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## March 11, 2007

### Genetic Algorithms for Power Supply Optimization

"This...was the most exciting thing I learned at APEC '07."** Power Electronics Analysis and Design Using Evolutionary Algorithms** was presented by Professor S. D. Sudhoff of the School of Electrical and Computer Engineering, Purdue University. This excellent introduction to genetic and evolutionary algorithms for optimizing the design power electronics circuits, or any other circuits, was the most exciting thing I learned at APEC '07.

**The seminar was a shortened version** of a ten-lecture, on-line, short course, "*Engineering Analysis and Design Using Genetic Algorithms*", spanning four weeks taught by Dr. Sudhoff. You can find out more about this and other Purdue on-line short courses at https://engineering.purdue.edu/CEE/professional_development_programs/

**Topics in the seminar,** which covered six of the ten lectures in the short course, were:

- Biological Genetics and Evolution
- Canonical Genetic Algorithms
- Real Coded Genetic Algorithms
- Genetic Optimization System Engineering Tool (GOSET)
- Single Objective GA Exercises
- A Design Example: An Electromagnet

**You have to know something about the biological background of DNA**, chromosomes, genes, linkage, mutation, parent-child inheritance, selection, etc. to understand the genetic algorithms used in this approach to optimization. Dr. Sudhoff smoothly led the audience through these concepts.

**Here is my understanding of the process as it would be applied to optimizing a switching-mode power supply design, say a forward converter.** First you start with a population of forward converter designs encoding each as a chromosome with the parameters of interest coded as genes in the chromosome. You then apply a fitness function to this population, say maximum efficiency or minimum weight. With this mating pool, you cross over the genes to get children, introduce some mutation, and then evaluate the children according to the fitness function. You let the population breed over time, selecting the new parents according to some fitness or selection guide, and sooner rather than later you get very close to an optimum design (highest efficiency, lowest weight, lowest cost, etc.)

**The actual design example used in the seminar was the design of an electromagnet to lift a mass.** The example was interesting in that it was a design problem assigned over the years by Dr. Sudhoff to those taking his power electronic course. He had come to what he thought was an optimum design using some rules of thumb. Some graduate students knew he was teaching genetic algorithms for optimization and asked if they could use them for this design problem. They did and came out with a better design than the professor's design. What they did was to remove the rules of thumb and let the algorithm find the best design on its own. It did, and exposed that a rule of thumb that seemed to make sense actually prevented getting a better design. Moral, let the algorithm do the work.

**In response to a question, Dr. Sudhoff stated that in his experience, if you have 20 or so parameters to vary, genetic algorithms do well**, but they start to shine when you get 39 to 50 parameters. The largest to date Dr. Sudhoff has run is 249 parameters. Dr. Sudhoff was co-author of two papers of the four papers presented at APEC '07 using genetic algorithms, "*EI Core Inductor Designs using Population-Based Design Algorithms*" and "*Evolutionary Optimization of Power Electronics Based Power Systems*".

**Why is this the most exciting thing I learned at APEC '07?**

**In the mid 1970's and into the 1980's** it looked like mathematical optimization was going to have the next major impact on reducing power supply weight and increasing efficiency. It barely happened because only highly trained PhDs could do it. It's true that mostly the PhDs and candidates are doing genetic algorithms now, but the software and methods and training are here now so that the journeyman power supply design should be able to learn and use them in a cost-effective way.

**I remember back when Gene Wester and David Middlebrook** planted the seeds for circuit averaging, Slobodan Cuk took it a step further in state-space-averaging and it has never stopped being refined. Averaging techniques are now an essential part of any power supply designers tool kit. Dr. Sudhoff and his co-workers may be planting a similar seed. If it takes root and bears fruit, you may want to be the first power supply designer on your block to know and use genetic algorithms in your designs. The early adoption of the next upcoming skill set is often good for your career.

**"Problem, Relevance, Solvability, Solution" is the theme of the SMPS Technology website.** You have now been made aware of genetic algorithms and that they can be applied to power supply design. You now have to learn enough about them to see if the are relevant to your designs. I think you are going to find the answer is yes. Dr. Sudhoff and his co-workers in the field have shown the solvability of this type of optimization for power electronics design. Now you only need to learn how to do it. Apparently an on-line short-course costing less the $500 will get you there.

**Is it really this simple?** Of course not. The Cale/Sudhoff inductor paper states some of the difficulties:

"However, there are significant difficulties that must be overcome in applying population-based algorithms to inductor designs. First, the design selection is limited by how well the material characteristics of the candidate magnetic materials are known. Second, the usefulness of the design algorithm is limited by the accuracy and computational efficiency of the underlying inductor model. This is especially true in the case of population-based methods which require a large number of analyses to be conducted (often on the order of 10E6). Third, the fitness function of candidate inductor designs must be well formulated to ensure that the candidate inductor designs are feasible and represent the desired end product."

**But it also states the strengths of the method:**

"Research has demonstrated the successful solution of optimization problems using population-based methods, e.g., genetic algorithms, swarm optimization, and Monte Carlo techniques. These algorithms offer advantages over traditional optimization routines including the avoidance of the requirement to evaluate objective function derivatives, the ability to effectively optimize over a large search space, and in their success in avoiding convergence to local extrema."

**The paper proves the utility by producing practical inductor designs** optimized to single and multiple parameters including cost of material considerations.

**Having taken a frustrating crack at an optimization technique** called "Sequential Unconstrained Minimization Technique", SUMT, a few decades ago, I would much prefer spending my time now exploring the genetic algorithm or other population-based approaches.

**Back in 1983 I taught a course, Introduction to Modelling and Analysis of Switching-Mode Power Supplies.** In looking through my notes, I see I had a two-hour segment on Optimization that with updating could make a topic in my Problem/Solution format. It is now on my to-do list.

Posted by smpstech at March 11, 2007 12:36 PM