Algorithms of optimization
1) Cover and partition of together:
The cover of an entirety is an entirety constituted from sottosets such covering all with of departure, if these sottosets do not have some intersection between they have one partition.
2) Difference between way and distance:
A way is to ollow itself of concerns to us and logons, are distinguished from the distance in how much for this last every apex can only once be crossed.
3) connected Graph :
All the braces of you concern are connected from at least a distance.
4) With stable of you concern and coloration to us:
With stable of you concern is an entirety constituted from you concern to us that they do not have some logon between they. The coloration is one partition in sottosets stable.
5) direct and indirect Difference between graph :
In a graph directed you concern the logons to us are unidirectional while in graph indirect they they are bidirectional.
6) Matrix of incidence:
It is the matrix that is obtained from a graph putting on the lines concerns and on the columns the logons to us, in the intersections places a 1 if the logon enters in the apex, a â?"1 if it exits and 0 if it does not arrive to you.
7) Matrix of adjacency and matrix of the weights:
It is a square matrix that obtains from a graph putting concerns in is ordered that in abscissa and placing then a 1 or 0 in the crossing to second that between the data you concern to us there is a connection or less, if instead the graph it is weighed, put the corresponding weights in the intersections.
8) decisional Problem:
It is a problem that one admits binary solution, true or false.
9) Problem of optimization:
It is a problem whose solution measure in terms of a function cost or objective that to second of the problem must be maximized or be diminished, usually the problem comes reduced to one sequence of decisional problems.
10) Algorithm and its typology :
It is a computazionale procedure having with of incomes and escapes, an ended number of instructions and comes executed in an ended number of steps, based on the precision of the solution have the following types of algorithms:
to) algorithm esatto it supplies always the exact solution
b) algorithm euristico supplies a next solution to the optimal one in the case is one excessive computazionale complexity of the problem
11) Complexity of an algorithm:
It holds account of the dimensions of the memory necessary to carry out the operations and of the time that is employed in order to reach the solution, it comes expressed in terms of O[f(n) ] where n it is the dimension of the problem, in kind polinomiali algorithms they are more feasible that esponenziali algorithms however are not necessary to hold account of one constant moltiplicativa that could as an example ribaltare the situation for n small. The optimal algorithm has O[n complexity ].
12) Classification of the algorithms based on the characteristics of the space of the solutions:
Subordinate to of linear ties speaks itself about linear programming LP in the case must itself be optimized a linear function, has instead linear programming entire ILP in the case the incognito carrier belongs to with of the entire numbers, in such case reaches the solution rounding off the obtainable solution by means of the linear programming. An ulterior one sottocaso of entire the linear programming is linear programming binary ZOLP in which the carrier of the solution is binary.
13) Classes of optimization algorithms:
The optimization algorithms are subdivided in the three following classes:
a) technical enumerative searches the solution in all the dominion of the function, the problem can be resolved subdividing it in simpler problems.
b1 ) technical numerical indirette tries the minimum of the function iterativamente resolving not linear equations, the algorithm is arrested when the gradient is cancelled.
b2 ) technical numerical dirette try the minimum of the function letting to guide from the gradient.
Numerical technical ) probabilistiche is technical enumerative that use for the search information add them, an example is the genetic Simulated Annealing and algorithms.
14) Problem of the minimal and maximum way:
It is a typical problem that can be represented by means of a graph direct connected and weighed, has an apex source and the minimal distance in the graph must be tried that door to one whichever of the others you concern to us. The complexity of the problem is O[n2] and in kind the algorithm of Bellman-Ford consisting in inizializzare the minimal way with the weights of the logons from the apex iterativamente source and in dawning the weights during the way is used.
15) Problem of the coloration:
It comes represented by means of a graph in which the logons represent of the incompatibilità between the processes represent to you from concern us for they as an example use contemporary of the same resource. The scope is to find the minimal number of colors that concur the coloration of the diagram or in other words as an example to find the minimal number of resources that concurs the execution of all the processes.
16) Algorithm of the gradient:
The search of a minimum of the function cost is not a simple problem in how much can capitare that the found minimum is only a local minimum, is how much happens with this algorithm, in fact the local minimum comes beginning from searched one point x0 in which the function is worth y0 , us a Pò is moved on the left and a Pò to right, if in one of the two it aims the cost is inferior, such point becomes the new minimum and the algorithm continues, otherwise the absolute minimum has been characterized that like asserted previously could instead be only a local minimum and the algorithm it is not in a position to noticing some. The following algorithms for the search of the best disposition belong to this category than a sure number of objects:
to) Constructive Initial Placement an object based on the number of other objects comes chosen which it must it are connected, comes placed so as to to diminish the total length of the connections regarding the previous positioning.
b) Pairwise Interchange posiziona all the objects accidentally, then selects two exchanges them and if the length of the connections does not diminish it replaces them to place.
c) Neighboorhood Interchange is like the Pairwise Interchange but stavolta the objects exchange to you are adjacent.
d) Steinberg' s Algorithm selects with of objects that do not have common connections and it removes them
and) Force Directed Relaxation to every object comes associated a carrier forces based on the distance of the objects which it must be placed, is attempted to posizionare the object in a point in which the force that on it acts it is null.
17) Algorithm of the simulated annealing:
It is an algorithm that concurs the search of the absolute
minimum also in presence of local minimums, in practical if the
difference of cost Dc, between
the minimum previous and the point candidate to being the new minimum,
is negative then the candidate becomes the new minimum otherwise if
the candidate is positive equally has a not null probability of being
accepted, in particular use the functions of distribution of Boltzmann
or of Dirac 
in which T it is
the temperature that initially comes high choice so as to to accept
many states in order then to decrease of step in step second the 
law with to comprised between 0,95 and 0,8.
18) genetic Rules:
Draft of rules drawn from the genetics and that they are considered to the base of the human evolution, they are:
to) the evolution it acts on the chromosomes and not on the living beings that it codifies.
b) the chromosomes are reproduced with greater probability that codify structures that better are adapted to the atmosphere.
c) the evolution is concentrated in the reproduction where mutation and recombination alter the chromosomes of the sons regarding those of the parents
d) the new generation comes beginning from created that one independently puts into effect them and from its genetic patrimony from the evolutionary distance.
19) genetic Algorithm:
In the first place it is necessary to codify the chromosomes, in kind they come codify to you in railroad and by means of Grey so that numerically near solutions have rappresentazioni with minimal distance of Hamming, it comes therefore inizializzata the population and estimated for all the function cost, the best trace of after which the new population is passed to the generation of one, in particular chosen two chromosomes with probabilistici criteria is kept legacies to the goodness of their solution, they comes cuts to you in probabilistica way and with such pieces the recombination process generates 2 sons, the mutation then concurs to change in accidental way but with low probability however of the bit of the chromosome sons. The population must remain constant therefore is necessary to eliminate a brace of chromosomes pertaining to the previous generation, to such aim still uses a probabilistico criterion so that individuals with a better solution have greater probability than to survive. To the end of every cycle it comes then estimated the better solution to the aim than to verify if the condition of arrest of the process has been caught up.