Simulated Annealing is an Algorithm that search for maximum/minimum value of a function.
This repository is my course work project.
The main problem of the project is to search the minimum value of the problem.
NB: The bigger the circle, the smaller the value
It is located inside visualization folder on the repository
func (a *Annealing) CostFunction(firstValue, secondValue float64) float64 {
var result float64
fVSquare := firstValue * firstValue
sVSquare := secondValue * secondValue
fVSin := math.Sin(firstValue)
sVCos := math.Cos(secondValue)
subtrahend := math.Sqrt(fVSquare+sVSquare) / math.Pi
insideExponential := math.Abs(1 - subtrahend)
exponent := math.Exp(insideExponential)
result = -1 * math.Abs(fVSin*sVCos*exponent)
return result
}Please open the detailed file main.go
The comment is already tell how the program work.
- Temperature: 100
Temperature is being set become 100 for more accuration purpose. The changes of temperature will effect the number of iterations
- Alpha: 0.8 - 0.95
Alpha is being set become 0.8 to 0.95 to maximize the accuration also. the changes of alpha will effect the number of iterations.
- Minimum Iterations: 1000
Minimum iterations is the number of iterations must be done before doing Temperature cooling.
It being set to be 1000 to increase the accuration of the model
- Goal: -19.208501
The Goal is actually obtained by running Simulated Annealing with Unlimited Temperatrue. The best Solution that I've reached is -19.208501
Temperature: 100.00
Alpha: 0.95
Minimum Value: -10.00
Maximum Value: 10.00
Goal: -19.208501
Minimum Temperature: 0.0001
Loop: 10
fV:= -8.025963 sV:= 9.697703 E:= -19.189334, Accuration:= 99.900214%
fV:= -7.990458 sV:= 9.825867 E:= -18.902097, Accuration:= 98.404851%
fV:= -8.010391 sV:= -9.619297 E:= -19.168004, Accuration:= 99.789171%
fV:= -8.014729 sV:= -9.612083 E:= -19.164561, Accuration:= 99.771247%
fV:= 8.025812 sV:= 9.530713 E:= -19.022823, Accuration:= 99.033353%
fV:= -7.889956 sV:= -9.697192 E:= -18.937114, Accuration:= 98.587153%
fV:= -7.987430 sV:= -9.484198 E:= -18.844195, Accuration:= 98.103413%
fV:= 8.086753 sV:= 9.655051 E:= -19.197690, Accuration:= 99.943718%
fV:= -8.119189 sV:= -9.708009 E:= -19.147802, Accuration:= 99.683999%
fV:= -8.034423 sV:= -9.605722 E:= -19.169468, Accuration:= 99.796792%
fV = First Value, sV = Second Value, E = Energy Cost
How the problem(CostFunction) solved by Simmulated Annealing is by picking a random function inside the range. The number of picking itself is based on the Temperature cooling and minimal iterations. Every solution that are being generated randomly are not directly thrown away. To maximize the accuration, every solution will be randomly picked or not picked by a certain probabilty that being calculated using AcceptanceProbability Function.
The Data visualization shows that the mainimum value of the problem are located at the very end of every quadrant inside of the cartesian axis. It basically tells that the minimum value can be reached on the maximum or minumum value on both x1 and x2.
- Go <= 1.10.3
- Already set $GOPATH and $GOROOT
$ go get github.com/pamungkaski/go-simulated-annealing
$ cd $GOPATH/src/github.com/pamungkaski/go-simulated-annealing
$ dep ensure
It is located inside .env
TEMPERATURE: Temperature that used as the params.
ALPHA: Cooling rate of the Temperature
MIN_ITERATION: Minimum iteration before start cooling
MIN_VALUE: Minimum Value of the solution point
MAX_VALUE: Maximum Value of the solution point
GOAL: Benchmark of the solution
MIN_TEMPERATURE: The value that end the algorithm
LOOP: The number of how many times the Algorithm will run
Modify the params by editing the .env file
$ cd $GOPATH/src/github.com/pamungkaski/go-simulated-annealing
$ go run app/main.go
DO NOT USE THIS PROJECT AS YOUR SUBMISSION FOR AI COURSE WORK ASSIGNMENT