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## Run Optimization  1. The following table summarizes the options available to specify an optimization objective:

2.  Optimization Goal: Minimize Maximize Multiple Output Metric: Weighted Sum Deviation from Target Weighted Sum Desirability Statistic: Mean Median1st quartile3rd quartileMinimumMaximum Standard DeviationVarianceMean Squared Error (Loss Function)SkewnessKurtosisRangeIQR (75-25) Span (95-5)Actual DPM (defects per million) Calculated DPM (defects per million assuming normal distribution) Mean Mean Median1st quartile3rd quartileMinimumMaximum Standard DeviationVarianceMean Squared Error SkewnessKurtosisRangeIQR (75-25)Span (95-5) PpPpuPplPpkCpm%Pp (Percentile Pp) %Ppu (Percentile Ppu)%Ppl (Percentile Ppl)%Ppk (Percentile Ppk) Mean

3. Minimize/Maximize Weighted Sum: minimize or maximize the weighted sum of statistic. Weights are specified for each output in the Output Response dialog. For example, if the selected statistic was the Mean, and there were two outputs, the objective function would be:

4.          Weight1Mean1 + Weight2Mean2

If there is a single output in the model, this simplifies to minimize or maximize the statistic value.

Note that the Output Goal specified in the Output Response dialog is not used here. It is only used in Maximize Desirability.

5. Minimize Deviation from Target: minimize the square root of weighted sum of deviations squared. A target must be specified for each output in the Output Response dialog. The only statistic available for this option is the mean. This is also known as the Taguchi or Quadratic Loss Function. If there were two outputs, the objective function would be:

6.         SQRT( Weight1(Mean1 – Target1)2 + Weight2(Mean2 – Target2)2)

7. Maximize Desirability: Maximize the weighted linear sum of the Derringer and Suich desirability measure (Derringer and Suich, 1980). Each output must specify:

• Weight (default = 1). This is also referred to as “Importance”. (Note, another factor, the desirability shape is sometimes called “weight”. In DiscoverSim, the desirability shape factor is fixed at 1.)
• Output Goal (Target, Maximize or Minimize) – this is specific to an output. For example, if Output 1 is production rate, the goal would be set to maximize, and Output 2, cost, would have a minimize goal. However the specified overall objective function goal is to maximize desirability.
• If the output goal is Target, then LSL, Target, and USL are required. LSL and USL are the lower and upper specification limits used for process capability and dpm calculations, but are also used as the lower and upper bounds for desirability.
• If the output goal is Minimize, then Target and USL are required.
• If the output goal is Maximize, then LSL and Target are required.

The only statistic available for this option is the mean.

8. DiscoverSim includes two algorithms for Global Optimization and one for Fast Local Optimization:
• DIRECT (Dividing Rectangles) Global Optimization – ideal for highly complex problem but with few inputs.
• Genetic Algorithm (GA) Global Optimization – use for general global optimization.
• Sequential Quadratic Programming (SQP) for fast local “smooth surface” optimization.
• Hybrid is a powerful hybrid of the above 3 methods

9. Replications value sets the number of replications used in optimization to obtain the Statistic. If the number of replications is set to 1 for deterministic optimization, the statistic used is the Mean, regardless of what has been selected.

10. Seed is set to Clock by default so that the starting seed of random number generation will be different with each run. If you want the optimization results to match every time (for example in a classroom setting where you want all students to obtain the same results), select Value and enter an integer number. Stochastic optimization requires a fixed seed in order to avoid “chatter” that would result in inconsistent comparisons. If the Seed is set to Clock, the initial seed value will be obtained from the system clock and then kept fixed throughout the optimization.

11. Select Monte Carlo (Random) for full randomization. Latin Hypercube Sampling is less random than Monte Carlo but enables more accurate simulations with fewer replications.

12. Accelerated Mode uses DiscoverSim’s Excel Formula Interpreter to dramatically increase the speed of calculations for rapid optimization. If unchecked, the calculations are performed using native Excel. The interpreter supports the majority of all Excel numeric functions (for more details see Appendix: DiscoverSim Engine and Excel Formula Interpreter). If the DiscoverSim interpreter sees a function that it does not support, you will be prompted to use Excel’s Native mode.

13. Check Independence (Ignore Correlations) to run the optimization with all inputs independent of each other (zero correlation).

14. Optimization in process may be paused or stopped. Upon completion, the user can paste the optimum control and/or parameter values in order to perform further simulation studies.

# Web Demos

Our CTO and Co-Founder, John Noguera, regularly hosts free Web Demos featuring SigmaXL and DiscoverSim