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LibOptimization

LibOptimization is a numerical optimization library that simplifies optimization using C#, VisualBasic.Net and other .NET Framework languages. This library is used by people who need optimization such as science (eg physics), engineering, sound, finance, statistics, medical care, structural design etc.

LibOptimizationは制約条件の無い数値最適化を行う.NET Frameworkのライブラリです。科学 (物理学など)、エンジニアリング、音響、金融、統計、医療、構造設計などの最適化を必要とする人に使用されているようです。

実装しているアルゴリズムは最急降下法、ニュートン法、HookeJeevesのパターンサーチ法、Nelder-Mead法（オリジナルの実装、Wikipediaの実装）、適応パラメータ Nelder-Mead法、実数値遺伝的アルゴリズム（BLX-α、UNDX、SPX（シンプレクス）、REX、世代交代はJGG、PCX（世代交代はG3））、進化戦略（Evolution Strategy、1+1 ES）、粒子群最適化（Basic PSO, LDIW-PSO, CDIW-PSO, CRIW-PSO, AIW-PSO）、Differential Evolution(差分進化？ DE/rand/1/bin, DE/rand/2/bin, DE/best/1/bin, DE/best/2/bin)、JADE（自己適応型DE）ホタルアルゴリズム、Cuckoo Search（Matlabコードの移植版）、焼きなまし法、山登り法です。

Tutrial

LibOptimization tutorial🚀

Contact

I may miss your Issues. When a reply is slow, please give me e-mail.

tomi.nori+github atmark gmail.com

Cite

If you use LibOptimization in your publication, please cite the following

@misc{LibOptimization,
  author = "N.Tomita",
  title = "LibOptimization",
  howpublished = "\url{https://github.com/tomitomi3/LibOptimization}",
}

Recent change

Changed absOptimiazation.NumberOfVariable from propety to function in ver1.9.0. Refactoring LibOptimization code with development branch. In the future, I will add new function to the new branch.

Introduction

LibOptimization has several optimization algorithms implemented. You design the objective function, you can use all the optimized algorithms implemented.

Implement Optimization algorithm

Require derivative algorithm

  • Steepest Descent Method
  • Newton Method

Derivative free algorithm (Direct search method)

  • Nelder Mead Method / Simplex Method (Original paper ver)
  • Nelder Mead Method (Wikipedia ver. add inside contraction)
  • Adaptive Nelder-Mead Simplex method
  • Hooke and Jeeves of Pattern Search (Direct Search)

Derivative free algorithm (Nature inspired algorithm)

  • Real-coded Genetic Algorithm
    • BLX-alpha and JGG(Just Generation Gap)
    • UNDX(Unimodal Normal Distribution Crossover) and JGG
    • SPX(Simplex Crossover) and JGG
    • REX(Real-coded Ensemble Crossover) and JGG
    • PCX(Parent Centric Recombination) and G3(Generalize Generation Gap)
  • Particle Swarm Optimization(PSO)
    • Basic PSO(GlobalBest, LocalBest)
    • PSO using Linear Decrease Inertia Weight
    • PSO using Chaotic inertia weight(CDIW-PSO, CRIW-PSO)
    • PSO using Adaptive inertia weight
    • Parallel Competitive Particle Swarm Optimization
  • Differential Evolution
    • DE/rand/1/bin
    • DE/rand/2/bin
    • DE/best/1/bin
    • DE/best/2/bin
    • JADE(self adaptation DE)
  • Evolution Strategy
    • (1+1)-ES )
  • Standrad Cuckoo Search
  • FireFly algorithm

Derivative free algorithm (Randomized algorithm)

  • Simulated Annealing
  • Hill Climbing

How to get

URL:https://www.nuget.org/packages/LibOptimization/

PM> Install-Package LibOptimization

How to use

Typical Use

  1. You inherit "absObjectiveFunction" class and design objective function.
  2. Choose an optimization method and implement code.
  3. Do optimization.
  4. Get result and evaluate.

See this link for details

Sample code

Typical use code

for VB.NET

'Instantiation optimization class and set objective function.
Dim optimization As New clsOptSteepestDescent(New clsBenchSphere(1))
'Initialize starting value
optimization.Init()
'Do calc
optimization.DoIteration()
'Get result. Check recent error.
If optimization.IsRecentError() = True Then
    Return
Else
    clsUtil.DebugValue(optimization)
End If

for C#

//Instantiation objective Function
var func = new RosenBlock();
//Instantiation optimization class and set objective function.
var opt = new clsOptNelderMead(func);
opt.Init();
//Do calc
opt.DoIteration();
//Check Error
if (opt.IsRecentError() == true)
{
    return;
}
else
{
    //Get Result
    clsUtil.DebugValue(opt);
}

Set boundary value for each variable.

  • Problem setting

objective function : clsBenchTest2(x1,x2) = x1^4 - 20x1^2 + 20x1 + x2^4 - 20x2^2 + 20x2

  • boundary variables

x1 -> 0.0 to 5.0

x2 -> 1.0 to 4.0

for VB.NET

'Set boundary variable
opt.LowerBounds = New Double() {0, 1.0}
opt.UpperBounds = New Double() {5, 4.0}
'Init
opt.Init()

for C#

//Set boundary variable
opt.LowerBounds = new double[] {0, 1.0};
opt.UpperBounds = new double[] {5, 4.0};
//Init
opt.Init();

Using my criterion

When using a typical code, internal criteria are enabled. For details, see EPS property, clsUtil.IsCriterion.

for C#

var opt = new LibOptimization.Optimization.clsOptDEJADE(new RosenBrock(10));
//Disable Internal criterion
opt.IsUseCriterion = false;

//Init
opt.Init();
clsUtil.DebugValue(opt);

//do optimization!
while (opt.DoIteration(100) == false)
{
    var eval = opt.Result.Eval;

    //my criterion
    if (eval < 0.01)
    {
        break;
    }
    else
    {
        clsUtil.DebugValue(opt, ai_isOutValue: false);
    }
}
clsUtil.DebugValue(opt);

set initial position

Generate initial positions around x1=10 and x2=10.

for VB.NET

optimization.InitialPosition = {10, 10}
optimization.Init()
optimization.DoIteration()
clsUtil.DebugValue(optimization)

for C#

opt.InitialPosition = new double[] { 10, 10 };
optimization.Init()
optimization.DoIteration()
clsUtil.DebugValue(optimization)

Set inital position and inital value range

Generate the initial position in the range of 7 to 10.

for VB.NET

Dim optimization As New Optimization.clsOptDE(New clsBenchSphere(2))
'set initialposition
optimization.InitialPosition = New Double() {10, 10}
'Initial value is generated in the range of -3 to 3.
optimization.InitialValueRangeLower = -3
optimization.InitialValueRangeLower = 3
'init and do optimization
optimization.Init()
optimization.DoIteration()
clsUtil.DebugValue(optimization)

for C#

var func = new RosenBrock(2);
var opt = new LibOptimization.Optimization.clsOptPSO(func);
opt.InitialPosition = new double[] { -10, -10 };
opt.InitialValueRangeLower = -3;
opt.InitialValueRangeUpper  = 3;
opt.Init();
opt.DoIteration();

Evaluate optimization result per N iteration

for VB.NET

Dim optimization As New clsOptSteepestDescent(New clsBenchSphere(2))
optimization.Init()
//per 5 iteration
While (optimization.DoIteration(5) = False)
    clsUtil.DebugValue(optimization)
End While
clsUtil.DebugValue(optimization, ai_isOnlyIterationCount:=True)
End With

for C#

//per 100 iteration
while (opt.DoIteration(100)==false)
{
    clsUtil.DebugValue(opt, ai_isOutValue: false);
}
clsUtil.DebugValue(opt);

fix Random Number Generator(RNG)

for VB.NET

//fix RND for random sequence
Util.clsRandomXorshiftSingleton.GetInstance.SetDefaultSeed()

Dim optimization As New Optimization.clsOptDE(New clsBenchSphere(2))
//fix RND for generate position
optimization.Random = New Util.clsRandomXorshift()

'init
optimization.Init()

for C#

//fix RND for random sequence
LibOptimization.Util.clsRandomXorshiftSingleton.GetInstance().SetDefaultSeed();

var func = new RosenBrock(2);
var opt = new LibOptimization.Optimization.clsOptPSO(func);
//fix RND for generate position
opt.Random = new LibOptimization.Util.clsRandomXorshift();

//init
opt.Init();

Retry optmization(Elite strategy).

for VB.NET

Dim optimization As New Optimization.clsOptRealGAREX(New clsBenchDeJongFunction3())

'1st try
optimization.Init()
While (optimization.DoIteration(100) = False)
    clsUtil.DebugValue(optimization, ai_isOutValue:=False)
End While
clsUtil.DebugValue(optimization)

'2nd try reuse
optimization.InitialPosition = optimization.Result().ToArray()
optimization.Init()
While (optimization.DoIteration(100) = False)
    clsUtil.DebugValue(optimization, ai_isOutValue:=False)
End While
clsUtil.DebugValue(optimization)

You can use other optimization method(inherit absObjctiveFcuntion).

Dim optimization As New clsOptRealGASPX(New clsBenchRastriginFunction(20))
optimization.Init()
clsUtil.DebugValue(optimization)
While True
    If optimization.DoIteration(10) = True Then
        Exit While
    End If
    clsUtil.DebugValue(optimization, ai_isOutValue:=False)
End While
If optimization.IsRecentError() = True Then
    Return
End If
clsUtil.DebugValue(optimization)

Multi point and MultiThread. Multipoint avoids Local minimum by preparing many values.

'prepare many optimization class.
Dim multipointNumber As Integer = 30
Dim listOptimization As New List(Of absOptimization)
For i As Integer = 0 To multipointNumber - 1
    Dim tempOpt As New clsOptNelderMead(New clsBenchAckley(20))
    tempOpt.Init()
    listOptimization.Add(tempOpt)
Next

'using Parallel.ForEach
Dim lockObj As New Object()
Dim best As LibOptimization.absOptimization = Nothing
Threading.Tasks.Parallel.ForEach(listOptimization, Sub(opt As absOptimization)
                                                       opt.DoIteration()
                                                       'Swap best result
                                                       SyncLock lockObj
                                                           If best Is Nothing Then
                                                               best = opt
                                                           ElseIf best.Result.Eval > opt.Result.Eval Then
                                                               best = opt
                                                           End If
                                                       End SyncLock
                                                   End Sub)

'Check Error
If best.IsRecentError() = True Then
    Return
Else
    clsUtil.DebugValue(best)
End If

Least squares method (最小二乗法)

You design the evaluation function to minimize residual sum of squares. The following example estimate a parameter of the multinomial expression.

Public Overrides Function F(x As List(Of Double)) As Double
    Dim sumDiffSquare As Double = 0

    For Each temp In Me.datas
        'e.g a * x^4 + b * x^3 + c * x^2 + d * x^4 + e
        Dim predict = x(0) * temp(0) ^ 4 + x(1) * temp(0) ^ 3 + x(2) * temp(0) ^ 2 + x(3) * temp(0) + x(4)
        Dim diffSquare = (temp(1) - predict) ^ 2
        sumDiffSquare += diffSquare
    Next

    Return sumDiffSquare
End Function

License

MIT License

This Library's license was MS-PL until this commit.

Support .NET Framework

  • .NET 5
  • .NET Core 3.1
  • .NET Core 3.0
  • .NET Core 2.1
  • .NET Framework 4.8
  • .NET Framework 3.5

Refference

  1. 金谷 健一, "これなら分かる最適化数学―基礎原理から計算手法まで", 共立出版株式会社, 2007年初版第7刷
  2. Hooke, R. and Jeeves, T.A., ""Direct search" solution of numerical and statistical problems", Journal of the Association for Computing Machinery (ACM) 8 (2), pp212–229.
  3. J.A.Nelder and R.Mead, "A simplex method for function minimization" ,The Computer Journal vol.7, 308–313 (1965)
  4. W.H.Press， B.P.Flannery，S.A.Teukolsky，W.T.Vetterlin, "NUMERICAL RECIPES in C 日本語版 C言語による数値計算のレシピ", 株式会社技術評論社, 平成19年 初版 第14刷,
  5. 北野宏明編著, "『遺伝的アルゴリズム』", 産業図書株式会社, 平成5年初版
  6. 北野宏明 (編集), "遺伝的アルゴリズム 4", 産業図書出版株式会社, 2000年初版
  7. 小野功，佐藤浩，小林重信, "単峰性正規分布交叉UNDXを用いた実数値GAによる関数最適化"，人工知能学会誌，Vol. 14，No. 6，pp. 1146-1155 (1999)
  8. 樋口 隆英, 筒井 茂義, 山村 雅幸, "実数値GAにおけるシンプレクス交叉", 人工知能学会論文誌Vol. 16 (2001) No. 1 pp.147-155
  9. 小林重信, "実数値GAのフロンティア"，人工知能学会誌 Vol. 24, No. 1, pp.147-162 (2009)
  10. James Kennedy and Russell Eberhart, "Particle Swarm Optimization．", Proceedings of IEEE the International Conference on Neural Networks，1995
  11. Shi, Y. and Eberhart, R.C., "A Modified Particle Swarm Optimizer", Proceedings of Congress on Evolu-tionary Computation, 79-73., 1998
  12. R. C. Eberhart and Y. Shi, "Comparing inertia weights and constriction factors in particle swarm optimization", In Proceedings of the Congress on Evolutionary Computation, vol. 1, pp. 84–88, IEEE, La Jolla, Calif, USA, July 2000.
  13. Y. Shi and Russell C. Eberhart, "Empirical Study of Particle Swarm Optimization, Proceeding Congress on Evolutionary Computation 1999, Piscataway, 1945-1949
  14. Y. Feng, G. Teng, A. Wang, Y.M. Yao, "Chaotic inertia weight in particle swarm optimization", in: Second International Conference on Innovative Computing, Information and Control (ICICIC 07), 2007, pp. 475–1475.
  15. A. Nickabadi, M. M. Ebadzadeh, and R. Safabakhsh, “A novel particle swarm optimization algorithm with adaptive inertia weight,” Applied Soft Computing Journal, vol. 11, no. 4, pp. 3658–3670, 2011.
  16. Nelder-Mead法(http://ja.wikipedia.org/wiki/Nelder-Mead%E6%B3%95)
  17. Storn, R., Price, K., "Differential Evolution – A Simple and Efficient Heuristic for Global Optimization over Continuous Spaces", Journal of Global Optimization 11: 341–359.
  18. Sk. Minhazul Islam, Swagatam Das, "An Adaptive Differential Evolution Algorithm With Novel Mutation and Crossover Strategies for Global Numerical Optimization", IEEE TRANSACTIONS ON SYSTEMS, MAN, AND CYBERNETICS—PART B: CYBERNETICS, VOL. 42, NO. 2, APRIL 2012, pp482-500.
  19. Price, K. and Storn, R., "Minimizing the Real Functions of the ICEC’96 contest by Differential Evolution", IEEE International Conference on Evolutionary Computation (ICEC’96), may 1996, pp. 842–844.
  20. Xin-She Yang, Suash Deb, "Cuckoo search via Lévy flights.", World Congress on Nature and Biologically Inspired Computing (NaBIC 2009). IEEE Publications. pp. 210–214. arXiv:1003.1594v1.
  21. Cuckoo Search (CS) Algorithm (http://www.mathworks.com/matlabcentral/fileexchange/29809-cuckoo-search--cs--algorithm)
  22. 焼きなまし法(http://ja.wikipedia.org/wiki/%E7%84%BC%E3%81%8D%E3%81%AA%E3%81%BE%E3%81%97%E6%B3%95)
  23. X. S. Yang, “Firefly algorithms for multimodal optimization,” in Proceedings of the 5th International Conference on Stochastic Algorithms: Foundation and Applications (SAGA '09), vol. 5792 of Lecture notes in Computer Science, pp. 169–178, 2009.
  24. Firefly Algorithm (http://www.mathworks.com/matlabcentral/fileexchange/29693-firefly-algorithm)
  25. Kalyanmoy Deb, Dhiraj Joshi and Ashish Anand, "Real-Coded Evolutionary Algorithms with Parent-Centric Recombination", KanGAL Report No. 2001003
  26. 進化戦略(https://ja.wikipedia.org/wiki/%E9%80%B2%E5%8C%96%E6%88%A6%E7%95%A5)
  27. Hillclimbing(https://en.wikipedia.org/wiki/Hill_climbing)
  28. Luu, Keurfon, et al. "A parallel competitive Particle Swarm Optimization for non-linear first arrival traveltime tomography and uncertainty quantification." Computers and Geosciences 113 (2018): 81-93.
  29. R. C. Eberhart and Y. Shi, "Comparing inertia weights and constriction factors in particle swarm optimization", In Proceedings of the Congress on Evolutionary Computation, vol. 1, pp. 84–88, IEEE, La Jolla, Calif, USA, July 2000.
  30. Gao, Fuchang, and Lixing Han. "Implementing the Nelder-Mead simplex algorithm with adaptive parameters." Computational Optimization and Applications 51.1 (2012): 259-277.