Solver & Population size, any data analysts mathematicians that can point me?

[ad9051]

In Solvers description of the term "population size" It quotes:

· "In the Population Size box, type the number of different points (values for the decision variables) you want the Evolutionary method to maintain at any given time in its population of candidate solutions. The minimum population size is 10 members; if you supply a value less than 10 in this box, or leave it blank, the Evolutionary Solver uses a population size of 10 times the number of decision variables in the problem, but no more than 200."

This description doesn't tell us what effect the population size will have on the speed/efficiency of the Solver algorithm, i have a very large model (only 11parameters however) on a high spec PC, will putting the population to 200 be the best option? I am willing to run this for a few days in order to get me the best result. Any further information would be greatly appreciated.

So essentially I would like to know in data analytics and possibly similar fields in computational mathematics, what does the population size actually mean and how do changes in it affect the results/timeframe/system use of the Solver algorithm?

Any information would be greatly appreciated

Cheers

Alan

[ad9051]

Well it seams no one else on the forum knows much about solver either. So I have emailed frontline solver, they company behind the solver addon.

Here is their reply for your info.

Ashley Naughton, Jun 19 11:45 am (PDT):
Hi Alan,

"When Solver has Converged to the Current Solution"

This message means that the “fitness” of members of the current population of trial solutions is changing very slowly. This may mean that Solver has found a globally optimal solution – if so, new members of the population (that replace other, less fit members) will tend to “crowd around” this solution. However, it may also mean that the population has lost diversity – a common problem in genetic and evolutionary algorithms – and hence the evolutionary algorithm is unable to generate new and better solutions through mutation or crossover of current population members. In this latter case, it may help to run the Evolutionary method again with a larger Population Size and/or an increased Mutation Rate, which increases the chances of a diverse population.

Increasing the Population Size and/or the Mutation Rate, and restarting the Evolutionary method will take more time, but will tend to increase the diversity of the population and the portion of the search space that is explored.

Select and examine the Population Report. If the Best Values are similar from run to run of the Evolutionary method, and if the Standard Deviations are small, this may be reason for confidence that your solution is close to the global optimum. Since optimization tends to drive the variable values to extremes, if the solution is feasible and the Best Values are close to the Maximum or Minimum Values listed in the Population Report, this may indicate that you have found an optimal solution.

Thanks,

Ashley

All the best

Alan

[roki4]

Fact of the matter is that statistical/data analysis is not as objective as it should be. While I am not familiar with this program, it depends what questions you're trying to answer statistically. Generally, a larger sample population provides a higher confidence interval and has a higher probability of being closer to the "true" answer.

Which population size is optimal? Well, I can not answer that unless I know what your variables and end-goals are.

Cheers.

[ad9051]

Hello, Essentially my model is a non smooth model and so i Solve it by the Evolutionary solver engine.

The aim of my model is ultimately to predict the likelyhood of event X. I have statistics for multiple variables that effect the likely hood of event X happening, however i cannot assume that these variables are not inter related.

I model each of these statistics to produce work out the likelihood of event X for each statistics individually.

My primary model simply added all of these individual Likelihoods together to provide a final %chance. However realizing that some of these statistics could be interrelated I set up a model using solver to multiply each individual Likelihood by a number to be defined by solver. I simply ranked the final %chance and found out the final strike rate of my data. I then set this final strike rate at my target cell for solver (to be maximized), and set my parameters as the Likelihood multiplication number

The model is non smooth due to functions within my formula taking into account anomalous data, and the data each statistic can be modeled by anything up to a 6th order polynomial regression.

The model has 11 variables, which looks at over 50000 rows of data which included over 2500 events/arrays.

Any further feedback comments etc would be greatly appreciated.

Many thanks

Alan

[roki4]

For the non-smooth functions, are you normalizing each part of the function, solving each individual one and then aggregating the results? In essence, you are using a genetic matrix to model your results?

I do agree that it can be difficult to see the inter-relation between variables. In econometrics, this is called omitted variable bias. This may be even more difficult with a genetic matrix. However, have you tried looking at the correlation of each variable with respect to each other variable? The R-squared?

I would be very interested in your results and exchanging more ideas.

Cheers.

[ad9051]

Thanks for the reply Roki, I have to admit i am not a trained statition, but i have found myself dabbling in it further and further until i have a hugely complex model.

With regards to each variable, I do review every variable individually by correlation and some are definitely related the r-square values are relatively high as i apply the best order polynomial relationship. I have enough data to assume that any trends are no mistake. In retrospect i should probably running something like this in Matlab, however it started off as my producing some graphs. But now it is a full scale model. I currently have a dedicated PC for running solver for days at a time, to produce the correct results.

Whats your background Roki?

Alan

[roki4]

Next question: when you take out one variable at a time from the model, do the results change significantly? Not at all?

My background, in short: engineering major turned into an economics major (graduated) and finished the first level of the chartered financial analyst designation. I enjoy analysis and have a burning desire for it.

[ad9051]

They do not change a huge amount each regression of data has been added to improve the strike rate of the result, although i would say this is dependent on the statistic. The method mentioned at the start of this thread is aiming to apply the exact correct weighting of each statistic in order to provide the maximal strike rate. This method has enabled me to greatly increase the strike rate of the data. However with such a complex model and 50,000 rows of data, i always wonder what percentage of the picture Solver is managing to get through!? I have it solving at the moment and it will only exit if it gets stuck for 25 hours. Id love to know if it is possible to analyse this data more accurately than i am at the moment. Do you have any experience with neural networks? Do they prove as clever as they sound?

Alan

[roki4]

Each regression analysis should go through the standard 7 assumptions. If all 5 of the 7 assumptions are met, it is a best linear unbiased estimator. If all 7 assumptions are met, it is a best unbiased estimator. See Gauss-Markov theorem, et al.

It really depends on the analyst and how much "feel" they have for the data. If you have gone through your data, model, and analysis and feel that you have explored all the problems and solutions possible then your analysis is sound. However, for me, analysis never ends and each question leads to further analysis.

Are you able to do a scatter plot and/or histogram of your data? Any noticeable frequency/distribution/cluster?

[ad9051]

Hi i think you should add me on skype i could share my screen and show you my analysis methods, i think i have most of the points covered and my feel for the data is very good. I have a few un-answered questions but, I simply need more data to answer them.

I have sent you a PM ,

Cheers

Alan