The Multi-Objective Distinct Candidates Optimization Approach

1. The Multi-Objective Distinct Candidates Optimization Approach A novel view promoting better use of “true” multi-objective optimization methods in industry • Rasmus K. Ursem, PhD • Optimization specialist • Stuctural and Fluid Mechanics, R&T • Grundfos Management A/S • Peter Dueholm Justesen, MsC • PhD student • Dept. of Computer Science • University of Aarhus

2. Disciplines at Grundfos using optimization – MODCO is a distill of challenges in these MO problems • Motor design • Geometry of motor parts • Fluid mechanics • Parts in contact with the water • (Inner surfaces) • 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. • Production • Assembly robots • Storage • Minimal invetory • Structural mechanics • Strength of parts so they • can withstand forces • Motor control • Steering algorithm of the motor • Hardware • Electronics for steering algorithm

3. 1) A priori 2) Progressive/interactive 3) A posteriori General Motivation for the MODCO approach – Incorporating Preferences in MO • 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]

4. 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.

5. 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 differencesbetween 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. ±5% ±1% Need for an algorithm keeping a minimal distance.

6. 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 designsexists 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.

7. Distill Observations from Industry and add MO  Multiobjective Distinct Candidates Optimization Five features of the ideal MODCO algorithm • Return Pareto-optimal solutions. • Obvious need for any MO-algorithm. • User-defined maximal number of solutions. • User should define how many solutions he wants to post-process. • User-defined distinctiveness of the returned solutions. • User defines how different the solutions should be in objective and design space. • User-defined accuracy of simulators. • Algorithm should not return solutions that are overlapping wrt. accuracy. • Return solutions in knee regions or according to user-defined preferences (if available) . • Algorithm should incorporate knee search and/or DM preferences if available.

8. 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.

9. Implications of the MODCO approach Revisiting the traditional three MO goals • Closeness: • We still want Pareto-optimal solutions. • 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. • 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.

10. 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.

11. An Example from an Earlier Published MODCO algorithm KPD investigation on DEB3DK True front KPD = 1.0 -- 20 Runs KPD = 0.5 -- 20 Runs KPD = 0.2 -- 20 Runs [Justesen & Ursem, 2009]

12. 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]

13. Bridging the gap… Insights in RWP, research opportunities MODCO algorithms Real-world insights Algorithmic knowledge MODCOApproach Industry EA-research 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.

14. Thank you for your attention! Peter will present a real-world application of the first MODCO algorithm after lunch Questions?