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2.SP 31.13330-2012. Water supply. External networks and facilities. Updated version of SNiP 2.04.02-84. - Enter. 2013-01-01. - Moscow: Publishing Standards, 2012. - 123 p.

3.SP 32.13330.2012. Sewerage. External networks and facilities. The updated version of SNiP 2.04.03-85. - Enter. 2013-01-01. - Moscow: Publishing Standards, 2012. - 85 p.

4.Methodical instructions MU “Sanitary Epidemiological Surveillance of Disinfection of Wastewater with UV-Irradiation”.

M.A. Bannova, E.A. Aleshugina

Nizhny Novgorod State University of Architecture and Civil Engineering

NONLINEAR OPTIMIZATION. RANDOM

MULTIDIMENSIONALSEARCH METHODS

Nonlinear optimization methods are used to find the minimum of the function f (x), when x R N in the absence of constraints on x, while f (x) is a scalar objective function that is continuously differentiable. Random search emerged as a scientific trend more than twenty years ago. Now it is famous and effective means of solving complex optimization problems.

This article describes 2 varieties of the random multidimensional search method: algorithm of search with a limit on the number of unsuccessful attempts and algorithm of random search by the best sample method.

The aim of the work is to describe these methods and write programs that implement them. The relevance of this work is that the written programs will simplify the application of these methods in the future.

The following function is used as an example:

f (x1 ; x2 ) 64x12 126x1 x2 64x2 2 10x1 30x2 13

Description of the nonlinear random search method:

The algorithm of the nonlinear random search method is based on the choice random directions of moving in the space. First of all it is needed to choose a starting point, a search step and a random direction. After that the next point is found in this direction by special way and the value of the objective function is calculated in it.

X(x1; x2) – starting point; search step - h; Direction= {napr1; napr2} – given by random; New point: Y=(x1+h*napr1; x2+h*napr2); Calculation of the function value: f1=f(X), f2=f(Y);

If f(y)<f(x) direction is promising. The movement in this direction continues.If f(y)>f(x)- direction is NOT promising. The counter of unsuccessful

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attempts j is increased by 1. If j>N, search can be continued with a smaller step (h=h/d and j=1). Stop: if h<e;

One of advantages of this method is ease of use. Also the nonlinear random search method can be used for any function, even if it is not unimodal.

Step by step algorithms of 2 varieties of the random multidimensional search method:

1) Algorithm of search with a limit on the number of unsuccessful attempts:

0 STEP. Set accuracy parameter > 0, starting step h > 0, d >1 - coefficient of step decreasing, N – limit of unsuccessful attempts, X – starting point. Calculate f(X);

1 STEP. Suppose a counter of unsuccessful attempts j =1;

2 STEP. Get an implementation of a unit vector napr having a uniform

distribution;

 

 

 

3 STEP. Find a trial point y

x h*napr , Calculate f (y) ;

4 STEP. If f (y) <f (x), then x =y, f (x) = f (y), j =1 and go to 3 step;

5 STEP. Suppose j=j+1. If j<=N then go to 2 step;

6 STEP. If h

< then stop search setting x =

x *, else reduce the step of

search (h =h /d

) and go to 1 step.

 

 

2) Algorithm of random search by the best sample method:

0 STEP. Set

0 accuracy parameter, h

0 initial step,

d 1 step reduction factor, N – the maximum number of unsuccessful attempts (most often N=3n), p – number of test points, х – the initial point of

search. Calculate f (x);

 

 

 

 

 

1 STEP. Suppose a counter of unsuccessful attempts r

1;

2 STEP. Get p implementations of the unit vector napr , having the

uniform distribution napr1, napr2,...,naprp, p

n;

 

3 STEP. Find

test

points

yi x h * napr i , i=1,..,p. Calculate

f ( y) min f ( yi ) ;

 

 

 

 

 

i

 

 

 

 

 

4 STEP. If f (y)

f (x) , then suppose x

y, f (x)

f (y) , suppose r

1 and go to step 3;

 

 

 

 

 

5 STEP. Suppose r

r

1, if r

N , then go to step 2;

6 STEP. If h

, complete the search, supposing x

x *, otherwise

reduce the search step (h

h

/d ) and go to step 1.

 

Two programs on C++ language were written that implement these

algorithms. Below a comparison of these is.

 

 

Comparison [Table 1]:

 

 

 

 

Exact value: Fmin(9.960299213 ;

-10.039700787)≈-187.39367675781

421

Algorithm

Starting

Preci-

Total

Extremum value

The

 

point x

sion e

amount

 

difference

 

 

 

of itera-

 

from the

 

 

 

tions

 

exact value

1) Algorithm of

 

 

 

 

 

search with a

 

 

 

х*=(9.96296875;

 

limit on the

 

 

 

-0.00017%

 

 

167

-10.0403125)

number of

 

 

 

 

 

 

 

 

Fmin=-187.3933571582

 

unsuccessful

 

 

 

 

1;1

0.02

 

 

 

attempts

 

 

 

 

 

 

 

 

2) Algorithm of

 

 

 

х*=(9.953125;

 

random search by

 

 

 

 

 

 

91

-10.033125)

-0.00009%

the best sample

 

 

 

 

 

Fmin=-187.393505469

 

method

 

 

 

 

 

 

 

 

 

1) Algorithm of

 

 

 

 

 

search with a

 

 

 

х*=(9.96058837890626;

 

limit on the

 

 

 

 

 

 

400

-10.0393237304687)

-0.00009%

number of

 

 

 

 

 

Fmin=-187.393505469

 

unsuccessful

 

 

 

 

1;1

0.0001

 

 

 

attempts

 

 

 

 

 

 

 

 

2) Algorithm of

 

 

 

х*=(9.96062072754;

 

random search by

 

 

 

 

 

 

186

-10.0393362793)

0.00001%

the best sample

 

 

 

 

 

Fmin=-187.393700787

 

method

 

 

 

 

 

 

 

 

 

1) Algorithm of

 

 

 

 

 

search with a

 

 

 

х*=(9.96055664062502;

 

limit on the

 

 

 

0.00001%

 

 

403

-10.039301147609)

number of

 

 

 

 

 

 

 

 

Fmin=-187.39370077608

 

unsuccessful

 

 

 

 

-14; 0.5

0.0001

 

 

 

attempts

 

 

 

 

 

 

 

 

2) Algorithm of

 

 

 

х*=(9.96062988281;

 

random search by

 

 

 

 

 

 

181

-10.0393725586)

0.00001%

the best sample

 

 

 

 

 

Fmin=-187.393700787

 

method

 

 

 

 

 

 

 

 

 

 

 

Table 1. Comparison

 

Both algorithms are based on the choice of random directions of moving in the space.

The main difference is that it is needed to choose one direction for one test point in first algorithm [Fig. 1.], while it is needed to choose some directions for some test points in second algorithm. [Fig. 2.]

422

Fig. 1. Algorithm of

search with a limit on the

Fig. 2. Algorithm of

random search by the best

number of unsuccessful

sample method

attempts

 

In the first algorithm the value of the function in the test point is compared with the previous value of the function [Fig. 3.] while in the second algorithm the minimum value of the function at all test points is found at first and then it is compared with the previous one. [Fig. 4.]

Fig. 4. F(y)=min{F(y1);

F(y2); F(y3)}=F(y3)

F(x)>F(y) x=y

Algorithm of random search by the best sample method

Fig. 3. F(x)>F(y) x=y

Algorithm of search with a limit on the number of unsuccessful attempts

In conclusion it is necessary to say that the number of iterations to achieve a given sequence of the second algorithm is required less than the first. This is due to the fact that in the second algorithm at some moment p points are tested at once, which is also the reason that the extremum values received by the second algorithm are closer to the analytical value than the extremum values received through the first algorithm. But it should be noted that this difference is very small (with precision e = 0.0001, it is only 0.00001% for both the first and the second algorithm). So, both algorithms can be considered effective.

423

Solopaeva Y.M., Aleshuigna E.M.

Nizhny. Novgorod State University of Architecture and Civil Engineering

SOFTWARE DEVELOPMENT LIFECYCLE MODELS

The object of the article is software development lifecycle models. The software development models are the various processes or methodologies that are selected for the development of the project depending on the project’s aims. There are many development life cycle models that have been developed in order to achieve different required objectives. The models specify the various stages of the process and the order in which they are carried out.

Today, the most widely used lifecycle models are the following:

1.WaterfallModel

2.IterativeModel

3.SpiralModel

Waterfall model is the simplest model of software development. It says the all the phases of SDLC will function one after another in linear manner. That is, when the first phase is finished then only the second phase starts and so on.

This model assumes that everything is carried out and takes place perfectly as planned in the previous stage and there is no need to think about the past issues that may arise in the next phase. This model does not work smoothly if there are some issues left at the previous step. The sequential nature of model does not allow us go back and undo or redo our actions [Picture 1].

Pic.1 Waterfall Model

Interactive model leads the software development process in iterations. It projects the process of development in cyclic manner repeating every step after every cycle of SDLC process.

The software is first developed on very small scale and all the steps are followed which are taken into consideration. Then, more features and modules

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are designed, coded, tested and added to the software in every next iteration. Every cycle produces a software, which is complete in itself and has more features and capabilities than that of the previous one.

Because every cycle includes small portion of whole software process, it is easier to manage the development process but it consumes more resources [Picture 2].

Pic.2 Interactive Model

Spiral model is a combination of iterative development process model and sequential linear development model i.e. the waterfall model with a very high emphasis on risk analysis. It allows incremental releases of the product or incremental refinement through each iteration around the spiral. The spiral model has four phases: Planning, Risk Analysis, Engineering and Evaluation. A software project repeatedly passes through these phases in iterations (called Spirals in this model) [Picture 3].

Pic.3 Spiral Model

In conclusion it’s necessary to remark that every model is used for projects of different scales. The waterfall model is suitable for small projects. The iterative model for small and medium projects and the spiral model for large projects.

425

Kazhaev M.A., Aleshugina E.A.

Nizhny Novgorod State University of Architecture and Civil Engineering

MINIMIZING FUNCTIONS BY A REGULAR SIMPLEX

This article describes method minimizing functions by a regular simplex. The aim of the work is to describe this method and write programs that

implement them. The relevance of this work is that the written programs will simplify the application of this method.

Description of the method minimizes a function by a regular simplex.

A regular simplex in a space is a set of n + 1 equidistant points (vertices of a simplex). A segment joining two vertices is called an edge of a simplex.

In space, the regular simplex is the set of vertices of an equilateral triangle. [Pic. 1]

Pic. 1. Start method

With help regular simplex it is possible to construct a new simplex by reflection of some vertex. The search for a minimum point of the function f (x) with help of regular simplexes is performed as follows. At each iteration , the values of the function at the vertices of the simplex are compared. Choose a point where f(x) max and make a reflection from this point. The search for a minimum point f(x) ends when difference between the values of the function at the vertices of the simplex become sufficiently small. This means that the minimum point is inside the simplex. [Pic. 2]

426

Pic. 2. End of method

Algorithm for minimizing by a regular simplex.

First stage. Choose the accuracy parameter l, the base point x0 (0; 0) we construct the regular simplex by the formula. [Pic. 3]

Pic. 3. The regular simplex formula

The main stage.

Step 1. Calculate the values of f(x) at the vertices of the simplex xk. Step 2. Choose a point where f(x) max

Step 3. Find xc and perform the reflection of the vertex

If F(x^k+1 n+1)<=F(x^k n+1) then we construct a new simplex and go to step 2. Otherwise, go to step 2 and take any other unverified point.

If all points are checked and a suitable one is not found, then the minimum point inside the simplex.

427

Results of software calculations with different accuracy:

Table 1. Comparison

Number

Accuracy

Number of

Extreme point

Deviation

 

 

iterations

 

 

1

0.01

16081

(49,1454;49,3363)

(0,7516;0,7517)

 

 

 

 

 

2

0.001

163107

(49,846;50,0369)

(0,051;0,0511)

 

 

 

 

 

3

0.02

7993

(48,8611;49,045)

(1,0359;1,043)

 

 

 

 

 

4

0.002

81425

(49,7676;49,9585)

(0,1294;0,1295)

 

 

 

 

 

Based on the results obtained [Table 1.] we can conclude method performs too many iterations. This is very bad, since the search for a minimum point will take a long time.

In conclusion, the method is not effective and takes a long time, because it performs a lot of iterations. This method is not used. However based on this method, a method irregular simplex has been created and this method use mathematical tasks for minimizing function.

Konysheva K.E., Aleshugina E.A.

Nizhniy Novgorod State University of Architecture and Civil Engineering

ADVERTISING IN THE INTERNET: VIRAL ADVERTISING AND

ADVERTISING VIRUS

Every person, who uses the Internet, has experienced in advertisements in the browsers at least once in his life. Various images, slogans and links, filling almost all web pages, video, pop-ups and spontaneously opening pages are only the most famous part of the full list. Mostly, the first thoughts arising in our mind are “this page is not safe” or “It is a harmful virus, so it should be removed as soon as possible”. From the information security’s perspective this kind of reaction is right and welcome. As a result, we have an enormous amount of discussions and sites dedicated to erasing of viral advertising or getting rid of advertising virus. However, have you ever mused upon distinctions between the terms viral advertising and advertising virus?

Advertising virus or advertisement software (adware) is a computer program which is needless absolutely for the computer’s work and has no useful functions. Show advertisements in all opened windows of Google Chrome,

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Opera, Mozilla Firefox, MS Internet Explorer, Yandex and other browsers is its single option.

Adware’s creators do not think about you watching this advertising or not.

Their main task is to demonstrate as many promotional websites as possible, because they get money for the number of runs.

This kind of computer viruses is generally classified as not dangerous, but it is important to have in mind, that the sites opened by the adware are not always safe and can contain a malicious code. In addition, the peculiarity of such viruses is that ordinary antivirus programs can not find them. As a result, it is “a bad idea” to go online after having an adware penetrated into your computer.

Examples of adware

The most common features of the adware are a great number of banner and pop-up ads on a page or independent start of a browser with an unknown to you advertising site. Examples of the adware can serve programs Winantivirus 2006, WUpd, SaveNow, VideoActiveXObject, cws, SpySheriff submitted by Interface in the article "Adware is the most widespread of spyware" in 2007. Also such adware like BlockAndSurf or webssearches.com, DNS Unlocker, Outrageous Deal, Offers4U, Adware: OpenCandy, Adware: Downware (Dr.Web) have recently become common in Russia.

Causes of infection

Adware infecting your computer goes through an ordinary software, downloaded from the Internet. Even loading the familiar programs can pick up one of the viruses showing advertisements. You should be especially careful when downloading free content. Another way of infection is suspicious Web pages that are viewed online. Some browsers, such as Yandex, warns about possible danger of suspicious websites.

Ways to fix

When unwanted advertising appears, it is necessary to check your computer as quickly as possible, find and remove adware, because his presence can lead to slowdown of the operating system reducing the speed of downloading Web sites, the browser hangs and even stealing personal information and data entered in the Internet browser. There are some recommendations how to get rid of a virus:

1.Carry out a scan of your computer using anti-adware utilities (for example, AdwCleaner, MALWAREBYTES Anti-Malware, Zemana Antimalware).

2.Remove any recently installed programs that look suspicious (they have names you are unfamiliar with or including addresses of sites).

3.Reset your browser and clear the cache.

4.Check the Task Scheduler (for users of Windows) for tasks that contain a browser’s start with certain sites.

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