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Mathematics programmers - Nakonechny S.I.

6.6. Nablistheni methods. Vector Decay Method

Розроблення та дослідження наближених алгоритмів є досить perspective straightforwardness of the quantitative optimization. Nablizheni methods to merit in respect of more than a practical glance, oskilki, yak zaschachalosya vishche, zastosuvannya exact methods, you will need unjustifiably significant vitrate hour, then yak poshuk nablizhenogo rozv'yuku daet zmogu sutstevo dorotiti prokodojzhennia optimal plan of tasks.

Especially in the long distance in literature, the problems of approaching the problems of methods, та taka іdea izdavaniya nablizheniyah algorіmіv rozv'yazuvannya tsіlokislіlіh zadach . Vobyaratetsya pochatkovy permissible task plan. W, such mozhliv varientom rozv'yazku po'yazuyetsya singing (not arched wide) multiply variants, yak i utzvoryut octil pobotkovogo varianta. Перебираючи елементи околу, здійснюється перехід до крашого плану під фіксується local optimality of the song warrior. In the first vipadku the process of local pokraschanya plan prodovzhuyutsya, and in another zdіysnyuetsya vipadkovy vibri offensive plan, a take for the ear of a new optimal plan. Otzhe, podibnyi method makut vkazuvati sposib viznachennya okolu ta mehanizm vipadkovogo poshuku. In addition, neobhidno takozh introduce a rule, for dopomogo yakogo viznachaetsya moment zakinchenna process poshuku nablizhenogo rozv'yaku.

Razglyanemo without detail, bring one in close proximity to the methods, but I will name the method of vector decay [27]. Yogo Rasping I. V. Sergienko in the middle of the 60th rock. In a fatal vipadku tsey, the method of letting the zemogu know the local minimum of the function, the prototype, yakshcho vyedpovidnі authorities vostokosty, then vin lead to viznachennya global mіnimumu.

It is permissible to look at the problem of the numerical programming:

(6.24)

For the mind:

(6.25)

(6.26)

- the number of numbers (6.27)

Перш ніж describe the algorithm to the method that is introduced in the necessary manner.

Nekhai M is an active discrete point source. - a multiplicity of admissible plans for the activities of physical and mathematical problems (6.24) - (6.27). The metric is introduced into the space M , that is, the function that is defined as the distance between the points of X and Y. Significantly through . Metrics Mya zadovolnyati three aksiomi:

1) аксіому тотожності: For the reason, X = Y ;

2) aksіому симетрії: ;

3) aksіому нерівності трикутника:

З аналітичної геометрії відомо, що відстань між точками (функцію It is possible viznachati in a riznomu. Zokrema, in direct Cartesian Cartesian coordinate systems, by the way of the vector vector Tobto , De - coordinate the point X and Y in the space M.

Nehai Actively permissible task plan for discrete programming. Take an action number Then the multiplier of all points For yakih vikonuetsya nervivnist To call in on the outside І radium r , and the multiplier of all points For yakih vikonuetsya nervivnist Be called an otkratim .

Visually active Points R radius r 1, such, shoob krim plan Він містив bi і інші schedules of problems, for which r 1 має buti not menshim vіd activity of magnitude R. Dali is visually discernable from the outset of the plan of tasks. Viznachimo funktsiyu У такий спосіб:

Called vector decay Functions At the politician o okolo Dovilnii points (Одним одним одним одним одним одним одним Such a vector, components of a certain quantity , De - tasks to be solved .

Obviously, if all the components of the vector of decay are unavailable In the point For the sake of value

Ostanja nervіnnost means, poo point Є point of local functionality Visually , Tobto:

Yaksho z component of the vector of the decline will be vid'єmnimi, then tse znacha, scho Not є point of the minimum in the designated okolі, oskilki in the active points of this or that function Nabuvaє least value. I prichomu that point Vidilenogo okolu, for the sake of a raspberry Bude naimenshoyu, viznachaє napisvideshogo straights (zmenshennia) tsіlової functції Oskilki Tse Obvious fact and lie in the basics of calculating schema zastosuvannya method of vector decay.

Іode to the method of polygas in the viznachennyi component of the vector recession for the activity of the pochatkoy point. Якщо всі вони невід'ємні, then the point of the local minimum is known, and the center of the new deviation is known, and the yogic component is turned into a non-existent one. Process poshuku rozv'yazku є poslidovnim sorting out the points, sho zmenenut znachenny tsil'ovoy funktsii.

Yak rule, on the skin korzi algorithm (tobto for cutaneous new ocular) do not subtract all the components of the vector of decline, but only a part of them, but it does not vigash in the tranche and triviality calculation.

One of the possible algorithms in the real-time recession method is introduced.

1. Vibrate the point 0 0 і radium around the corner R so that the point X 0 of the bullet is admissible by the plan for the tasks of the numerical program And okol buv such, sho mistit takozh іnshi permissible tasks tasks. Tsey vibir can zdіysnjuvatis Vipadkova z povatkovoi perevirkoi vikonannya zaznacheniyu minds.

2. The component of the vector should vanish in a vibrating environment. Yaksho all i yogo componenti nevіd'єmnі, then the point of the local minimum is known (the task is rooted and optimized by the plan є ).

3. Yaksho not all the components of the vector fall off, then the component Yaka maє namenshe znachennia і viznachaєe point , Що зменшує значення цільової functції і є the center of a new break.

4. Turn to the point 2. The process prodovzhuemo, left for the active All components of the vector of the recession will not become invisible.

Rozv'yazhemo tsilochislovu problem, vikoristovoychi zmist rifle 6.1.

Rozvjazannya . Nehai Vibrana point is the permissive task plan, the secrecy is satisfied with all the interference and the need for celibacy, and the circle of the vibrational radiance is the plan of tasks, the application, the point

Viznachaemo point, yaki nalezhat otlozhennomu otolu (Figure 6.6). There are three points:

The components of the vector are signifi- cantly declining, thus introducing knowledge:

Naimenshoyu - third of the component of the vector decay, annealing, the point of departure is the center of the approaching impulse Radius

In the new windows, you will enter the points with the coordinates:

Need to compute the value of the vector component of the decay for the designated points. However, for three points, the value of the bulb is rooted in the cross, and you compute the component of the vector for the new points.

Pislya vyznaniya occhislen maemo, scho namenshogo znachennya nabuvaє component of the vector, yaka vidpіdaiє exacti To the forthcoming cent, to the end, to move to a new point Nehai

The components of the vector that are calculated are reckoned as falling off in two points:

Having zistavshi ti znachennya, viznachaemo point of the new center of the window З радіусом The components of the vector fall into a circle around them. The repetition, the procedure for the near completion is completed, and the point is the optimal plan for the number of tasks:

Zauvazhimo, scho method of the vector decline, it is clear from the description of the real-world algorithm, additions to the knowledge of the numerical value of such and non-linear tasks.