How to tune up the parameters of a multiparametric algorithm

Genetic algorithms are multiparametric procedures. Their operations depend on a variety of parameters these usually are the size of the initial population, the number of generations, probability thresholds that define the crossover and mutation procedures and sometimes heuristics that some developers use. One of the open problems on genetic algorithms is the determination of the optimal values for these parameters. It is also called parameter tuning.
Like genetic algorithms, there are other multiparametric were the determination of the optimal values for their parameters is crucial for their operation. In all the above cases, sensitivity analysis is used for reaching optimality.
As parameter tuning is actually an optimization problem and genetic algorithms are optimization techniques, I thought it would be interesting to build a genetic algorithm for parameter tuning. The result of this work may be found here and it is released as an open source project.
The tuning algorithm examines the program that implements some multiparametric algorithm as a black box. The internal operations of the program are not examined; it only considers the output of the program given some valuation on its parameters. The population of the tuning algorithm consists of set of such valuations. It is an effective approach as I have tested it extensively.
It is a very interesting approach as we do not have to consider the functionality of the program under study, as the tuning algorithm adapts its functionality on the program. And this is the essence of artificial intelligence; the algorithms have to adapt to their subject of study.
When the program under study implements a genetic algorithm then we have a genetic algorithm that tunes up another genetic algorithm, which is a cool idea.
Of course the tuning algorithm is also multiparametric, but in it we do not seek optimality. It is enough to set some high values on its parameters, wait some time until it terminates and compute the optimal values for the program. Then run the program with optimal performance.

 

 https://github.com/rodispantelis/GeneticAlgorithms

A thesis on virtual network embedding with genetic algorithms

Recently I finished my master thesis which is a study on the problem of virtual network embedding (VNE). It concerns the virtualization of network resources and topologies so as to create a fully functional virtual network embedded in a detacenter, instead of using a physical stand alone network. There are many advantages in this approach as it is much easier to update and maintain virtual devices and links instead of physical ones.

There are many ways to map virtual on physical resources, a relatively small virtual topology may be embedded in many ways in the physical network of a datacenter. The problem of VNE concerns the finding of the ideal mapping so that virtualized network will have the optimal performance.

It is a hard problem to solve so traditional analytical methods are inefficient for its solution. Artificial intelligence methods provide in such cases good and efficient solutions. In the thesis I developed a genetic algorithm that approaches the problem as an optimization problem and provides good practical solutions. 

My thesis is written in Greek and is accessible in the repository of the Hellenic Open University.  A direct download of the paper is possible in this link.

A Fibonacci complexity class

While working on a project that will come out soon, I developed an algorithm with strange asymptotic behavior. In one of the functions of the algorithm there was an arithmetic progression that had to be computed. It was not a big deal as it concerned small sets of numbers each time, at least that's what I thought.

So instead of using the formula of arithmetic progression, I just put a recursive function for it. Something like

int d = 1000;
public void progression(a){
    while(d>0){
         progression(a+1);
    }
    d--;

}
progression(0);

Where d was proportional to the input.

It worked fine, but it was slower than it should be. The reason was that the progression was computed quite a lot of times and eventually such a simple function was a huge computation burden. I was really surprised to discover that the asymptotic behavior of the algorithm could be described by the Fibonacci sequence.
So that, given n input the complexity of the algorithm was O(f(n)∙c), where f(n) is the n-th member of the Fibonacci sequence and c is constant.
After replacing the function with the formula of arithmetic progression the complexity became polynomial, thankfully. 

There are two remarks about all these.

An innocent, simple and naive function may become a problem. We have to be careful on how many times this function will be executed.

Although the first edition of the algorithm was not optimal, there comes the question. Could we define a Fibonacci complexity class? Perhaps even find problems in this class.

A function for the Fibonacci sequence

A very fast and easy function to compute Fibonacci sequence

import java.math.BigInteger;

public class main {
    int cnt=0; 
    public static void main(String[] args) {
        main m=new main();
        m.f();
    }
   
    public void f(){
        BigInteger a = new BigInteger("0");
        BigInteger b = new BigInteger("1");
        System.out.println("F("+cnt+"): "+0);
        cnt++;
        System.out.println("F("+cnt+"): "+1);
        cnt++;
        while(cnt<22001){
            BigInteger i = new BigInteger("0");
            i=i.add(a);
            i=i.add(b);
            a=b;
            b=i;
            cnt++;
        }
        System.out.println("F("+(cnt-1)+"): "+b);
    }
}

The output, the 22000th member of the sequence

F(22000):

23911151843088049549559913282124240747696450497332393096044892530723732731293925768111253903890731043326256888603201506944633327289997819833277130504901675470982030552507094162859800238507116975505854341394434948447565033026221210674687237739231690676803475798182981709459374260692436901977628581806475354563630219526845715243350120708966860434133018586240550140499321343707423004223534607204678776111145268537233116243802761082543246510402792429498707827152647989073216179648475243965598252066378230654130470829925986857896675242722600485435164105264916456225839778968745829788512608356363913804761755901467120731200188413083136579975059928902776220812920982189971242379916708698973621766751597334216368620508938142664716772647688988834270374687235249785796824594603884916806990714534340114784869357840251209972361365742785864148242067483656445079559019489390577428621648443326010160477386933121033620560251402766516093547505148407529090149475348773752540043271767234242084292100628738483524181221019416392799181393231992347653438406600914228647401007351836588160487756479497407968315031381589638689295174823322470087642165598672121365266344137564858444622711576081771078496641844937390545682240273855295137238355228099317669135050155578932164209299731907594076460356882408869295135953607469229651099120705693263857034687843626991261121860614751345764505435552449681904020194972948652249854216623551013979700998791070339585263264828474927294673678682855378403136525049646034651097985005523792023353505230733318315806249870620106255127740873138847984020791508370779261660785053242257951531507791170889410085082494377608208359506865872052269194573000651768246582561397589379054459666059728582161757153393761840155076715427874951737024712380325595601597280455609229448744861922777558470731225112774660744411373183007786591379470772659610931545615527361828527091916649882203801119543947473205919119948687005839582793430636346335172367632567614224230754519059566437786383250603562336173795450845023555052163775749567488680209929301733953771659440841851896501176310938478061013508743746794886211545059385083016686715569969754105054345618188437480456355103779247725818147048349484128145728116464124348995944145983490657741814168978702539394407772782423978914262812859165776960650497186523875998775018517623119052276070479290941716138770758463104282213404679330007239145717905126309090972993970782474750784981648644639346866248972640808995649185451943534239803644658697695716458521133485188727182407257352988202971646888599939358651008064484936913916373530359894095131542041397727523148718163746575229775017491009940588025249473123594753441211634435730001790835648327090911035577452758024952482629199328590011397832889757271508213625527057331090954110825073969299898958013994599894944208687850453500173980744223000760078898697128052192071515006870831715957325971845783409157683811011917636814704595836802955582938763983561376453999740428687093957605525631048148288024553370500665522100169024309239057322581866840037497559911574765827496593193700042249031389395129435568195231113075207830333318500469629193676005498811061550348234102052774122312886541766341471582469457347117636205703661078984515116258554803095676657019285090837775746036193164235341465548098904615127611062939206161346093617265405906367027661546845621356149559040798776562241563525511725505792648393371898115939776591096309370497408492873254883402409802564872039524422858633347863626333558155009162515951780107533626468012894434520530192845273457409548744656177387603307356149287599938730196582636274410931646393247886112418444661056857161146184933011078210524893794117348746892516723498126540948178477524603638775070638523850390891025039264400618873393052111880108096369408947789274041790558597294722651729924404836342862376149286822275330813331363925609055924677777163416615796764181780714265864396474084320765015608284585854217131086151555790325994153510435163207497453674171928909161205383175664268065518581620152617418382937870516278875447542815346729709387258529667056688675843466545834345387745629279011899890664127165078236901460104874038389111495950291594316779654469302636244158996341777359509518944948859542336178551804878882015290324970263731030303062802591853791022670735831866555863543199284768114955047509691099289344617944901044767695479022055197983956300649586454906832181127379710025435852700124842320460296470665284849646627146368239854763930002211169617338509922746447728861929093704279396632724922533039876469981523255796252507976652376398665656696184253857275835860915242223337528463584609575885682566329602411550875

Killing time while in quarantine

There are many posts in blogs and social networks these days about what some people do or what suggest to others to do while they are isolated in quarantine. Well, this is my suggestion.
Find a difficult and interesting open problem and try to solve it. Some problem that you may understand its definition but you and the rest of the world have no idea about its resolution. In computer science and logic good candidates are the famous NP vs P problem or the Continuum Hypothesis; of course there are numerous others.
Reading about the problem and working on any idea that you may have about it will not only be an interesting task but will probably make you learn something interesting and it will surely help you in killing time. Who knows, eventually you might actually solve the problem and gain fame and fortune.
In case you follow this advice here is another one on how you should approach it. If you want to solve an open long standing problem you have to think innovative and differently than everybody else. If thinking like everybody else and following the mainstream would be enough to solve the problem then it wouldn’t have been open as someone would have already solved it.