Method for developing and deploying an improved configuration of an active network and acoustic buoys

Abstract

Method for developing and deploying an improved configuration of an active acoustic buoy network. Method for developing (1) and deploying (2) an improved configuration (Rc) of an active acoustic buoy network over a geographic area divided into a grid of squares, wherein: ● the improved configuration (1) is determined iteratively; and ● the improved configuration (Rc) is deployed (2). Figure for the abstract: [Fig.1]

Description

Title of the invention: Method for developing and deploying an improved configuration of an active network of acoustic buoys

[0001] The present invention relates to a method for developing and deploying an improved configuration of an active network of acoustic buoys.

[0002] The scope of the invention is that of acoustic buoy networks or "sonobuoy" in English. A configuration of an acoustic buoy network is understood to mean the positions of the different acoustic buoys.

[0003] Anti-submarine warfare, abbreviated as ASW, refers to the search for submarines at sea, in deep waters, or in coastal waters using active and passive means. The means considered include sonars, deployed from various vehicles such as frigates or autonomous vessels, helicopters, aircraft or aerial drones, and submarines.

[0004] An active acoustic buoy network is understood to mean a network operating with active and / or passive acoustic buoys.

[0005] Maritime patrol in anti-submarine warfare (ASW) relies on the use of acoustic buoys, deployed from the air and expendable (they are scuttled after use), from an aircraft or helicopter (more rarely from a ship). They can be released in large numbers and activated remotely (via UHF radio link), possibly long after being released, after a period of inactivity. Their range varies depending on environmental conditions, the target, and the sonar modes used. The buoy signals are received by radio (VHF) and processed by the aircraft.

[0006] Acoustic buoys are devices comprising a surface portion and a submerged portion. The submerged portion includes acoustic sensors that measure and record the underwater sound field at a specific depth and emit an acoustic wave at a specific frequency. The measured signal is transmitted to the surface portion, which has an antenna for transmitting the signal to an aircraft. Acoustic buoys are generally deployed by an aircraft. An active sonar system consists of a transmitter and a receiver. When the transmitter and receiver are located on the same device (an acoustic buoy), this is called a "monostatic situation," and when the transmitter and receiver are located on different devices, and not in the same location, this is called a bistatic situation.Multi-static refers to the case of a network of active and passive acoustic buoys, which allow for the creation of multiple sonar systems.

[0007] During an operation, depending on its objectives, an aircraft will have to drop buoys, exploit them and decide in real time on the next tactical actions in depending on the outcome of the processing: detection or not, acquisition of kinematic elements of the target,...

[0008] Since the beginnings of airborne ASW in the 1940s, and up to the present day, the number of buoys in the water has increased considerably, from a few units at the beginning, to two dozen in the 1990s, and now to several dozen, or even a hundred. Under these conditions, the time spent by the aircraft during deployment is no longer negligible, nor is the time required to traverse the area to be covered, which makes it impossible to simultaneously deploy the buoys, control all the buoys (modes and pulse transmissions), and monitor the buoy signals.

[0009] During an operation, a carrier agent deploying acoustic buoys for their mission must be able to do so while maximizing their chances of success. To achieve this, the acoustic buoys are deployed according to a plan that maximizes a success criterion (called MOE for "Measurement of Efficiency") adapted to the mission.

[0010] For example, the success criterion may aim to ensure that the detection of an underwater vehicle in the surface of the mission area is safe, or that the detection of an underwater vehicle along the length of the barrier is safe.

[0011] Defining a useful deployment plan is complex due to the large number of possible combinations: there are a very large number of possible locations for the acoustic buoys and a significant number of different sensor types, not all of which are compatible with each other. A discrete approach is taken by dividing the operating area into a grid of regular cells (for example: rectangular, square, hexagonal, or any other tiling of the plane relevant to the problem); denoting the number of cells E, and the number of acoustic buoys to be placed B (only one type of buoy for simplicity), the number of possible sonar systems is on the order of:

[0012] N = E B

[0013] By way of illustration, for an area 100 kilometers on each side, with a discretization step of 500 meters, we count: 200 cells per side, and E=40,000 cells in total. For 10 buoys (an aircraft load can reach 100 buoys), we obtain an enormous figure:

[0014] N = 40.0001-1,05 1046

[0015] The number of calculations required to estimate the value of a solution is even greater since it would be necessary to estimate the detection capacity of each buoy network at each point, i.e., NCalculs = N*E = EB+1

[0016] The number of sonar system configurations is gigantic, and a systematic approach cannot be achieved in a reasonable time.

[0017] Furthermore, the deployment plan must also take into account the performance of the active sonar systems formed by the acoustic buoys (wireless sensors), and meet a multitude of constraints: • Performance calculations must take into account underwater topography, including coastlines. • The choice of acoustic buoys must take into account the compatibility or incompatibility of the sensors of the acoustic buoys with each other (frequency band, performance), • The load of the carrier agent is fixed once on mission, and it is only possible to exploit the available acoustic buoys.

[0018] The problem posed is therefore complex. The computational context requires that a solution be proposed within a limited time (30 minutes). An exact solution can only be proposed within a reasonable time for small areas, and therefore a small number of cells to cover, which does not correspond to operational uses.

[0019] A multistatic sonar network, or MSN (Multistatic Sonar Network), is defined as a set of active sonar systems in a monostatic and / or bistatic configuration. These sonar systems result from the combination of a source and a receiver originating from a single buoy or from two separate buoys.

[0020] In the scientific literature related to the deployment and configuration of wireless sensor networks or WSNs (Wireless Sensor Network), of which MSNs are a special case of WSNs, the following three types of problems are found: - Barrier cover, or BC for "Barrier Coverage" in English, - Point (target) coverage, or PC for "Point (target) Coverage" in English, and - Area coverage or AC for acronym of “Area (blanket) Coverage” in English.

[0021] It is known, for AC area coverage, to use a multi-objective particle swarm optimization (PSO) algorithm to determine the location of sensors by maximizing coverage and simultaneously minimizing the number of sensors required. It is known to use a genetic algorithm to optimize both the location of individual sensors (including depth) and the emission times of individual acoustic buoys in a non-homogeneous environment (known as SCOUT). Different geometric arrangements have been studied in open water to find the most effective one for coverage of a large area. Some use a genetic algorithm to determine the positions of the different sensors. Some derive an analytical theory to predict the probability of detection based on randomly deployed sensors and use it to determine optimal models. Building on this work, some use simulations to quantify the impact of the direct path effect on coverage. Some use simulations to quantify the coverage of a moving source performing parallel scans in a stationary receiving field. Others propose several models with different linearizations and compare them in the context of two problems: maximizing the covered area with a limited number of sensors and minimizing the network cost (the number of sensors) to achieve 100% coverage (fixed performance).

[0022] For barrier coverage in the field of multistatic radar networks, a method for optimally placing radars on a segment to maximize worst-case intrusion detectability is known. A method based on the "equipartition strategy" is known for determining the optimal deployment schemes of multistatic radars for a subproblem. These models are then used in an integer linear program (ILP) and an exhaustive search for solving the overall problem. An ILP and an exhaustive search are known for determining several barrier coverages of unequal widths of the area of ​​influence (with different deployment sequences).

[0023] Regarding point coverage PC, an algorithm called DiBS (Divide Best Sector) is known for placing a single source when a number of receivers are already positioned (with an iterative extension for placing multiple sources). The optimal placement of sources and receivers for this type of problem in open water (without obstacles) is known, using two ILPs (DISC-LOC-M and DISC-LOC-ENUM) as well as two heuristics, Adapt-LOC and Iter-LOC, based on a procedure called LOC-GEN-II (an improved version of LOC-GEN). Also known are an exact OPT-LOC solution method and a greedy-LOC heuristic for placing sources when receivers are already deployed.

[0024] One object of the invention is to provide a method for developing and deploying an improved configuration of an active network of acoustic buoys.

[0025] According to one aspect of the invention, a method is proposed for developing and deploying an improved configuration of an active network of acoustic buoys over a geographical area divided into a grid of squares, in which:

[0026] The improved configuration is determined by the iterative steps of: updating a current configuration initialized by an initial coverage rate configuration; determination of a first neighborhood corresponding to the application of a first neighborhood operator from an ordered increasing list of neighborhood operators; updating a current neighborhood initialized by the first current neighborhood; random selection of a random configuration in the current neighborhood; determination of an improved sub-configuration through the iterative steps of: updating a current sub-configuration initialized by the random configuration; determination of a first sub-neighborhood corresponding to the application of a first neighborhood operator from an increasing ordered sub-list of neighborhood operators; updating a current sub-neighborhood initialized by the first current sub-neighborhood; determination of a candidate neighboring subconfiguration by exploring the current subneighborhood; first test if the coverage rate of the candidate sub-configuration is greater than the coverage rate of the current sub-configuration; If the first test is negative, the coverage rate of the candidate subconfiguration being lower than the coverage rate of the current subconfiguration, a second test is performed if all subneighborhoods have been explored; if the second test is negative, the current subneighborhood is expanded by applying the next neighborhood operator from the ordered sublist which is passed on to the update of the current subneighborhood; if the first test is positive, the value of the neighboring candidate subconfiguration is assigned to the current subconfiguration by returning to the update step; if the second test is positive, the coverage rate of the neighboring candidate subconfiguration being less than the coverage rate of the current subconfiguration, we leave the iterative determination step for a third test step; third test if the coverage rate of the current sub-configuration is greater than the coverage rate of the current configuration; - if the third test is negative, the rate of the current configuration being greater than the coverage rate of the current sub-configuration, a fourth test is performed if all neighborhoods have been explored; - if the fourth test is negative, the current neighborhood is expanded by applying the next neighborhood operator from the ordered list which is passed on to the update of the current neighborhood; - if the third test is positive, with the current configuration's coverage rate being lower than the current sub-configuration's coverage rate, the current configuration's value is updated with the current sub-configuration's value; and - if the fourth test is positive, the improved current configuration is deployed.

[0027] In one embodiment, the increasing ordered list of neighborhood operators and / or the ordered sublist of neighborhood operators, includes knm-shift operators, corresponding to the shift of k buoy(s) in a ring corresponding to a ring of squares located around the buoy in question at a distance of n squares to m squares inclusive, ordered according to the growth of k, and between shift operators of identical values ​​of k, according to the decrease of n, and between shift operators of identical values ​​of k and n, according to the growth of m.

[0028] Alternatively, the increasing ordered list of neighborhood operators and / or the ordered sublist of neighborhood operators, includes k-swap exchange operators, corresponding to k exchanges of positions of k pair(s) of buoys, ordered according to the growth of k, and ordered after any possible offset operators.

[0029] According to one embodiment, the descent-by-exploration step of the current subneighborhood is a simple descent in which the first improving subconfiguration is chosen in the current subneighborhood.

[0030] Alternatively, the determination step by descent by exploration of the current subneighborhood is a deep descent in which the best of the improving subconfigurations in the current subneighborhood is chosen.

[0031] In one embodiment, the method includes a test step of another stopping criterion including reaching a threshold calculation time, and / or a number of iterations, and / or a successive number of iterations without improvement in the coverage rate, and / or an average improvement in the coverage rate over a successive number of iterations less than a threshold, and / or a threshold coverage rate reached.

[0032] According to one embodiment, a step of determining isolated buoys and modifying their position by relocation, using a contribution score.

[0033] In one embodiment, the geographical space is divided into a grid of square-shaped cells.

[0034] According to one embodiment, the geographical space is divided into a grid of hexagonal-shaped squares.

[0035] The invention will become clearer upon reading the following description, given solely by way of non-limiting example, and made with reference to the drawings in which:

[0036] [Fig. 1] schematically illustrates a method for developing and deploying an improved configuration of an active network of acoustic buoys over a geographical space divided into a grid of squares, according to one aspect of the invention;

[0037] [Fig.2] schematically illustrates a neighborhood operator, with a grid of square cells, according to one aspect of the invention;

[0038] [Fig.3] schematically illustrates a neighborhood operator, with a grid of hexagonal squares, according to one aspect of the invention.

[0039] Across all figures, elements with identical references are similar.

[0040] Figure 1 schematically represents a method for developing and deploying an improved configuration of an active network of acoustic buoys over a geographical area divided into a grid of squares, according to one aspect of the invention,

[0041] The improved configuration 1 is determined iteratively, and the deployment 2 of the improved configuration is carried out.

[0042] An initial Rinit configuration with an initial coverage rate TCinit is chosen, for example at random from acceptable configurations.

[0043] Alternatively, it is also possible to use Rinit as the initial configuration, the result of a known configuration development process, for example that disclosed in the article "An improved two-phase heuristic for active multistatic sonar network configuration" by Owein Thuillier, Nicolas Le Josse, Alexandru-Liviu Olteanu, Marc Sevaux, and Hervé Tanguy, Expert Systems with Applications 238 (2024), page(s): 121985, issn: 0957-4174, doi: 10.1016 / j.eswa.2023.121985.

[0044] The improved configuration Rc of an active network of acoustic buoys is determined over a geographical space divided into a grid of squares, by the iterative steps of: - update 3 of a current configuration Rc initialized by the initial configuration Rinit of initial coverage rate TCinit; - determination 4 of a first neighborhood V1 corresponding to the application of a first neighborhood operator of an increasing ordered list LO of neighborhood operators; - update 5 of a current neighborhood Vc initialized by the first current neighborhood V1; random choice 6 of a random configuration RA in the current neighborhood Vc; Determination 7 of an improved sub-configuration through the iterative steps of: update 8 of a current sub-configuration RD initialized by the random configuration RA; determination 9 of a first sub-neighborhood SV1 corresponding to the application of a first neighborhood operator of an increasing ordered sub-list SLO of neighborhood operators; update 10 of a current subneighborhood SVc initialized by the first current subneighborhood SV 1; determination 11 of a candidate neighboring subconfiguration RL by exploration Expl of the current subneighborhood SVc; first test 12 if the coverage rate of the candidate subconfiguration RL is greater than the coverage rate of the current subconfiguration RD; if the first test 12 is negative, the coverage rate of the candidate subconfiguration RL being less than the coverage rate of the current subconfiguration RD, a second test 13 is performed if all sub-neighborhoods have been explored; if the second test 13 is negative, we expand 14 the current subneighborhood by applying the next neighborhood operator of the ordered SLO sublist which is passed to the update 10 of the current subneighborhood SVc; if the first test 12 is positive we assign the value of the neighboring candidate subconfiguration RL to the current subconfiguration RD by returning to the update step 8; if the second test 13 is positive, the coverage rate of the neighboring candidate subconfiguration RL being less than the coverage rate of the current subconfiguration RD, we leave the iterative determination step 7 for a third test step 16; third test 16 if the coverage rate of the current sub-configuration RD is greater than the coverage rate of the current configuration Rc; if the third test 16 is negative, the rate of the current configuration Rc being greater than the coverage rate of the current sub-configuration RD, a fourth test 17 is performed if all sub-neighborhoods have been explored; if the fourth test 17 is negative, we widen 18 the current neighborhood Vc by applying the next neighborhood operator from the ordered list LO which is passed to the update 5 of the current neighborhood Vc; - if the third test 16 is positive, the rate of the current configuration Rc being less than the coverage rate of the current sub-configuration RD, the value of the current configuration Rc is updated with the current sub-configuration RD; and - if the fourth test 17 is positive, deployment 2 of the improved current Rc configuration is carried out.

[0045] The coverage rate is for example clearly defined in the article ("An improved two-phase heuristic for active multistatic sonar network configuration", by Owein Thuillier, Nicolas Le Josse, Alexandru-Liviu Olteanu, Marc Sevaux, and Hervé Tanguy, Expert in Systems with Applications 238 (2024), page(s): 121985, issn: 0957-4174, doi: 10.1016 / j.eswa.2023.121985).

[0046] The coverage rate is defined as the proportion of sea cells covered by the multistatic sonar array. A cell is considered covered if the probability of detecting a target positioned at the center of that cell is greater than a threshold (in our case, for example, 0.95). The probability of detecting a target at the center of a cell t is calculated by the following steps: - For a compatible transmitter s / receiver r pair; - Calculate the equivalent acoustic distance:

[0047] _ H Pt,s,r -\at,sat,r - Calculate the probability of detection: Pd(t,s,r) (equation 7 of the cited article):

[0048] 1+1OW - The probability of detecting a target positioned in the middle of cell t by the co network is calculated by assuming that it would be detected at least once (equation 8 of the cited article): [00491(t) = 1 - ^1 - P^(t) - The number of squares covered is calculated using the following formula (equation 3 from the cited article):

[0050] - I being the function that returns 1 if the argument is greater than a value q>, and 0 otherwise.

[0051] The increasing ordered LO list of neighborhood operators and / or the ordered SLO sublist of neighborhood operators, includes knm-shift operators, corresponding to the shift of k buoy(s) in a ring corresponding to a ring of squares located around the buoy in question at a distance of n to m squares inclusive, ordered according to the growth of k, and between operators of shift of identical values ​​of k, according to the decrease of n, and between shift operators of identical values ​​of k and n, according to the growth of m.

[0052] The increasing ordered LO list of neighborhood operators and / or the ordered sublist (SLO) of neighborhood operators, includes k-swap exchange operators, corresponding to k exchanges of positions of k pair(s) of buoys, ordered according to the growth of k, and ordered after any possible offset operators.

[0053] The current subneighborhood exploration descent step is a simple descent in which the first improving subconfiguration in the current subneighborhood is chosen. Alternatively, the current subneighborhood exploration descent step is a deep descent in which the best subconfiguration in the current subneighborhood is chosen. The method may include a step 19 for testing another stopping criterion, including reaching a threshold computation time, and / or a number of iterations, and / or a successive number of iterations without improvement in the coverage rate TC, and / or an average improvement in the coverage rate over a successive number of iterations below a threshold, and / or a threshold coverage rate being reached. In which case, the value of the current subconfiguration RD is assigned 21 to the current configuration Rc.

[0054] The method may include a step 20 of determining isolated buoys and modifying their position by relocation, using a contribution score.

[0055] The relocation process uses the calculation of a contribution score or isolation score for a given buoy, and its comparison to a threshold. If the score is below the threshold, then the buoy is considered isolated (i.e., it contributes little or nothing to the detection of targets in the area).

[0056] In more detail, the relocation is carried out as follows: - We choose a buoy to test b. This choice can be made by drawing lots, or by a systematic analysis of all the buoys. - We calculate the list L(b) of all sonar systems having at least one source or receiver belonging to the buoy of interest. - The contribution score S is calculated as follows: • S = sum h(p(s,r) p for all cells t (where a target could be located), and for all sonar systems (source-receiver s,r) in the list L(b) • The function h is calculated by: h(p) = log (1-p) / log(l-<])) • ¢) is a parameter representing the probability of detection that one wants to reach at each point (threshold), and for example chosen equal to 0.95 - If the score S is less than an epsilon threshold, buoy b is relocated • The epsilon threshold is a parameter of the algorithm. • The epsilon threshold value can be high, to systematically move an isolated buoy. However, the higher the threshold, the less chance there is of finding new configurations (sonars will not be able to be temporarily isolated). • Buoy b will be moved in the vicinity of a compatible buoy bc (Tx or TxRx if b is Rx or TxRx, and Rx or TxRx if b is Tx or TxRx, and within compatible frequency ranges) • We calculate the LC(b) list of compatible buoys • A buoy bc is randomly drawn from LC(b) • We calculate a neighborhood V(bc) of type 1-5-1 shift around the buoy bc • A position is randomly selected in the neighborhood V(bc) • Buoy b is moved to this position (in this way, we ensure that its contribution in its new location will be significant)

[0057] Geographic space can be divided into a grid of square-shaped squares, as illustrated in [Fig.2] or into a grid of hexagonal-shaped squares, as illustrated in [Fig.3] or into squares of other shapes.

[0058] The present invention allows for simplicity, with few parameters, and the use of a choice between a few variants (deterministic or stochastic operation, systematic or limited local search).

[0059] This is a process for which the computational budget can be fixed in advance, and the best solution obtained at the end of this computational budget can be accepted (an algorithm called "anythne").

[0060] The method of the invention allows a choice of expressive and varied neighborhoods, which allows an efficient exploration of the solution space and a better quality of solutions.

[0061] The solutions proposed by this algorithm are sufficiently close to the optimum to be exploited by an aircraft dropping a network of acoustic buoys.

[0062] The neighborhood variation operation allows for the generation of multiple candidate solutions with varying characteristics. This gives an operator a choice between several solutions of equivalent quality.

[0063] The reliability of the proposed method could make it possible to consider embedding such a system in a drone operating autonomously, without human supervision.

[0064] The process is ideally implemented on an embedded computer (with a programming language adapted to scientific calculations), and connected to the mission system: - The operator provides information on the tactical situation, including the area of ​​interest (its size) and the nature of the target being sought, as this determines the performance of the sonars available in the cargo. - The operator defines the calculation conditions: the discretized model, for example a square, rectangular or hexagonal pattern; the cell size, for example: cells of 500m on each side, or less, or more (for example from 1 meter to 10 kilometers); and the computation budget (number of iterations, maximum calculation time), - The mission system performs the optimization using a neighborhood-based metaheuristic that utilizes the neighborhoods described previously. - The operator chooses from the algorithm's proposals and transmits his order to the mission system, which plans the deployment of the buoys by the aircraft.

[0065] The aircraft could also be a remotely piloted or autonomously operating drone. In this case, the robustness of the method would be a tool enabling the drone to automatically and autonomously calculate the best configuration for an acoustic buoy network.

Claims

13 Demands

1. A method for developing (1) and deploying (2) an improved configuration (Rc) of an active acoustic buoy network over a geographic area divided into a grid of squares, wherein: the improved configuration (1) is determined by the iterative steps of: update (3) of a current configuration (Rc) initialized by an initial configuration (Rinit) of initial coverage rate (TCinit); determination (4) of a first neighborhood (VI) corresponding to the application of a first neighborhood operator of an increasing ordered list (LO) of neighborhood operators; update (5) of a current neighborhood (Vc) initialized by the first current neighborhood (VI); random choice (6) of a random configuration (RA) in the current neighborhood (Vc); determination (7) of an improved subconfiguration through the iterative steps of: update (8) of a current subconfiguration (RD) initialized by the random configuration (RA); determination (9) of a first sub-neighborhood (SV1) corresponding to the application of a first neighborhood operator of an increasing ordered sub-list (SLO) of neighborhood operators; update (10) of a current subneighborhood (SVc) initialized by the first current subneighborhood (SV1); determination (11) of a candidate neighbor subconfiguration (RL) by exploration (Expl) of the current subneighborhood (SVc); first test (12) if the coverage rate of the candidate subconfiguration (RL) is greater than the coverage rate of the current subconfiguration (RD); if the first test (12) is negative, the coverage rate of the candidate subconfiguration (RL) being less than the coverage rate of the current subconfiguration (RD), a second test (13) is performed if all subneighborhoods have been explored; if the second test (13) is negative, the current subneighborhood is expanded (14) by applying the next neighborhood operator of the ordered sublist (SLO) which is passed to the update (10) of the current subneighborhood (SVc); - If the first test (12) is positive, the value of the candidate neighboring subconfiguration (RL) is assigned to the current subconfiguration (RD) by returning to the update step 8; - If the second test (13) is positive, the coverage rate of the candidate neighboring subconfiguration (RL) being less than the coverage rate of the current subconfiguration (RD), the iterative determination step (7) is exited for a third test step (16); - Third test (16) if the coverage rate of the current subconfiguration (RD) is greater than the coverage rate of the current configuration (Rc); - If the third test (16) is negative, the coverage rate of the current configuration (Rc) being greater than the coverage rate of the current subconfiguration (RD), a fourth test (17) is performed if all neighborhoods have been explored;- if the fourth test (17) is negative, the current neighborhood (Vc) is expanded (18) by applying the next neighborhood operator from the ordered list (LO) which is passed to the update (5) of the current neighborhood (Vc); - if the third test (16) is positive, the rate of the current configuration (Rc) being less than the coverage rate of the current sub-configuration (RD), the value of the current configuration (Rc) is updated (3) with the current sub-configuration (RD); and - if the fourth test (17) is positive, the deployment (2) of the improved current configuration Rc is carried out.

2. A method according to claim 1, wherein the increasing ordered list (LO) of neighborhood operators and / or the ordered sublist (SLO) of neighborhood operators comprises knm-shift operators, corresponding to the shift of k buoy(s) in a ring corresponding to a ring of squares located around the buoy in question at a distance of n squares to m squares inclusive, ordered according to the increase of k, and between shift operators of identical values ​​of k, according to the decrease of n, and between shift operators of identical values ​​of k and n, according to the growth of m.

3. A method according to claim 1 or 2, wherein the increasing ordered list (LO) of neighborhood operators and / or the ordered sublist (SLO) of neighborhood operators, includes k-swap exchange operators, corresponding to k exchanges of positions of k pair(s) of buoys, ordered according to the growth of k, and ordered after any offset operators.

4. A method according to any one of claims 1 to 3, wherein the determination step (11) by exploration descent (Expl) of the current subneighborhood (SVc) is a simple descent in which the first improving subconfiguration is chosen in the current subneighborhood.

5. A method according to any one of claims 1 to 3, wherein the determination step (11) by exploration descent (Expl) of the current subneighborhood (SVc) is a deep descent in which the best of the subconfigurations in the current subneighborhood is chosen.

6. A method according to any one of the preceding claims, comprising a test step (19) of another stopping criterion comprising reaching a threshold computation time, and / or a number of iterations, and / or a successive number of iterations without improvement in the coverage rate (CR), and / or an average improvement in the coverage rate over a successive number of iterations below a threshold, and / or a threshold coverage rate reached.

7. A method according to any one of the preceding claims, comprising a step of determining (20) isolated buoys and modifying their position by relocation, using a contribution score.

8. A method according to any one of claims 1 to 6, wherein the geographical space is divided into a grid of square-shaped cells.

9. A method according to any one of claims 1 to 6, wherein the geographical space is divided into a grid of hexagonal-shaped squares.

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