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# Evolutionary algorithm Optimization with Differential Evolution

## Overview

One of the optimization problems is that when input variables are discrete, it is more difficult to find the optimum solution compared to continuous values. Equipped with various optimization algorithms, Optimus, an optimized design support tool, helps you efficiently search for the optimum solution even when input variables are discrete. Here are two cases where optimization problems related to discrete values are dealt with using Differential Evolution, an evolutionary algorithm that has recently been drawing attention.

## Optimization Case 1

### Overview

To position a magnetic head on a fast-running hard disk drive, it is necessary to suppress oscillation of the head tip. In this optimization case, the node of oscillation is utilized to control the mode shape so that the magnetic head tip hardly moves from the original position.

### Optimization problem

• Objective:Minimization of head tip displacement (Participation function: dimensionless quantity)
• Constraint:Natural frequency > 12,000 Hz
• Input variables:Material type (*),plate thickness (*), geometries of the holes in the circled part x 6 (*: Discrete variables)

### Optimization result

• Basic model:Participation function 2279
• Optimum:Participation function 232
• Iteration:Approx. 300 times

Optimization reduces head tip displacement by 90% compared to the basic model.

## Optimization Case 2

### Overview

Switching power supplies are widely used as power for electronic devices, but noise suppression is becoming essential given faster speeds. In this case, the most appropriate combination of switching element, noise filter and snubber circuit is defined as a measure to reduce noise.

### Optimization problem

• Objective:Minimization of noise terminal voltage (dBuV) (Evaluation target is 100kHz or higher.)
• Input variables:Switching element (23 types), noise filter (6 types), snubber circuit (3 types) (All string variables)

### Optimization result

• Worst case:Noise terminal voltage 105 dBuV
• Optimum:Noise terminal voltage 72 dBuV
• Iteration:82 times

Noise is reduced by 30% compared to the worst case in the optimization process.

## Summary of Differential Evolution

Differential Evolution is one of the evolutionary algorithms proposed by R. Storn and K. Price in 1995. As an optimization method to obtain the global optimum, it is receiving significant attention along with Particle Swarm Optimization and Ant Colony Optimization.

### Algorithm outline

The optimum solution can be obtained even when input values contain discrete values.