A method and related apparatus for optimizing meme islands for complementary sequence sets.

Abstract

This invention discloses a meme island optimization method and related apparatus for complementary sequence sets, belonging to the field of complementary sequence design. The method includes: constructing multiple island subpopulations that evolve in parallel; initializing a global archive for recording the history of search space region visits; performing population evolution in parallel on multiple islands; evaluating each candidate complementary sequence set according to a fitness function that incorporates region guidance; exchanging elite individuals among multiple islands when a preset migration condition is met; and outputting the optimal complementary sequence set found among all islands when an iteration condition is satisfied. By introducing region guidance based on the global archive into the fitness function, the search is actively guided to unexplored regions, systematically avoiding the search process from stagnating in the same basin, avoiding getting trapped in local optima, significantly improving global exploration capability, and reducing the risk of premature convergence.

Description

Technical Field

[0001] This invention relates to the field of complementary sequence design, and more particularly to a meme island optimization method and related apparatus for complementary sequence sets. Background Technology

[0002] In key technology fields such as wireless communication and radar sensing, designing complementary sequence sets with specific correlation characteristics (such as spreading codes and pilot sequences in communication systems, and transmit waveform codes in radar systems) is a fundamental and highly challenging task. This type of design task directly determines the key performance characteristics of the system: in communication, the correlation characteristics of complementary sequence sets affect multiple access interference suppression, channel estimation accuracy, and system capacity; in radar, the performance of complementary sequence sets is related to resolution, ranging and velocity measurement accuracy, and anti-jamming capability. Mathematically, this task can be abstracted as a combinatorial optimization problem with high computational complexity and a vast and rugged search space.

[0003] Existing technologies mainly fall into two categories: the first is traditional algebraic construction methods, which can generate complementary sequence sets with provably optimal properties under specific sequence lengths and character sets. However, due to their structural constraints, they generally lack flexibility and are difficult to adapt to diverse design needs (such as complementary sequence sets for specific channel environments or interference modes). To overcome these limitations, the second approach is metaheuristic search algorithms such as genetic algorithms and simulated annealing, which are widely used for complementary sequence sets due to their versatility in unconstrained optimization problems. However, in scenarios like complementary sequence set design, where the search space is vast and the structure is complex, these methods are often constrained by the trade-off between "exploration and exploitation," exhibiting unavoidable convergence limitations and making the algorithm prone to prematurely falling into local optima. Based on this, the Memetic Algorithm (MA) introduces a mechanism combining global population search and local fine-grained search, improving the search efficiency of complementary sequence sets through collaborative exploration and exploitation, and demonstrating excellent performance in multiple fields. Nevertheless, in complex scenarios like communication and radar complementary sequence set design, which have vast search spaces and numerous suboptimal local optima, this algorithm still faces the risk of converging to suboptimal solutions.

[0004] In recent years, with the development of deep learning and reinforcement learning, intelligent optimization methods have been gradually introduced into the field of complementary sequence set design. For example, AlphaSeq, inspired by AlphaZero, models the complementary sequence set discovery problem as an agent game task; while generative models such as HpGAN learn the distribution of high-quality sequences using generative adversarial networks. Although these methods have shown strong search potential, their model structures are complex, training costs are high, and they are highly dependent on large-scale high-quality training data, which greatly limits their applicability to the complementary sequence set design problem in scenarios where prior data is lacking or data is scarce, such as emerging communication standards or new radar applications. Summary of the Invention

[0005] The purpose of this invention is to overcome the problems of the prior art and provide a meme island optimization method and related apparatus for complementary sequence sets.

[0006] The objective of this invention is achieved through the following technical solution: a meme island optimization method for complementary sequence sets, comprising the following steps:

[0007] Construct multiple islands that evolve in parallel, each island being an independent subpopulation. Individuals in the subpopulation are a set of candidate complementary sequences to be optimized. At the same time, initialize a global archive to record the access history of the search space region.

[0008] Population evolution based on the meme algorithm is performed in parallel on multiple islands. During the population evolution process, each candidate complementary sequence set is evaluated according to a fitness function that integrates a complementary sequence signal quality index and a region-guided approach. When a preset migration condition is met, elite individuals selected by the fitness function are exchanged between multiple islands. The complementary sequence signal quality index is at least one of the autocorrelation, cross-correlation, or spectral characteristics of the complementary sequence. The region-guided approach is calculated based on the access frequency of the candidate complementary sequence sets in the global archive mapped to the search space region, with a higher access frequency resulting in a greater penalty.

[0009] When the iteration condition is met, output the final set of complementary sequences with the optimal fitness function value found in all islands.

[0010] In one example, a hash function is used to map the set of candidate complementary sequences to a search space region, and the calculated hash value is stored as a key in a global archive, recording only the number of times the region is accessed.

[0011] In one example, the region guidance is quantized based on the Hamming distance between the candidate complementary sequence set and the historical complementary sequence set corresponding to the regions already recorded in the global archive.

[0012] In one example, a hybrid operation of global and local search is performed within each island. The global search includes selection, crossover, and mutation operations, while the local search includes optimization of a selected set of candidate complementary sequences using a simulated annealing algorithm.

[0013] In one example, the local search step size of the simulated annealing algorithm is adaptively adjusted based on the quality of the set of candidate complementary sequences to be optimized.

[0014] In one example, the mutation probability of the mutation operation is adaptively adjusted based on the diversity of the candidate complementary sequence set in the population.

[0015] In one example, a shared fitness mechanism is used to assess the fitness of individuals during population evolution.

[0016] It should be further noted that the technical features corresponding to the above examples can be combined or replaced to form new technical solutions.

[0017] The present invention also includes a computer program product comprising a computer program that, when executed by a processor, implements the steps of the meme island optimization method for complementary sequence sets formed by any or a combination of the above examples.

[0018] The present invention also includes a storage medium storing computer instructions that, when executed, perform the steps of the meme island optimization method for complementary sequence sets formed by any or more of the above examples.

[0019] The present invention also includes a terminal comprising a memory and a processor, the memory storing computer instructions executable on the processor, the processor executing the steps of the meme island optimization method for complementary sequence sets formed by any or more of the above examples when running the computer instructions.

[0020] Compared with the prior art, the beneficial effects of the present invention are:

[0021] 1. In one example, the method of the present invention introduces a region-guided approach based on a global archive into the fitness function, actively guiding the search to unexplored areas. This systematically avoids the search process from stagnating in the same basin, fundamentally changing the behavior of traditional genetic algorithms and simulated annealing, which rely solely on current population information and are prone to getting trapped in local optima. This significantly improves global exploration capabilities and reduces the risk of premature convergence. At the same time, through the random search framework of "island model + meme algorithm", it breaks free from the strict mathematical constraints of traditional algebraic construction methods, enabling the optimization of various signal quality indicators for design requirements such as low sidelobe waveforms in radar and low cross-interference spreading codes in communication, and generating novel high-performance sequences that cannot be constructed by traditional methods.

[0022] In addition, the method of this invention is based on a mature evolutionary computation paradigm, which does not require expensive model training and a large amount of labeled data. The computational overhead mainly comes from parallelizable population evaluation. While maintaining powerful search capabilities, it also has computational efficiency and versatility, and is especially suitable for emerging scenarios where prior data is lacking or data is scarce.

[0023] 2. In one example, a high-cardinality hash function is used, which ensures that hash collisions will hardly occur during the meme algorithm search process, thus guaranteeing that the novelty measurement of the region is always accurate and effective, thereby maintaining the driving force of exploration and making the method of the present invention more robust.

[0024] 3. In one example, the island model supports parallel and diverse exploration and has good parallelism. It can be expanded by increasing the number of islands (computation nodes) to cope with larger-scale search problems. The meme algorithm achieves fine local optimization. Through the collaborative design of "macro-parallel exploration of the island model + micro-fine optimization of the meme algorithm", the method has both a broad search vision and a powerful local mining capability. Attached Figure Description

[0025] The specific embodiments of the present invention will be further described in detail below with reference to the accompanying drawings. The accompanying drawings are provided to provide a further understanding of the present application and constitute a part of the present application. The same reference numerals are used in these drawings to denote the same or similar parts. The illustrative embodiments of the present application and their descriptions are used to explain the present application and do not constitute an improper limitation of the present application.

[0026] Figure 1 A flowchart illustrating a method provided as an example of the present invention;

[0027] Figure 2 This is a method block diagram provided as an example of the present invention. Detailed Implementation

[0028] The technical solution of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0029] Furthermore, the technical features involved in the different embodiments of the present invention described below can be combined with each other as long as they do not conflict with each other.

[0030] To address the problem of complementary sequence design, this invention proposes a meme island optimization method for complementary sequence sets, which can be applied to radar signal design, communication coding design, and other fields. The embodiments of this invention are illustrated using radar complementary sequence design as an example, demonstrating how the method outputs one or more radar waveforms with extremely low peak sidelobe levels. Figure 1 As shown, the method includes the following steps:

[0031] S1: Each island is an independently evolving subpopulation, which consists of multiple sets of candidate complementary sequences as individuals. At the same time, a global archive (global novelty archive) is initialized to record the access history of the search space region.

[0032] Specifically, randomly generated Initial population Each individual in the population Each candidate complementary sequence represents a candidate radar transmit waveform in this example.

[0033] S2: Population evolution based on meme algorithm is performed in parallel on multiple islands. During the population evolution process, each candidate complementary sequence set is evaluated according to a fitness function that integrates the quality index of complementary sequence signals and the region guidance. When the preset migration conditions are met, elite individuals selected according to the fitness function are exchanged between multiple islands.

[0034] Specifically, the fitness function is designed based on a complementary sequence signal quality index and region guidance. The complementary sequence signal quality index is at least one of the autocorrelation, cross-correlation, or spectral characteristics of the complementary sequence; in this example, the signal quality index is the peak sidelobe level of the waveform. Region guidance is calculated based on the access frequency of the candidate complementary sequence set mapped to the search space region in the global archive; the higher the access frequency, the greater the penalty. For each individual in the population... Calculate its original objective function value It then queries the global archives and calculates the individual's punishment fitness value according to the punishment fitness formula. Specifically, in this example, the fitness function is expressed as:

[0035] ;

[0036] in, Represents an individual The penalty fitness value; This represents a novelty penalty factor, used to balance quality and exploration. The region hash value representing the complementary sequence set; Indicates the number of visits to the region; The original objective function, which is used to evaluate the quality index of complementary sequence signals, needs to be minimized. Its optimization objective is:

[0037] ;

[0038] in, Indicates the globally optimal solution; This represents the search space.

[0039] Furthermore, the area access count is updated after each assessment:

[0040] ;

[0041] in, Represents elite individuals; Represents a hash function; Indicates the global archive;

[0042] By designing the fitness function as described above, the optimization is transformed from a single pursuit of quality to a dual-objective search of quality and novelty, encouraging the exploration of unvisited or less visited regions.

[0043] Furthermore, the evolutionary algorithm is run independently and in parallel on multiple islands (subpopulations), and each island meets the migration conditions. At that time, each island selects elite individuals and sends them to neighboring islands, replacing the worst individuals from those islands. This introduces superior external genes, preventing premature convergence on a single island and maintaining global diversity. Specifically, the migration and exchange mechanism is as follows:

[0044] ;

[0045] in, Indicates the generation number; Indicates the migration interval; This represents the modulo operation; Indicates the first The islands in the The new population at the next generation, in this example, is a set of radar transmission waveforms used for next-generation optimization after migration and exchange have been completed; Indicates the first The first island Population at that time; Indicates a person of inferior quality; It indicates the influx of elite individuals.

[0046] Preferably, during population evolution, it is determined whether the population has fallen into a local optimum:

[0047] To check if an island has not shown any improvement in fitness for several consecutive generations, the stagnation condition is:

[0048]

[0049] in, Indicates the first The islands as of the end of the The continuous stationary algebra of the generation; This indicates the threshold for detecting stagnation.

[0050] If stagnation occurs, a small number of elites are retained, and the population is completely reorganized through high-intensity perturbation and random initialization to escape the local optimum.

[0051] S3: When the iteration condition is met, output the set of optimal complementary sequences with the best fitness function value found in all islands as the final result, that is, obtain one or more radar waveforms with extremely low peak sidelobe levels.

[0052] Among them, when the maximum number of iterations is reached When the iteration condition is met.

[0053] In one example, a hash function is used to map the candidate complementary sequence set to a search space region, and the calculated hash value is stored as a key in a global archive to record the visited search space regions and their frequency of access. The initial state is empty. The hash function is calculated as follows:

[0054] ;

[0055] in, Indicates the current cumulative hash value; This represents the previous accumulated hash value; This represents the left shift operator; This indicates the current input byte value.

[0056] In one example, based on the individual's behavioral characteristics (mapped to a certain search space region via a hash function), the Hamming distance between the candidate complementary sequence set and the historical complementary sequence set corresponding to the recorded regions in the global archive is calculated. The greater the distance, the higher the novelty score, measuring its uniqueness. In this example, the region guidance is calculated using Hamming distance. Represented as:

[0057]

[0058] in, These represent two complementary sequences to be compared; Indicates the length of the complementary sequence; complementary sequences In the The element value at each position.

[0059] In one example, a hybrid operation of global and local search is performed within each island. The global search includes selection, crossover, and mutation operations based on penalized fitness, while the local search involves fine-tuning a selected set of candidate complementary sequences using simulated annealing to escape local optima.

[0060] The cooling strategy for simulated annealing is as follows:

[0061]

[0062] in, Indicates the first Temperature during local search; Indicates the first Temperature during local search; This represents the temperature attenuation coefficient. In radar waveform design applications, the high-temperature stage allows for significant structural adjustments to the coded sequence to explore new waveform patterns, while the low-temperature stage focuses on subtle optimizations of existing high-quality waveforms to further reduce their sidelobe levels.

[0063] Preferably, the local search step size of the simulated annealing algorithm is adaptively adjusted according to the quality of the candidate complementary sequence set to be optimized, as expressed by:

[0064] ;

[0065] in, This represents the total number of local search steps allocated to an individual; Indicates the number of steps in the baseline local search; Indicates the reference target value; Represents a constant.

[0066] In one example, the mutation probability of the mutation operation is adaptively adjusted based on the diversity of the candidate complementary sequence set in the population, and the calculation expression is:

[0067] ;

[0068] in, Indicates the probability of the mutation operation; This represents the preset baseline probability of variation; , For adjustment coefficients; The structural diversity index can be quantified by calculating the standard deviation of the Hamming distance between each pair of individuals in the population.

[0069] In one example, during population evolution, a shared fitness mechanism is used to assess the fitness of individuals, further maintaining diversity. The calculation expression is as follows:

[0070] ;

[0071]

[0072] in, Indicates the shared fitness of an individual; Represents an individual Punishment adaptability; Indicates population size; For shared functions, when the distance is less than the shared radius When, the function value is Otherwise, it is 0.

[0073] Combining the above examples yields preferred examples of the present invention, such as... Figure 2 As shown, the method of the present invention includes the following steps:

[0074] S10: Addressing radar waveform design issues, generating... The initial population of each island, where each individual is a candidate radar phase-coded sequence, creates an empty global profile;

[0075] S20: In each generation, the following island optimization process is executed in parallel:

[0076] Assess the current population: Calculate the peak sidelobe level of each candidate radar phase-coded sequence as a quality index of the complementary sequence signal (original objective function value). Simultaneously, based on the individual's behavioral characteristics, i.e., mapping the individual to a specific region of the search space using a hash function, quantify the difference between the individual's region and historical search regions, and evaluate the novelty of the candidate complementary sequence. Then, fuse the quality index and novelty evaluation results to calculate the individual's fitness value. Finally, update the access count of the corresponding region in the global archive.

[0077] Evolutionary decision-making and operations: Detect whether the island has stalled in the search. If so, reorganize the population. If not, perform selection, crossover, and mutation operations on the population based on the penalty fitness value to explore new phase coding structures. Trigger simulated annealing local search on some candidate radar phase coding sequences to finely optimize their sidelobe characteristics.

[0078] Migration preparation: If the current generation meets the migration interval condition, individuals with excellent sidelobe characteristics and novel structure are selected from the local population as elite waveforms to be migrated out.

[0079] Parallel exploration and migration of islands: If the migration interval condition is met, all islands will synchronously exchange elite individuals to be migrated out according to the predetermined topology, and replace inferior individuals in the target island with the migration waveform to form the next generation of population;

[0080] Step S30: Loop judgment: If the maximum number of generations has not been reached, return to step S20 for the next generation iteration; otherwise, exit the loop and output the radar phase-coded waveform sequence with the best sidelobe characteristics found in all islands.

[0081] This invention proposes a region-guided meme island optimization method. Based on a mature island model paradigm, this method organizes the evolutionary process into parallel, semi-isolated subpopulations, thereby enhancing population diversity and improving global exploration capabilities.

[0082] Furthermore, the hash region function guidance mechanism effectively avoids premature convergence. The system explores unknown regions, actively driving the search flow towards unexplored areas, systematically preventing the search process from stagnating within the same basin, thus significantly reducing the risk of premature convergence. Simultaneously, the island model supports parallel and diverse exploration, while the adaptive meme algorithm achieves fine-grained local optimization. This collaborative design of "macro-parallel exploration of the island model + micro-fine-grained optimization of the meme algorithm" gives the framework both a broad search perspective and powerful local mining capabilities.

[0083] The present invention also provides a computer program product, comprising a computer program that, when executed by a processor, implements the steps of the meme island optimization method for complementary sequence sets formed by any or a combination of the above examples. The processor may be a single-core or multi-core central processing unit or a specific integrated circuit, or one or more integrated circuits configured to implement the present invention.

[0084] The present invention also provides a storage medium having the same inventive concept as the meme island optimization method for complementary sequence sets formed by any or more of the above examples, wherein computer instructions are stored thereon, which, when executed, perform the steps of the meme island optimization method for complementary sequence sets formed by any or more of the above examples.

[0085] Based on this understanding, the technical solution of this embodiment, or the part that contributes to the prior art, or a part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of this invention. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0086] This invention also provides a terminal having the same inventive concept as any example or combination of examples corresponding to the above-described method for optimizing meme islands for complementary sequence sets, including a memory and a processor. The memory stores computer instructions executable on the processor, which, when executing the computer instructions, performs the steps of the above-described method for optimizing meme islands for complementary sequence sets. The processor may be a single-core or multi-core central processing unit or a specific integrated circuit, or one or more integrated circuits configured to implement this invention.

[0087] In one example, the terminal, i.e., the electronic device, is represented in the form of a general-purpose computing device. The components of the electronic device may include, but are not limited to: at least one processing unit (processor) mentioned above, at least one storage unit mentioned above, and a bus connecting different system components (including storage units and processing units).

[0088] The storage unit stores program code that can be executed by the processing unit, causing the processing unit to perform the steps described in the "Exemplary Methods" section above, based on various exemplary embodiments of the present invention. For example, the processing unit can execute the aforementioned meme island optimization method for complementary sequence sets.

[0089] The storage unit may include a readable medium in the form of a volatile storage unit, such as a random access memory (RAM) 3201 and / or a cache storage unit, and may further include a read-only memory (ROM).

[0090] The storage unit may also include a program / utility having a set (at least one) of program modules, including but not limited to: an operating system, one or more application programs, other program modules, and program data, each or some combination of these examples may include an implementation of a network environment.

[0091] A bus can represent one or more of several types of bus structures, including a memory cell bus or memory cell controller, a peripheral bus, a graphics acceleration port, a processing unit, or a local bus that uses any of the various bus structures.

[0092] The electronic device can also communicate with one or more external devices (e.g., keyboards, pointing devices, Bluetooth devices, etc.), one or more devices that enable a user to interact with the electronic device, and / or any device that enables the electronic device to communicate with one or more other computing devices (e.g., routers, modems, etc.). This communication can be performed via input / output (I / O) interfaces. Furthermore, the electronic device can communicate with one or more networks (e.g., local area networks (LANs), wide area networks (WANs), and / or public networks, such as the Internet) via a network adapter. The network adapter communicates with other modules of the electronic device via a bus. It should be understood that other hardware and / or software modules can be used in conjunction with the electronic device, including but not limited to: microcode, device drivers, redundant processing units, external disk drive arrays, RAID systems, tape drives, and data backup storage systems.

[0093] Through the above description, those skilled in the art will readily understand that the exemplary embodiments described herein can be implemented by software or by combining software with necessary hardware. Therefore, the technical solution according to this exemplary embodiment can be embodied in the form of a software product, which can be stored in a non-volatile storage medium (such as a CD-ROM, USB flash drive, external hard drive, etc.) or on a network, including several instructions to cause a computing device (such as a personal computer, server, terminal device, or network device, etc.) to execute the method of the exemplary embodiment of this application.

[0094] The above detailed embodiments are a description of the present invention. It should not be considered that the specific embodiments of the present invention are limited to these descriptions. For those skilled in the art, several simple deductions and substitutions can be made without departing from the concept of the present invention, and all of these should be considered to fall within the protection scope of the present invention.

Claims

1. A method for meme island optimization oriented to a complementary sequence set, which can be applied to the field of radar signal design, characterized in that, Includes the following steps: Multiple islands that evolve in parallel are constructed, each island being an independent subpopulation. Individuals in the subpopulation are a set of candidate complementary sequences to be optimized, and the candidate complementary sequences are candidate radar transmission waveforms. At the same time, a global archive for recording the access history of the search space region is initialized. Population evolution based on the meme algorithm is performed in parallel on multiple islands. During the population evolution process, each candidate complementary sequence set is evaluated according to a fitness function that integrates a complementary sequence signal quality index and a region-guided function. When a preset migration condition is met, elite individuals selected according to the fitness function are exchanged between multiple islands. The complementary sequence signal quality index is the peak sidelobe level of the radar waveform. The region guidance is calculated based on the access frequency of the candidate complementary sequence set in the global archive mapped to the search space region; the higher the access frequency, the greater the penalty. When the iteration condition is met, the final complementary sequence set with the optimal fitness function value found in all islands is output, which is the radar phase-coded waveform sequence set with the optimal sidelobe characteristics.

2. The complementary sequence set-oriented epigenetic island optimization method according to claim 1, wherein, A hash function is used to map the candidate complementary sequence set to the search space region, and the calculated hash value is stored as a key in the global archive, recording only the number of times the region is accessed.

3. The complementary sequence set-oriented epigenetic island optimization method according to claim 1, wherein, The region guidance is quantified based on the Hamming distance between the candidate complementary sequence set and the historical complementary sequence set corresponding to the regions already recorded in the global archive.

4. The meme island optimization method for complementary sequence sets according to claim 1, characterized in that, A hybrid operation of global and local search is performed within each island. The global search includes selection, crossover, and mutation operations, while the local search includes optimization of a selected set of candidate complementary sequences using a simulated annealing algorithm.

5. The meme island optimization method for complementary sequence sets according to claim 4, characterized in that, The local search step size of the simulated annealing algorithm is adaptively adjusted according to the quality of the candidate complementary sequence set to be optimized.

6. The meme island optimization method for complementary sequence sets according to claim 4, characterized in that, The mutation probability of the mutation operation is adaptively adjusted based on the diversity of the candidate complementary sequence set in the population.

7. The meme island optimization method for complementary sequence sets according to claim 4, characterized in that, In the process of population evolution, a shared fitness mechanism is used to assess the fitness of individuals.

8. A computer program product, comprising a computer program, characterized in that, When the computer program is executed by a processor, it implements the steps of the meme island optimization method for complementary sequence sets as described in any one of claims 1-7.

9. A storage medium storing computer instructions thereon, characterized in that, When the computer instructions are executed, they perform the steps of the meme island optimization method for complementary sequence sets as described in any one of claims 1-7.

10. A terminal comprising a memory and a processor, wherein the memory stores computer instructions executable on the processor, characterized in that, When the processor executes the computer instructions, it performs the steps of the meme island optimization method for complementary sequence sets as described in any one of claims 1-7.

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