FR2846180A1 - Mathematical function optimizing method for determining path among digital signal samples, involves separating initial population into groups to form solutions, selecting another population best solutions to form third population - Google Patents

Abstract

The method involves determining initial population of function evaluation solution based on evaluation criteria, and separating the population into exploration and local optimization groups to form respective solutions. A constructive genetic operator is applied on the optimization group to form other solutions. Another population with two solutions is formed and best solutions of it are selected to form a third population. The initial population is separated into the exploration and local optimization groups based on evaluated result of the solution application of disruptive genetic operator on a exploration group, so as to form respective solutions. Independent claims are also included for the following: (a) a function optimization device (b) an apparatus for processing a digital image.

Description

The present invention relates generally to optimization

  math of functions that cannot be solved

  analytically or by a known heuristic method.

  Genetic algorithms are particularly suitable for this type

  of optimization because they are methods which can function without strong hypothesis of regularity.

  An optimization technique for this type of problem is calculation

  evolutionary of which for example a description is in the article entitled "Evolutionnary Algorithms" by Thomas Bâck, ACM SIGBIO Newsletter, pp.

26-31, 1992.

  Evolutionary calculus (in English: evolutionary computation) is a research technique applied to problems which, on the one hand cannot be formulated mathematically continuously and on the other hand do not have a sufficiently reduced set of possible solutions to can

be listed.

  Evolutionary calculus is thus part of the random techniques, and more specifically is part of the so-called random search techniques

  guided, that is to say which have a global or local function to optimize.

  If, in an analytical approach, we seek to design a single solution to solve a problem, evolutionary calculus considers a set of solutions and makes this set of solution evolve according to rules which are

  modeled on the evolution of life: reproduction, mutation and selection.

  The main idea is that multiple individuals can explore different strategies and combine their ability to converge on an effective solution. Reproduction allows combination, mutation allows

  exploration and selection allows convergence.

  The evolutionary calculus uses the following functions: generation, which produces an initial population of individuals, evaluation, which measures the performance of each individual with regard to the problem to be solved, - selection, which selects a sub - set of individuals from the current population, - reproduction, which produces a new set of individuals. Reproduction uses the combination of two selected individuals and the resulting mutation of the new individual. The mutation is the introduction of a slight difference in the individual child resulting from the combination, and - replacement, which replaces the individuals whose performance is weakest with regard to the problem to be solved, by individual children

generated by reproduction.

  These functions are used iteratively until a

  convergence criterion is satisfied.

  For example, document US 4,697,242 describes an application which uses genetic algorithms for an electronic program which allows

  to learn and discover a language.

  Document US 4,935,877 describes an evolutionary algorithm which brings into play solutions composed of functions and of arguments which form a program. Programs are evolved to find a solution to a given problem. This technique is known as

  name of genetic programming.

  In general, the convergence of an evolutionary algorithm

requires a long calculation time.

  The invention applies particularly to the field of compression with loss of digital signals. The digital signals considered here are of any kind, for example still images, of the

  video, sound, computer data.

  In the following, we consider more particularly the coding and the

decoding of a still image.

  In this context, certain coding modes use an established route among a set of digital samples. For example, French patent applications Nos. 01 06933 and 01 13922 relate to such

coding modes.

  In order for the coding to be effective, that is to say that it has a good speed-distortion ratio, it is necessary to determine the path appropriately. There are techniques for determining a route among a set of samples. These techniques are known as

  techniques for solving the traveling salesman problem.

  Again, the calculation time to find the route can be long.

  The present invention aims to provide a method and a device for optimizing a function which make it possible to find a value close to the optimal solution of a problem posed, more quickly than according to the prior art. To this end, the invention proposes a method for optimizing a function, characterized in that it comprises the steps of: - determination of an initial population of solutions of the function, - evaluation of the solutions of the initial population , according to an evaluation criterion, - separation of the population into an exploration group and into a local optimization group, according to the result of the evaluation of the solutions, - application of a genetic operator disruptive on the 3o exploration group, so as to form second solutions, - application of a constructive genetic operator on the local optimization group, so as to form third solutions, - formation of a second population comprising minus the second and third solutions, - evaluation of the solutions of the second population, according to the evaluation criterion, - selection of the best solutions of the second population, according to

  the evaluation criterion, to form a third population.

  The invention makes it possible to find a value close to the solution

  optimal of a problem posed, more quickly than according to the prior art.

  According to a preferred characteristic, the method comprises the reiteration of the selection separation steps until a stop criterion is satisfied. Thus, the solution is improved with each iteration. According to a preferred characteristic, the separation of the population involves the formation of the local optimization group by the selection of solutions among the best according to the evaluation criterion. This group of

  solution allows to converge towards the optimal solution.

  According to a preferred characteristic, the separation of the population involves the formation of the exploration group by the selection of solutions among the least good according to the evaluation criterion. This group of solutions makes it possible to explore the space of solutions and avoids converging too quickly

  2 5 towards an optimal solution which could be only a local optimum.

  According to a preferred characteristic, the disruptive genetic operator

has a mutation.

  According to a preferred characteristic, the constructive genetic operator 30 comprises a crossing, a mutation, a duplication or the combination of the three. These operators give good experimental results and are

simple to implement.

  According to a preferred characteristic, the second population comprises

  in addition the local optimization group. Indeed, this group includes 5 "good" solutions within the meaning of the evaluation criterion, so it is interesting to keep them.

  According to alternative preferred characteristics, the stopping criterion is satisfied if the evaluation of the best solution of the third population satisfies a predetermined criterion or if the third population does not evolve more from one iteration to another or even if a predetermined duration of treatment is reached. According to a preferred characteristic, the method is applied to the

  formation of a path among coefficients of a signal, the solutions being possible paths, and it involves the selection of the best solution in the third population.

  More particularly, the method according to the invention applies to the

  formation of a path among coefficients of a digital image.

  According to a preferred characteristic, the criterion for evaluating a route is a minimization of a cost of coding the signal, the coding

  2 0 using the route considered.

  Correlatively, the invention relates to a device for optimizing a function, characterized in that it comprises: - means for determining an initial population of solutions of the function, - means for evaluating solutions of the initial population, according to an evaluation criterion, - means of separating the population into an exploration group and a local optimization group, according to the result of 3 o the evaluation of solutions, - means of applying a disruptive genetic operator to the exploration group, so as to form second solutions, - means of applying a constructive genetic operator to the local optimization group, so as to forming third solutions, - means for training a second population comprising at least the second and third solutions, - means for evaluating solutions of the second population, according to the evaluation criterion, - means of selecting the best second solutions

  population, according to the evaluation criterion, to form a third population.

  The device according to the invention comprises means for implementing the features previously presented.

  The device according to the invention has advantages similar to

those previously presented.

  The invention also relates to a digital apparatus including the device according to the invention or means for implementing the method according to the invention. This digital device is for example a digital camera, a digital camcorder, a scanner, a printer, a photocopier, a fax machine. The advantages of the device and the device

  digital are identical to those previously exposed.

  A means of storing information, readable by a computer or by a microprocessor, integrated or not in the device, possibly removable,

  stores a program implementing the method according to the invention.

  A computer program readable by a microprocessor and comprising one or more sequence of instructions is capable of implementing

  implements the methods according to the invention.

  The characteristics and advantages of the present invention will appear more clearly on reading a preferred embodiment illustrated by the attached drawings, in which: - Figure 1 is an embodiment of a device implementing the invention, - figure 2 represents a coding device according to the invention, - figure 3 represents an embodiment of coding method according to the invention, - figure 4 represents an amplitude model used according to the present invention , - Figure 5 shows an embodiment of location coding included in the method of Figure 3, - Figures 6 and 7 show examples of the application of disruptive genetic operators to genomes,

  - Figures 8 and 9 show examples of application 10 of constructive genetic operators to genomes.

  According to the embodiment chosen and represented in FIG. 1, a device implementing the invention is for example a microcomputer 10 connected to different peripherals, for example a digital camera 107 (or a scanner or any means of acquisition or image storage) connected to

  a graphics card and providing information to be processed according to the invention.

  The device 10 includes a communication interface 112 connected to a network 113 capable of transmitting digital data to be processed or, conversely, of transmitting data processed by the device. The device 20 also includes a storage means 108 such as for example a hard disk. It also includes a disc drive 109. This disc 110 can be a floppy disk, a CD-ROM or a DVD-ROM, for example. The disc 110 as the disc 108 can contain data processed according to the invention as well as the program or programs implementing the invention which, once read by the device 10, will be stored in the hard disc 108. According to a variant , the

  program allowing the device to implement the invention, may be stored in read-only memory 102 (called ROM in the drawing). In a second variant, the program can be received to be stored in an identical manner to that described previously via the communication network 30 113.

  The device 10 is connected to a microphone 111. The data to be processed

  according to the invention will in this case be an audio signal.

  This same device has a screen 104 making it possible to view the data to be processed or to serve as an interface with the user who can thus configure certain processing modes, using the keyboard 114 or any

other means (mouse for example).

  The central unit 100 (called CPU in the drawing) executes the instructions relating to the implementation of the invention, instructions stored in the read-only memory 102 or in the other storage elements. During power-up, the processing programs stored in a non-volatile memory, for example the ROM 102, are transferred to the random access memory 10 RAM 103 which will then contain the executable code of the invention as well as registers for storing the variables necessary for the implementation of the invention. More generally, a means of storing information, readable by a computer or by a microprocessor, integrated or not in the device, possibly removable, stores a program implementing

  implements the method according to the invention.

  Communication bus 101 allows communication between the

  various elements included in the microcomputer 10 or connected to it. The representation of the bus 101 is not limiting and in particular the central unit 100 20 is capable of communicating instructions to any element of the microcomputer 10 directly or through another element of the microcomputer 10.

  With reference to FIG. 2, an embodiment of coding device 2 according to the invention is intended to code a digital signal in order to compress it. The coding device is integrated into a device, which is for example a digital camera, a digital camcorder, a scanner, a printer, a photocopier, a fax machine, a

  database management system or even a computer.

  An image source 1 provides a digital IM image to the device

  coding 2, which includes a transformation circuit 21, a coding path determination circuit 22 and an entropy coding circuit 23.

  The operation of the coding device and more particularly of the

  determination of coding path 22 will be detailed below.

  The device according to the invention comprises: - means for determining an initial course population, 5 - means for evaluating the course of the initial population, according to an evaluation criterion, - means for separation of the population in an exploration group and in a local optimization group, according to the result of the evaluation of the routes, - means of application of a disruptive genetic operator on the exploration group, so to form second courses, - means of applying a constructive genetic operator to the local optimization group, so as to form third courses, - means of training a second population comprising at least the second and third routes, - means of evaluating the routes of the second population, according to the evaluation criterion, - means of selecting the best routes of the second

  population, according to the evaluation criterion, to form a third population.

  The coding device supplies a file containing data representing the compressed image to transmission and / or transmission means.

  memorization 3. These means are conventional and will not be described here.

  FIG. 3 represents an embodiment of an image coding method according to the invention. This process is implemented in the

  coding device and comprises steps E1 to E7.

  The method generally comprises a transformation of the signal to be coded, then the determination of an amplitude model of the coefficients resulting from the transformation. The locations of these coefficients are then coded

  according to a method which uses a path established among the coefficients.

  Such a coding method is described for example in French patent application no. 01 06933 or in French patent applications no.

  02 00330 and 02 00332 filed by the plaintiff.

  The method is carried out in the form of an algorithm which can be stored in whole or in part in any information storage means capable of cooperating with the microprocessor. This storage means can be read by a computer or by a microprocessor. This storage means is integrated or not to the device, and can be removable. For example, it may include a magnetic tape, a floppy disk or a CD-ROM (compact disk 10 with frozen memory).

  Step E1 is a linear or non-linear transformation of a digital image IM to be processed according to the invention. The image has for example a size

of 512 x 512 pixels.

  In the preferred embodiment of the invention, the transformation 15 is a decomposition into frequency sub-bands.

  The signal is broken down into frequency sub-bands at several resolution levels by a transformation into discrete wavelets called DWT

  (from English Discrete Wavelet Transform) at M resolution levels.

  It should be noted that the low sub-band can be coded according to the method described below or in a conventional manner by linear prediction.

  Other types of transformation can be used, for example the discrete cosine transformation called DCT or the Fourier transformation or a non-linear transformation such as a morphological transformation. The next step E2 is the selection of a first sub-band resulting from the previous decomposition. The sub-bands are considered

one by one.

  The next step E3 is a classification of the coefficients of the current subband. The sign of the coefficients is first of all coded independently. The coefficients are then considered in absolute value and

  are ranked from largest to smallest.

  The next step E4 is the determination of an approximation function of the sequence of classified coefficients. This function is for example a decreasing exponential defined by a set of parameters which

are determined by regression.

  FIG. 4 represents an example of an amplitude model A. To each integer value k on the abscissa corresponds a value A (k) supplied by the amplitude model. The value A (k) is an approximation of the amplitude of the

  kme coefficient classified in descending order.

  The next step E5 is the coding of the locations of the coefficients. This step includes the determination of a path among the coefficients of the current sub-band so that the coding cost of this path is minimal. The route includes an initial coefficient and the list of 15 vectors joining the other coefficients. Each coefficient of the course different from the initial coefficient is represented by a vector describing its location with respect to the previous coefficient in the course. It should be noted that the route does not necessarily pass through all the coefficients of the current sub-band. Indeed, it is possible to code only part of the 20 coefficients and to set the other coefficients to zero when

subsequent decoding.

  Once the route has been determined, the coordinates of the initial coefficient are coded by binary coding and the vectors are coded by entropy coding. Step E5 is detailed below. It is in the area of techniques for solving the problem of a traveling salesman. More specifically, this is the problem of the time-varying traveling salesman. Indeed, the cost associated with the passage from one sample to another depends on the path already taken, since the decoding distortion of a sample depends on the rank at which it is decoded and the bit rate depends on the vector.

  generated and vectors already present in the route taken.

  The coded form of a sub-band of the image includes a model

  of amplitude which provides an approximation of the amplitude of the coefficients and a path which provides an ordered sequence of the locations of the coefficients.

  The location of the kth coefficient of this sequence is determined by the path 5 and its amplitude is determined by the ordinate corresponding to the abscissa k according to the amplitude model.

  The next step E6 is a test to determine if the sub-band

  current is the last sub-band of the image to be coded.

  If the answer is negative, this step is followed by step E7 to 11 which a next sub-band is considered. Step E7 is followed by

  step E3 previously described.

  If the response is positive in step E6, then the coded data undergoes an entropy coding known per se, such as Huffman coding or arithmetic coding, and the coding of the image is finished. FIG. 5 represents an embodiment of step E5 of coding the locations of the coefficients. This coding includes steps

E51 to E60.

  This coding generally comprises the determination of a path 20 among the coefficients and the coding of the coefficients as a function of the path. A route has a coefficient of the sub-band, called the initial coefficient, and a

  list of vectors joining at least some of the other coefficients.

  The route determination is optimized according to the invention.

  We consider a population of solutions which each define a possible path among the coefficients.

  One possible solution is described by a genome. A genome is here a list of Q + 1 indices, where Q is the number of points in the frequency sub-band considered. The coefficients of the sub-band are considered from left to right and from top to bottom in the sub-band. Each coefficient of the sub-band is associated with an index according to this reading order. An additional index X is reserved at the stopping point of the route. Beyond that

  period, the coefficients are no longer coded.

  So, for example, the route of points 1-5-8-10-4 in a ten-point image can be coded as follows:

(1 58104X23679).

  The order of the points after the breakpoint X has no importance.

  For a set of points to be traversed of given size, paths of different lengths in this set are represented by

fixed length genomes.

  Step E51 is an initialization of the genome population. 10 For this, a random draw is carried out to determine pL solutions. As a variant, it is possible to choose at least part of the genomes of the

initial population.

  The next step E52 is an evaluation carried out by an adaptation function which measures the performance of each previously determined genome. For this, a coding cost R + k.D is calculated for each

path represented by a genome.

  The coding cost represents a compromise between bit rate and distortion. The coding cost of a signal S is here the function C (S) = R (S) + XD (S), in which R (S) represents the transmission rate of the coded form of the signal S, D ( S) represents the distortion generated in the reconstructed signal after coding and decoding, with respect to the original signal and X; East

  a setting parameter between compression and distortion.

  It should be noted that the minimization of the function C (S) on the signal S is equivalent to the minimization of the function C (S) on each element of a partition of the signal, in particular on each sample of the signal. This is due

  to the fact that the distortion and the flow are respectively additive.

  The next step E53 is a selection or separation of the population into two groups. For this, we consider a coefficient P in the closed interval [0, 1]. The population of Ii genomes is then divided into a local optimization group comprising P.Ft genomes and a group

  exploration comprising (1-P) .pt genomes.

  It should be noted that the same genome cannot belong to the two groups. On the other hand, if two genomes are identical, it is possible that they

  are each in a different group.

  Preferably, the local optimization group includes the P.pi 5 best genomes of the population, within the meaning of the evaluation previously carried out. The best genomes are the genomes that produce the lowest coding costs. Alternatively, the genomes of the local optimization group are determined by a random draw according to which the probability of being

  selected increases with the performance of the genome.

  The local optimization group makes it possible to find an optimum solution, but which may only be a local optimum if the search is limited to

this group.

  The exploration group includes the (1-P) .It other genomes. On the contrary, this group makes it possible to explore the entire search space in such a way that the algorithm does not converge too quickly and that the solution is not

not a local optimum.

  Step E53 is followed by steps E54 and E55.

  In step E54, a disruptive genetic operator is applied to the

  exploration group. This operator has a mutation which is applied to all the genomes of the exploration group.

  For example, the disruptive operator is a mutation that causes large jumps in the search space. The mutation "Scramble Mutation" described by P. Larranaga, C. M. H. Kuijpers and R.H. Murga in "Tackling the traveling Salesman Problem with Evolutionary Algorithms: Representation and 25 Operators", page 36, satisfies this criterion. This document is available in the "Scientific Literature Digital Library" database at the internet address:

  http://citeseer.ni.nec.com/2 10802.html.

  An example of application of the “Scramble Mutation” mutation is shown in FIG. 6. This mutation randomly selects part 61 of a given genome 60 and withdraws it from it. The indices of the removed part 61 are randomly reordered and are then reintroduced into the genome

  initial to form a second genome 62.

  As a variant, the disruptive operator has one or more applications of the mutation called "Exchange mutation" which consists in exchanging the location of two indexes chosen randomly in the genome. Figure 7 shows the application of this mutation to a genome

  70. The indexes 8 and 3 are exchanged, which produces a new genome 71.

  In step E55, a constructive genetic operator is applied to the local optimization group. This operator includes a cross followed by a

  mutation. A cross is a binary stochastic operator which combines one or more characteristics of two parent genomes in a random manner so as to generate one or more new genomes. As a variant, the crossing is replaced by a duplication of the parent genomes, that is to say a copy of these.

  Each of the genomes in the local optimization group is a parent genome and is used only once. Alternatively, the parent genomes

  are selected by random draw.

  The crossover operator is applied to two parent genomes. A mutation is then applied to the two genomes generated by the cross. For example, we use the cross called "Order crossover"

  described by P. Larranaga, C. M. H. Kuijpers and R.H. Murga in "Tackling the traveling Salesman Problem with Evolutionary Algorithms: Representation and 25 Operators", pages 24-25.

  This crossing is represented in FIG. 8. Two cut points 82 are randomly selected inside each of the parent genomes 80 and 81. Each generated genome 83, 84 receives the indices of one of the 30 parent genomes 80, 81 between the cut points. Then the other positions receive the index values of the other parent which are different from those already assigned and in the order they appear in the other parent from the

second cut-off point.

  According to another example, we use the cross called "The

  position based crossover "described by P. Larranaga, C. M. H. Kuijpers and R.H. 5 Murga in" Tackling the traveling Salesman Problem with Evolutionary Algorithms: Representation and Operators ", page 26.

  This crossing is represented in FIG. 9. Positions are selected randomly in the parent genomes 90 and 91. These are the

  second, third and sixth positions.

  A genome generated 92, 93 receives at these positions the index values located at the same positions of one of the parents. The other positions receive the index values of the other parent which are different from those already

  affected and in the order they appear in the other parent.

  Two genomes are thus generated.

  For the mutation that follows the crossing, we use the operator described above or alternatively, we use the mutation operator called "Insertion mutation" described by P. Larranaga, CMH Kuijpers and RH Murga in "Tackling the traveling Salesman Problem with Evolutionary Algorithms:

  Representation and Operators ", page 34.

  This operator randomly selects an index in a genome,

  remove it from the genome and reinsert it at a randomly determined position.

  According to a variant of step E55, the crossing operators,

  mutation and duplication are applied randomly to the parent genomes.

  Each operator has a probability of being chosen. The choice of operator to apply is made for each pair to be reproduced.

  The next step E56 is the meeting of the local optimization group, of the population resulting from the local optimization and of the population resulting

of exploration.

  The local optimization group contains by construction 30 efficient genomes within the meaning of the evaluation carried out in step E52. The population resulting from local optimization is likely to contain efficient genomes, due to the operators chosen and the parent genomes. The population resulting from the exploration comprises genomes which are likely to redirect the search for the optimum towards another zone

search space.

  As a variant, the local optimization group is not included in the new population, which makes it possible to reduce the memory size necessary to store the data being processed.

  The next step E57 is an evaluation of the current population.

  This step is analogous to step E52 previously described. It results in a performance for each genome, established according to a criterion 10 which is here a coding cost.

  The next step E58 is a selection to keep only j

  genomes. We use here a selection called roulette draw described in the book "Evolutionary Computation 1: Basic Algorithms and operators" by John Grefensette, "the Institute of Physic Publishing, Bristol and Philadelphia", 15 edited by T. Back, B. Fogel and T. Michalewicz, pages 175-176.

  This method assigns to each genome a probability of being

  selected which is proportional to its performance.

  Alternatively, a selection called "rankedselection", described in the previous work on pages 187 to 194, can be used. This selection orders the genomes of the population according to their performance. The

  probability of selection then depends on the rank of the genome in the population.

  Furthermore, in all variants, the best genome is

  systematically kept in the new population.

  The next step E59 is a test to determine whether a stop criterion 25 is satisfied. The stopping criterion is for example: - the performance of the best genome is satisfactory for the problem to be solved, - there is convergence and the population does not evolve from one iteration to another,

  3 0 - a processing limit has been reached.

  The stopping criterion can also be a combination of several

  criteria. When one of the criteria is verified, treatment is stopped.

  As long as the termination criterion is not met, the treatment is repeated

  and for this step E59 is followed by step E53 previously described.

  When the stopping criterion is satisfied, the best genome in the sense of performance is selected in step E60. In the example chosen, this genome represents a route among a set of samples. Of course, the present invention is in no way limited to the embodiments described and shown, but includes, on the contrary,

  any variant within the reach of the skilled person.

Claims (29)

  1. Method for optimizing a function, characterized in that it comprises the steps of: - determination (E51) of an initial population of solutions of the function, - evaluation (E52) of the solutions of the initial population, according to an evaluation criterion, separation (E53) of the population into an exploration group and into a local optimization group, according to the result of the evaluation of the solutions, - application (E54) d a disruptive genetic operator on the exploration group, so as to form second solutions, application (E55) of a constructive genetic operator on the local optimization group, so as to form third solutions, training (E56 ) of a second population comprising at least the second and third solutions, - evaluation (E57) of the solutions of the second population, according to the evaluation criterion, - selection (E58) of the best solutions of the second population,   according to the evaluation criterion, to form a third population.   2. Method according to claim 1, characterized in that it comprises the reiteration of the separation steps (E53) with selection (E58) until a stop criteria be met.   3. Method according to claim 1 or 2, characterized in that the separation (E53) of the population comprises the formation of the local optimization group by the selection of solutions among the best according to the evaluation criteria.   4. Method according to any one of claims 1 to 3,   characterized in that the separation (E53) of the population involves the formation of the exploration group by the selection of solutions among the least good according to the evaluation criterion.   5. Method according to any one of claims 1 to 4,   characterized in that the disruptive genetic operator includes (E54) a mutation.   6. Method according to any one of claims 1 to 5,   characterized in that the constructive genetic operator includes (E55) a   crossing, mutation, duplication or combination of the three.   7. Method according to any one of claims 1 to 6,   characterized in that the second population also includes (E56) the group local optimization.   8. Method according to any one of claims 1 to 7, characterized in that the stopping criterion (E59) is satisfied if the evaluation of the   best solution of the third population satisfies a predetermined criterion.   9. Method according to any one of claims 1 to 7,   characterized in that the stopping criterion (E59) is satisfied if the third population does not evolve more from one iteration to another.   10. Method according to any one of claims 1 to 7,   characterized in that the stopping criterion (E59) is satisfied if a predetermined duration of treatment is reached. 30   11. Method according to any one of claims 1 to 10,   characterized in that it is applied to the formation of a path among the coefficients of a signal, the solutions being possible paths, and in that it comprises the selection (E60) of the best solution in the third population . 12. Method according to claim 11, characterized in that it is applied to the formation of a path among coefficients of a digital image. 13. Method according to claim 11 or 12, characterized in that the criterion for evaluating a course (E52, E53) is a minimization of a cost   signal coding, coding using the route considered.   14. Device for optimizing a function, characterized in that it comprises (22): - means for determining an initial population of solutions of the function, - means for evaluating solutions of the initial population , according to an evaluation criterion, - means of separating the population into an exploration group and into a local optimization group, according to the result of the evaluation of the solutions, - means of applying a disruptive genetic operator to the exploration group, so as to form second solutions, means for applying a constructive genetic operator to the local optimization group, so as to form third solutions , - means of training a second population comprising at least the second and third solutions, - means of evaluating solutions of the second population, according to the evaluation criterion, - means of selecting the best other solutions of the second   population, according to the evaluation criterion, to form a third population.   15. Device according to claim 14, characterized in that the selection separation means are adapted to reiterate their operation   until a stop criterion is satisfied.   16. Device according to claim 14 or 15, characterized in that the means for separating the population are adapted to form the local optimization group by selecting among the best solutions according to the evaluation criteria.   17. Device according to any one of claims 14 to 16,   characterized in that the means for separating the population are suitable for forming the exploration group by selecting solutions from among the least   good according to the evaluation criterion.   18. Device according to any one of claims 14 to 17,   characterized in that it is suitable for implementing a genetic operator   disruptive that involves a mutation.   19. Device according to any one of claims 14 to 18, 20 characterized in that it is adapted to use a genetic operator   constructive which involves a crossing, a mutation, a duplication or the combination of the three.   20. Device according to any one of claims 14 to 19, characterized in that the means for training the second population are   adapted to train it so that it also includes the local optimization group.   21. Device according to any one of claims 14 to 20, 30 characterized in that it is adapted to implement a stopping criterion which is   satisfied if the evaluation of the best solution of the third population   meets a predetermined criterion.   22. Device according to any one of claims 14 to 20,   characterized in that it is suitable for implementing a stopping criterion which is   satisfied if the third population does not evolve more than one iteration to another.   23. Device according to any one of claims 14 to 20,   characterized in that it is suitable for implementing a stopping criterion which is   satisfied if a predetermined duration of treatment is reached.   24. Device according to any one of claims 14 to 23,   characterized in that it is suitable for forming a path among coefficients of a signal, the solutions being possible paths, and in that it comprises   means of selecting the best solution in the third population.   25. Device according to claim 24, characterized in that it is   adapted to form a path among coefficients of a digital image.   26. Device according to claim 24 or 25, characterized in that it is adapted to implement a criterion for evaluating a path which is a minimization of a coding cost of the signal, the coding using the path considered. 27. Optimization device according to any one of   Claims 14 to 26, characterized in that the means for determining, evaluating, separating, applying, training and selecting are incorporated   in: - a microprocessor (100), - a read only memory (102) comprising a program for processing the data, and 30 - a random access memory (103) comprising registers adapted to   save variables modified during the execution of said program.   28. Apparatus for processing (10) a digital image, characterized in that it comprises means suitable for implementing the method according to   any one of claims 1 to 13.   29. Apparatus for processing (10) a digital image, characterized   in that it comprises the device according to any one of claims 14 to 27.