences (if available) .– Algorithm should incorporate knee search and/or DM preferences if available.

Parameters Controlling a MODCO Algorithm

MODCO parameters

Interpretation of distinctiveness parameters

Please note: The MODCO approach does not prescribe HOW to implement these parameters – that is up to an algorithm implementing the approach.

Implications of the MODCO approach

Revisiting the traditional three MO goals1. Closeness:

– We still want Pareto-optimal solutions.2. Distribution Global Distinctiveness:

– We are not requiring Pareto coverage, but a low number of solutions. – We are not requiring even distribution, but clearly different solutions.

3. Spread Local Multiobjective Optimality:– We are not requiring large spread, but locally optimal solutions in knee

regions.

Preferences are divided into generalized and domain-specific

• Generalized preferences – the MODCO parameters.

– Preferences controlling the set of returned solutions.• Domain-specific preferences.

– Knee search or explicitly stated preference rules may be added.

Applying the MODCO Approach

Setting the MODCO parameters• Number of distinct candidates: KNC

– Ask the DM how many solutions he can afford to post-process (time and money).

– Ask the domain expert (DE) how difficult it is to inspect each solution.

• Design distinctiveness: KDD

– Ask the DM and DE if they want highly different designs (yes high KDD value).

• Performance distinctiveness: KPD

– Ask the DM what the project is ”after”.

• Good trade-offs (exploitative search): Set a low KPD value.

• Extreme solutions (explorative search): Set a high KPD value.

• Mix of the two strategies: Set KPD = 0.5.

– Ask the DE if he knows if multiple equally good solutions exists (yes low KPD).

– Ask the DM and DE if they want overall distinctiveness or on certain objectives.

• Simulator accuracy: KSA

– Ask the DE if he knows how accurate the involved simulators are.

An Example from an Earlier Published MODCO algorithm

KPD investigation on DEB3DK

[Justesen & Ursem, 2009]

True frontKPD = 1.0 -- 20 RunsKPD = 0.5 -- 20 RunsKPD = 0.2 -- 20 Runs

Algorithmic Benefits of the MODCO approach

Observations from initial study• No requirement on population distribution

allows MUCH more focused search and better results.

• Most improvements occurred at low diversity.– Contradicts traditional MO thinking.

• MO MODCO resembles the focus shift unimodal multimodal optimization on single objective problems.– A huge body of research may be

revitalized in a MODCO context.

[Justesen & Ursem, 2009]

Conclusions

The MODCO Approach• The approach addresses all challenges distilled from the observed industrial

problems.• The MODCO parameters allows a “closer-to-project” control of the algorithm.

– Parameters are set from asking the “customer” concrete questions.• Initial study on benchmark problem was promising.

– MODCO parameters controlled performance distinctiveness well.– Algorithm outperformed the other algorithms used in comparison –

focused search.

Real-world insights Algorithmic knowledge

Bridging the gap…

Industry

MODCOApproac

hEA-research

Insights in RWP, research opportunities

MODCO algorithms

Thank you for your attention!

Peter will present a real-world application of the first MODCO algorithm after lunch

Questions?