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The Optsee® Optimizers™

Optsee® Pro and Optsee® Plus allow you to study the behavior of portfolios under multiple parameters, and displays charts and lists of projects ranked in order of Overall SMART Score. This information alone is often not adequate to easily select an optimized set of projects based on business constraints such as budget dollars, available human resources, acceptable risk, timing, etc. For example, you may have 20 potential projects that would cost a sum total of $40 million and would require 30 full-time employees to complete. If you only have a budget of $20 million and 22 full-time employees, it can be very difficult and time consuming to manually determine the best selection of projects to resource. In this 20-project example, there are over 1 million different possible portfolios. In a 30-project portfolio, there are over 1 billion different possible portfolios, and the number continues to rise exponentially as shown in the chart below:

An optimization finds optimal or close to optimal portfolios based on your constraints from many potential solutions. The surface map below shows all the possible solutions meeting limited cost and limited employee constraints for a small (12 project) portfolio. This portfolio has 4,096 potential solutions and an exhaustive search of all possible solutions (a "brute force" search) identified 2,773 solutions. Of these 2,773 solutions, three optimal solutions were can be seen among many local smaller maxima.

Even though this was a small portfolio with only two constraints that was easy to solve using the "brute force" technique, it illustrates the challenges of optimizing larger portfolios with multiple constraints and billions of potential solutions :

  • The optimizer must be able to "explore" the optimization surface to find potential optimal solutions
  • The optimizer must avoid converging prematurely on a maxima that is not close to optimal
  • The optimizer must be able to find optimal solutions in a reasonable time period

Optsee provides you with three different optimizer projects:

  • The Brute Force Optimizer: (Optsee® Pro only) Use this optimizer to find an optimal solution for portfolios consisting of not more than 20 projects (1,048,576 possible solutions). It can be used for larger portfolios, but portfolios larger than 20 projects quickly require days, weeks, years or more of computation time to optimize.
  • The Genetic Optimizer: (Optsee® Pro only) This optimizer uses a proprietary genetic algorithm to find an optimized set of projects that satisfy up to thirty different constraints. The genetic algorithm allows the Optimizer to efficiently test millions of possible combinations of projects, if necessary, to determine an optimized set that meets your constraints.
  • The Branch and Boound Optimizer: (Optsee® Plus and Optsee® Pro) This is a proprietary “Branch and Bound” algorithm designed to quickly explore the optimization surface and find an optimal solution, if one exists. It is designed for portfolios containing less than 35 projects.

The choice of which optimizer to use depends on the particular optimization challenge. Optimizations of large portfolios with large numbers of constraints or tight constraints take longer than smaller portfolios with looser constraints. Optimizing using average value constraints takes longer. We generally recommend testing several optimizer and optimization parameters to determine which optimizer and settings give you the best performance and results for your particular portfolio/constraint combination.

Simultaneous Monte Carlo Simulations on Optimized Portfolios in Optsee® Pro

When you run a simulation-prioritization using the Optsee® Pro prioritizer, you create a distribution of value outcomes for each individual project that can be displayed in a histogram:

A Project Distribution Histogram from a Prioritization Simulation:

This distribution represents the range of values that you could expect to see if you ran the project multiple times and each time the final value was based on a combination of the individual attribute values that fell within their respective assigned uncertainty and/or you used different weights each run. This allows you to see the upside and downside value associated with each project as well as the "most-likely" value (as the mean of the distribution).

When Optsee® optimizes a portfolio against constraints (such as limited money and resources), it uses and sums the individual "most-likely" values for each project to calculate the total value of the portfolio. This total portfolio value outcome represents the outcome if each project delivered its "most-likely" value. For the optimization purposes, this is a necessary and useful model.

However, once an optimized portfolio has been found, finding the portfolio distribution of value outcomes gives you a much more realistic representation of its value than just using the single point values.

A Portfolio Distribution Histogram from a Portfolio Simulation:

Optsee® creates these portfolio distributions by automatically running a Monte Carlo simulation on the optimized portfolio automatically during the optimization process, and saving the results as a "Portfolio View."

This allows you to see and compare the upside and downside value associated with different portfolios as well as the "most-likely" value (as the mean of the distribution), so you get a much more realistic and accurate picture of your portfolio value. This is only possible when you use the Optsee® Prioritizer to rank your projects, otherwise, you won't have the necessary individual project distributions to work from.

These views can then be compared with each other and against the efficient frontiers by opening the optimized portfolio, the corresponding Portfolio Views List form, and the corresponding portfolio efficient frontier chart.

When a histogram resulting from a simulation is created, Optsee® draws several lines to display the statistics associated with the distribution.

In the "mean and standard deviation view," (above) these lines indicate the mean (average) value and the standard deviations (shown as the "sigma" symbol "σ") on either side of the mean. Assuming that the population is normally distributed (i.e. a bell shaped curve), the standard deviations can be interpreted as follows:

  • 68.2% of the values fall between ±1σ
  • 95.4% of the values fall between ±2σ
  • 99.6%  of the values fall between ±3σ
  • 0.4% of the values are outside ±3σ

 So, given this distribution, you can consider that

  • There is a 68.2% probability that the actual mean value is between ±1σ
  • There is a 95.4% probability that the actual mean value is between ±2σ
  • There is a 99.6% probability that the actual mean value is between ±3σ
  • There is a 0.4% probability that the actual mean value is outside ±3σ

These probabilities are important to keep in mind as you examine your results because often times the distribution curves have long tails with maximum and minimum values that are well outside ±3σ. While these are real values in the distribution, it's important to recognize that the probability of portfolio value being at either end of these extremes is approximately less than 0.5%.

If a distribution is not normal (bell-shaped) or is discontinuous, then you need to consider that the probability of any given actual value is approximately proportional to the area of the bar corresponding to range of values that encompass the particular value.

In the "median and 90%, 10% view" (below), the 10% value is where the probabilty of the actual SMART score being less than the 10% value is 10%. The 90% value is where the probabilty of the actual SMART score being greater than the 90% value is 10%. Therefore, there is an 80% probability that the actual SMART score will fall between the 10% and 90% values.

The Brute Force Optimizer, Genetic Optimizer, Branch and Bound Optimizer, and Optsee Optimizer™ form pages all provide additional detail on using the optimizers.