Systematic Literature Review of the Use of Computational Intelligence in the Routing and Spectrum Assignment Problem in Elastic Optical Networks

Abstract

Elastic optical networks (EONs) have characteristics that meet the growing demand for current and future bandwidth, such as 5G and Internet of Things. In EONs, connections must have a route and a spectrum slice available between the nodes to establish communication. The process associated with this task is named routing and spectrum allocation (RSA) problem. The RSA problem is NP-hard and several approaches have been proposed in the literature using computational intelligence (CI). This paper provides a systematic literature review (SLR) regarding applying CI to solve the RSA problem in EONs. We offer a research roadmap encouraging the community to address identified limitations and open questions requiring further investigation. This study selects 40 primary studies for analysis and data extraction out of the 659 initially obtained papers. The main conclusions indicate that the community still needs to explore the RSA problem with the freedom to solve it without considering a fixed order of the two subproblems: routing and spectrum allocation. The studies reveal that efficient solutions are achieved with the techniques used in the RSA problem, which made them excellent tools. Furthermore, this SLR presents a set of open questions, suggesting valuable topics for future research through a research guide.

Index Terms
Routing and spectrum allocation; Computational Intelligence; Elastic optical networks; Systematic Literature Review.

I. INTRODUCTION

With the development of communication technologies, such as 5G, Internet of Things (IoT), cloud computing, and 4K video, data traffic in communication networks has been growing exponentially. In response to the exponential growth of network traffic and increased complexity of network operations, it is imperative to improve resource allocation and automation in communication networks [¹].

Optical networks have large transmission capacity, low transmission signal loss, and strong confidentiality, among other advantages. Therefore, there are opportunities for developments in this area since it is the central network technology to support high-capacity traffic demands [²]. In this scenario, wavelength division multiplexing (WDM) optical networks and elastic optical networks (EON) stand out.

In WDM optical networks, multiple wavelengths are transmitted over a single link. In this type of network, a connection request is admitted after solving the routing and wavelength assignment problem (RWA). WDM optical networks use a frequency grid with a fixed size for any transmission rate requested in a connection. Elastic optical networks use a flexible frequency grid to adapt and serve connections with different transmission rates, enabling more efficient spectrum use compared to WDM networks [³]. The Routing and Spectrum Assignment (RSA) problem in elastic optical networks is analogous to the RWA problem in WDM optical networks. In the case of elastic optical networks, a connection between a pair of nodes requires a route and a slice of spectrum to be established. The spectrum slices assigned to the connections can be made up of different slots and can be assigned in different quantities of slots. This multiplicity of assigned bandwidths impacts the increased complexity of the problem when comparing RSA to RWA. In WDM networks, which use a fixed frequency grid, the transmission rates requested by each connection can vary, leading to inefficient bandwidth utilization because the spectrum cannot be sliced into different sizes [³].

A request requiring a n-size spectrum portion can only be fulfilled if there are n contiguous slots along the route in all links. Like RWA, RSA is an NP-hard problem, and using heuristics or computational intelligence to solve it is expected. In addition, RSA has one more degree of freedom than RWA, which is the variable size of the spectrum, causing the high impact of requiring contiguous slots to be available along the route. It can then be said that RSA and RWA would correspond to the same type of problem if all connection requests demanded the same slice of spectrum [⁴].

The goals of RSA are to ensure that connection establishments obey all imposed constraints and available solutions are picked up in order to minimize eventual bandwidth blockings. With the advent of more advanced technologies, such as space division multiplexing (SDM) in multicore fiber (MCF) systems and spectrally efficient modulations, the problem has become more complex. Routing, modulation, spectrum and core allocation (RMSCA) incorporates not only the allocation of routes and spectrum, but also the selection of cores and modulations, taking into account the interactions between these elements [⁵].

Computational Intelligence has become an ally to optical networks, promoting some interesting advances. Among them, we can mention [⁶]:

• Optimization of Network Performance: computational intelligence techniques can optimize various aspects of optical networks, such as spectrum allocation, traffic prediction, traffic classification, and Quality of Transmission (QoT) estimation, leading to better performance and resource utilization.

• Dynamic and Flexible Networks: computational intelligence allows for the development of dynamic and flexible networks that can adapt to changing conditions and user demands, enhancing the user experience.

The works [¹], [²], [⁶] present applications of machine learning techniques in problems related to optical networks; however, their scope differs from that presented in this article. The scope of this article is to discuss the use of computational intelligence in the RSA problem. Gu et al. [¹] present a comprehensive review of the application of machine learning techniques in optical networks. Villa et al. [⁶] present a systematic study to identify and organize machine learning techniques applied to solve problems related to the functioning and operation of optical networks. They differ from this work because machine learning is one area of computational intelligence and they focus in more than one area of optical networks. Finally, Zhang et al. [²] provide a comprehensive overview of the use of machine learning techniques in routing and resource allocation in optical networks. Again, it considers only one area of computational intelligence, in this case, machine learning. This SLR focuses on these pillars: elastic optical networks, routing and spectrum assignment, and computational intelligence offering an overview of how computational intelligence techniques are used to solve the RSA problem, especially investigating the strategies deployed to analyze the approaches to route and assign spectrum, considering the order of processes and interchangeability.

Fig. 1 shows the structure of this paper. It is organized as follows: Section II presents an overview of introductory concepts; Section III explains the method used in this study, describing the planning, execution, and results phase; Section IV discusses the results considering the research opportunities detected and related works. Finally, this article concludes in Section V.

Fig. 1
Structure of this systematic literature review.

II. BACKGROUND

This section presents the main concepts used in this article. They are routing, spectrum allocation, and computational intelligence applied to the RSA problem.

A. Routing and Spectrum Allocation

The RSA problem can be addressed using different traffic patterns: static and dynamic. The static traffic pattern provides connection requests between source and destination pairs in advance. The goal in this case is usually to minimize total resource consumption while accommodating all connections, and the static RSA problem is formulated as an Integer Linear Programming (ILP) model with slot continuity and contiguity constraints. On the other hand, in a dynamic traffic pattern, connection requests arrive sequentially and randomly, and connections are terminated after a specific duration. In this context, routing and resource allocation decisions must be made when connection requests arrive at the network. The overall goal of the dynamic RSA problem is to minimize the blocking probability and consequently establish as many lightpaths as possible. Therefore, spectrum fragmentation may block future connection requests in this scenario, making online spectrum fragmentation management a critical issue to consider in dynamic traffic [²].

In elastic optical networks with dynamic traffic, when a connection request arrives at the network’s control and management center, the admission procedure must determine the route and spectrum slice to be used by the connection, if one is available that meets all the request requirements. This solution can be obtained using three approaches. The first one is to determine the route pair and spectrum slice jointly; however, as RSA is an NP-hard problem, its complexity can be reduced when divided into two subproblems: routing and spectrum allocation [⁴]. The other ways to solve the RSA problem consist of choosing the order in which the subproblem will be executed first. They are the solution that follows the sequence routing and then the allocation of the spectrum with the minimum amount of contiguous slots required (R-SA) or the solution that prioritizes the slice of spectrum to be used and then finds a route in that spectral band available (SA-R) [⁷]-[¹⁰].

When routing is prioritized network R-SA may provide the shortest possible routes, for instance, with fewer hops, so that network resources may be saved. On the other hand, the SA-R technique, which prioritizes spectrum allocation, can promote higher spectrum compression and load distribution in the network, as the allocation can be determined by taking slots with the lowest possible indices through an ordered list of frequency slots [¹⁰].

RSA problem in SDM-EONs requires an approach that considers both the available spectrum and the efficient allocation of fiber cores in MCF cables. This challenge is known as the routing, core, and spectrum allocation (RCSA) problem. Along with the increased capacity in SDM-EONs, an additional issue arises: crosstalk, which occurs when there is interference between signals transmitted in neighboring cores. This effect is more severe when adjacent cores transmit signals at the same frequency simultaneously, compromising signal quality and network performance, making crosstalk management a critical challenge in MCF transmission [²].

Heuristic and metaheuristic approaches are often used to find approximate solutions to complex optimization problems under constraints, such as in RSA problems, where efficient spectrum allocation is crucial to meet traffic demands and maximize the utilization of available resources. These techniques allow solutions to be found faster and more practical, compared to analytical methods that can be computationally intensive and unfeasible in high-demand situations [¹].

Calculating the physical layer impairments for solving the RSA problem is essential due to the limitations that directly impact signal quality and overall network performance. Attenuation, dispersion, nonlinearities, and noise introduce cumulative degradations in the signal along the links. Therefore, considering signal degradation at the physical layer during RSA is crucial for fulfilling quality of transmission requirements, and their adequate integration with spectral efficiency requirements positively impacts network performance. Impairment-aware RSA is essentially an RMSA problem [¹¹]. In this scenario, artificial neural networks have been used in solving the RMSA problem [⁵], [¹²]-[¹⁶].

B. Computational Intelligence

This subsection deals with the computational intelligence techniques used in the selected articles.

Computational intelligence is a methodology capable of providing a system with the ability to learn and deal with new situations so that the system is perceived as possessing one or more attributes of reason, such as generalization, discovery, association, and abstraction. They are often designed to mimic one or more aspects of biological intelligence [¹⁷].

The Computational Intelligence Society (CIS) of the Institute of Electrical and Electronics Engineers (IEEE) uses three pillars of computational intelligence: machine learning, metaheuristics and fuzzy systems. Fig. 2 shows the three pillars and where the computational intelligence techniques listed in this work are located.

Fig. 2
The three pillars of computational intelligence and techniques listed in this work

1) Machine Learning: Machine learning (ML) is a branch of artificial intelligence that uses algorithms with the unique ability to learn the behavior of systems. With these algorithms, it is possible to represent such systems through models capable of estimating the future responses of these systems. The model obtained by a machine learning algorithm is a computational representation of a phenomenon to perform a specific task, given a certain environment [¹⁸]. Fig. 3 shows a typical block diagram for machine learning application [¹⁹].

Fig. 3
Typical block diagram for machine learning application.

Problem formulation helps to decide what kind of and the amount of data to collect and the learning model to be employed. The goal of data collection is to collect a large amount of representative data without bias. Data analysis attempts to extract the effective features of the problem. Model construction involves model selection, training and tuning. Model validation evaluates if model is working well, avoiding overfitting and underfitting. Deployment and inference works on performance issues of the machine learning model in real-time operation [¹⁹].

ML approaches can be categorized according to the objectives of learning tasks, such as identifying patterns for classification or prediction, learning for action, or inductive learning methods. ML algorithms can be classified as supervised learning (SL), unsupervised Learning (USL), and reinforcement Learning (RL).

Supervised learning uses knowledge of input data and its known outputs, labels, or examples for training. In this scenario, the ML algorithm constructs a mapping between the input and output datasets, and the weights of the chosen ML model are updated to generate good responses. Thus, the algorithm generalizes the answer to any input given that it contains a subset of inputs and their respective known outputs. In problems with a discrete nature, the algorithm is said to learn to classify the data, while in problems with a continuous nature, the algorithm is said to learn to regress the data [¹⁸], [²⁰]. Examples of supervised learning techniques are K-th nearest neighbors (KNN), Artificial Neural Network (ANN), and random forests.

KNN is a supervised machine learning algorithm used for classification and regression. This algorithm classifies objects based on the predominant class among the k nearest neighbors in the feature space. The KNN algorithm calculates the distance between the point to be classified and the existing data points in the training set. The closest prototypes are identified, and the most frequent class among these neighbors is assigned to the point to be classified. For regression, the KNN algorithm calculates the average (or other centrality measure) of the target values of the k nearest neighbors to predict the point value to be estimated [²¹].

An artificial neural network is an analysis paradigm inspired by the massively parallel structure of the brain. It simulates a parallel and highly interconnected computational structure with many relatively simple individual elements named artificial neurons [¹⁷].

Random forests are a machine learning algorithm combining multiple decision trees to form an architecture for decision-making. Each decision tree in a Random Forest is trained independently on a random dataset sample, and the final prediction is made based on the average or majority of individual tree predictions. This method is often used in classification and regression problems. Random Forests are often used due to their ability to handle large and complex data sets and to handle categorical and numeric input variables [²²].

Unsupervised learning occurs when there are no known input and output labels. In this case, the ML algorithm tries to build a representation model of the input and output data without feedback from unlabeled examples. Then, the ML algorithm aims to group the data according to a similarity criterion between them [¹⁸], [²⁰].

Reinforcement learning is positioned between supervised and unsupervised learning because the algorithm is informed when the answer is wrong but is not told how to correct it. It must explore the environment and try different possibilities until it discovers how to get the correct answer. Reinforcement learning is sometimes called learning with a critic because of this monitor that scores the response but does not suggest improvements [²⁰].

Deep learning is a machine learning variation that achieves great power and flexibility by learning to represent the world as a nested hierarchy of concepts. In this case, each concept is defined as having more straightforward and more abstract representations computed in terms of less abstract ones [²³].

2) Metaheuristics: According to Blum and Rolin [²⁴], metaheuristics are high-level strategies for exploring search spaces using different methods. Their goal is to find solutions that are at least close to optimal. Metaheuristics usually use non-deterministic processes and some mechanisms to avoid traps of local minimums or maximums.

Metaheuristics can be applied to different optimization problems because they are not specific to a problem. Some examples of metaheuristics are Simulated Annealing (SA), Tabu Search (TS), Genetic Algorithm (GA), Differential Evolution (DE), Particle Swarm Optimization (PSO), Grey Wolf Algorithm (GWO), Ant Colony Optimization (ACO), Invasive Weed Optimization (IWO) and Spotted Hyena Optimizer (SHO).

SA is an algorithm for optimizing generic functions. The step length for each iteration is defined by an arbitrarily defined parameter, which plays the role of temperature, as in annealing metals. The temperature is higher at first to make it easier to explore; then, it is gradually lowered to make it easier to exploit [¹⁷]. It can be successfully deployed for low-dimensional problems.

TS is an optimization metaheuristic used to solve combinatorial optimization problems, in which the goal is to find the best possible solution in a complex search space. TS is based on performing movements between neighboring solutions in a search space, seeking to improve the current solution. During the search, the algorithm maintains a tabu list that records recent moves, preventing the algorithm from returning to previous solutions. An essential feature of TS is the ability to accept worse solutions at certain times in the search. It helps to avoid getting stuck in sub-optimal locations. This ability to explore the search space more broadly can lead to better final solutions [²⁵].

The GA is a variant of stochastic bundle search in which successor states are generated by the combination of two parent states, sexual reproduction [²⁶]. It is part of a class of population-based metaheuristics in which each individual is a possible solution to the problem. With each iteration, the population goes through a process of evolution. The best individuals are selected to generate new ones, using operators such as crossover and mutation. Finally, the new solutions generated start replacing the individuals with the lowest performance values, updating the population for the next iteration [²⁷].

DE is an optimization algorithm that belongs to the class of evolutionary algorithms and is often used to solve complex optimization problems. DE operates iteratively, evolving a population of candidate solutions over several generations to find the optimal or near-optimal solution to a given optimization problem [²⁸]. Differential Evolution generally presents high performance in continuous optimization.

PSO algorithm shifts potential solutions, called particles, through the problem space. The particles are accelerated toward selected points in the problem space, where the previous fitness values were high [¹⁷]. PSO presents a high capability the find high precision solutions in continuous optimization.

GWO is an optimization algorithm based on the social behavior of gray wolves in the wild. It draws inspiration from the social hierarchy and cooperation of wolves to solve optimization problems. This algorithm divides the wolf population into four categories: alpha, beta, delta, and omega, representing the leading wolf, the subordinate wolf, the third wolf in the hierarchy, and the other wolves, respectively. Each wolf adjusts its position in the search space based on the positions of alpha, beta, and delta wolves, simulating the hunting and cooperation behavior of wolves in the wild [²⁹].

ACO is a technique inspired by the behavior of ants in search of food, and it uses indirect communication to find solutions to complex problems. The fundamental principle of ACO is to simulate the behavior of ants that leave pheromone trails when encountering food. Ants reinforce pathways with pheromones when they find a good food source, which attracts other ants to follow suit. Over time, pathways with more pheromones become more attractive, leading to a convergence towards the best solution. ACO is used in combinatorial optimization problems, such as the traveling salesman problem, network routing, and resource allocation [³⁰]. ACO is often deployed for combinatorial optimization.

The IWO algorithm is an optimization algorithm based on models inspired by the behavior of invasive plants. It simulates the process of plant invasion in a competitive environment, where plants seek resources, such as sunlight, water, and nutrients, to grow and reproduce. The IWO algorithm uses this concept to explore and find efficient solutions in complex search spaces, dynamically adapting to the environment and challenges presented by the optimization problem. By modeling the behavior of invasive plants, IWO employs strategies for searching and updating solutions that aim to find the best set of parameters or variables that optimize a given objective function. These strategies include generating new solutions, selecting the best solutions for reproduction, and adapting the solutions over time to improve the performance of the algorithm [³¹].

The SHO is an optimization algorithm based on the behavior of spotted hyenas in the wild. SHO was developed based on spotted hyenas’ hunting strategies and social behavior, which are known for their efficiency and group hunting abilities. This algorithm uses these characteristics of hyenas to guide searching for optimal solutions in multidimensional search spaces. SHO employs adaptive and collaborative search strategies, where individuals in the population interact with each other to share information and coordinate the search for high-quality solutions to the optimization problem [³¹].

3) Fuzzy Systems: A fuzzy system deals with uncertainty and vagueness similarly to human reasoning. Unlike conventional boolean logic, which operates with binary values (true or false), fuzzy logic allows you to deal with continuous and imprecise values, representing uncertainty in many real-world problems. In a fuzzy system, the input and output variables are described by fuzzy sets, which assign degrees of pertinence to different values. Fuzzy inference rules are used to map fuzzy inputs to fuzzy outputs, taking into account the inaccuracy and ambiguity of the data. The defuzzification step converts the fuzzy outputs into crisp values for decision-making [¹⁷], [³²].

Fuzzy systems are widely used in various fields, such as process control, decision support systems, pattern recognition, optimization and more. They are especially useful when systems are complex, poorly defined or subject to unpredictable variations, allowing for a more flexible and adaptive modeling compared to traditional boolean logic-based approaches [³²].

III. RESEARCH METHOD

This section describes the method used in this work, from the problem description to the analysis of the selected studies.

A. Description of the Reference Method Used

This systematic review of the literature was based on the method proposed in [³³], which consists of three major phases: Planning, Conduction, and Preparation of the review report.

The research questions were developed using the PICOC framework [³⁴], which encompasses Population, Intervention, Comparison, Outcome, and Context, ensuring that systematic reviews are focused, specific, and address all relevant aspects of the research topic.

B. Application of the Reference Method Used

The research protocol consists of the following elements: a list of research questions, a list of research sources, a list of search queries, a list of inclusion/exclusion criteria, a data extraction form, and a quality assessment form. The following subsections describe each activity involved in forming these elements.

The main objective of this systematic review is to characterize the state of the art in applying computational intelligence to the RSA problem in elastic optical networks. It involves gathering and analyzing scientific publications on how computational intelligence is employed in the RSA problem and what network parameters are relevant in deciding between R-SA and SA-R. To achieve this goal, the main research question of this systematic review is: How has computational intelligence been applied to the problem of routing and spectrum assignment in elastic optical networks?

Secondary questions are also investigated to structure the acquisition of relevant information to answer the main research question. Thus, the secondary questions defined in this RSL are:

• Secondary 1: What computational intelligence techniques are used in the RSA problem in elastic optical networks?

• Secondary 2: What network parameters are used in RSA algorithms?

• Secondary 3: How do we decide between the R-SA and SA-R approach in the RSA solution?

1) Definition of Search Engines: This work conducts automatic searches in previously selected digital libraries. Thus, within this context, the sources of digital libraries selected are Web of Science, ACM digital library, IEEE Xplore, Science Direct (Elsevier), Scopus, and Springer Link.

2) Definition of Search Strings: The main objective of this activity is to define keywords that will be used as boolean expressions in automatic searches in digital libraries. Thus, the first step in defining the search queries is identifying the keywords. This list is drawn up based on the PICOC’s structure and the systematic review’s objectives, ensuring that no relevant term is omitted from the outset. The final search sequence used is as follows:

$$\begin{array}{}(("elasticopticalnetwork"\mathbf{\text{OR}}\text{("elastic optical networks")}\\ \mathbf{\text{AND}}\\ \text{("routing and spectrum assignment"}\mathbf{\text{OR}}\text{"spectrum assignment and routing")}\\ \mathbf{\text{AND}}\\ \text{("algorithm"))}\end{array}$$

4) Definition of Inclusion and Exclusion Criteria: The inclusion and exclusion criteria establish rules to filter out unnecessary studies. It ensures the selection process is systematic, transparent, and aligned with the research objectives [³⁵]. The criteria established in this study is as follows:

• Inclusion 1 (I1) - Peer-reviewed articles published in journals and conferences that present RSA and SAR algorithms using computational intelligence;

• Inclusion 2 (I2) - Relevant studies cited by the authors of the articles found during the snowball search process;

• Exclusion 1 (E1) - Articles with unavailable access;

• Exclusion 2 (E2) - Extended abstract or papers with less than five pages;

• Exclusion 3 (E3) - Duplicate articles;

• Exclusion 4 (E4) - Articles that do not address the research questions;

• Exclusion 5 (E5) - Articles written in a language other than English;

• Exclusion 6 (E6) - Articles that did not meet the quality criteria.

4) Definition of the Data Extraction Strategy: This activity aims to establish a strategy for extracting data from selected primary studies. The information collected is organized as follows:

• Section 1 (mandatory): records basic information to identify the article, such as title, place of publication, and year, among others;

• Section 2 (mandatory and associated with the first secondary question): records the computational intelligence techniques used in the RSA problem in elastic optical networks;

• Section 3 (mandatory and associated with the main question): records how computational intelligence techniques are employed in the RSA problem in elastic optical networks;

• Section 4 (optional and associated with the second secondary question): records the network parameters used in the RSA algorithms;

• Section 5 (optional and associated with the second secondary question): records information on how the R-SA and SA-R approaches are used to solve the RSA problem in elastic optical networks.

The data extraction form must be completed with the required section and at least one of the optional sections, as not all papers answer all secondary research questions.

5) Definition of Quality Assessment: The definition of quality activity aims to establish criteria to measure the quality of each primary study. Although there is no agreed definition of a high level of quality, it is widely recognized that the quality of primary studies is critical to obtaining more reliable results [³⁵]. Four quality assessment criteria (QA1-QA4) are established to be considered when applying exclusion criterion E6, based on an approach similar to [³⁶] and using bibliometric impact information.

QA1 is calculated using the Quality Score (QS), according to Equation 1,

(1) $$\begin{array}{}S=[\frac{\sum _{i=1}^3{G}_i}{3}+\left(\frac{\sum _{i=1}^3{S}_i}{3}\right)\times 3],\end{array}$$

where the general evaluation factors (G) and the specific evaluation factors (S) are presented in the described below:

• General Criteria (G) - Weight 25%:

  • - G1 - Definition of the problem and motivation of the study:

    • ∗ It describes in details (1.0);

    • ∗ It briefly describes (0.5);

    • ∗ It does not describe (0.0).

  • - G2 - Methodological description of the study:

    • ∗ It describes in details (1.0);

    • ∗ It briefly describes (0.5);

    • ∗ It does not describe (0.0).

  • -G3 - How the contributions of the study refer to the results of the study:

    • ∗ It explains the correlation between contributions and results (1.0);

    • ∗ There is no correlation between the contributions and the results (0,5);

    • ∗ There is no description between the contributions and the results (0,0).

• Specific Criteria (S) - Weight 75%:

  • - S1 - The proposed RSA algorithm considers how many network characteristics:

    • ∗ More than one (1.0);

    • ∗ Only one (0.5);

    • ∗ None (0.0).

  • - S2 - The article compares the R-SA approach with the S-AR approach:

    • ∗ Yes, and it shows performance results (1.0);

    • ∗ Yes, but it does not show performance results (0.5);

    • ∗ It does not compare (0.0).

  • - S3 - The article compares its proposed algorithm(s) with others in the literature:

    • ∗ Yes, and it has better performance results (1.0);

    • ∗ Yes, but it does not show better performance results (0,5);

    • ∗ It does not compare (0,0).

The result is a numerical calculation that classifies the selected studies. The quality assessment checklist, with G and S consisting of three items with a maximum score of 1 each, presents a medium weighting, where S weighs three times more than G. Thus, it considers that a study’s specific contributions are more important than its general contributions.

After the QS is calculated, studies are ranked as follows, depending on their scores:

• Studies with a QS of 3.0 or higher are considered to be of high quality, marked as QA1 = ’High’;

• Studies with a QS of 1.5 or more but less than 3.0 are considered to be of medium quality, indicated as QA1 = ’Medium’;

• Studies with a QS of less than 1.5 are considered low quality and excluded from the analysis, marked as QA1=’Low’.

The second quality evaluation criterion (QA2) classifies articles based on the publication forums. Thus, we chose to use the median of the h5 factor of Google Scholar for this classification [³⁷]. The h5 factor is the number h of articles published in a journal in the last five years that have received at least h citations each. Articles are considered "high" quality if published in conferences or journals with a median of h5 equal to or greater than 25. The "average" classification is assigned to articles published in conferences or journals with a median of h5 between 20 and 25. On the other hand, articles published in conferences or journals with a median of h5 of less than 20 are classified as of "low" quality.

The third quality assessment criterion (QA3) ranks articles based on the number of citations they have received using the following metrics:

• Articles with more than five citations are considered of "high" quality;

• Articles with fewer than five citations are considered "average" quality.

• Articles without citations are considered of "low" quality.

The QA3 criterion evaluates the relevance and impact of articles based on the number of citations received, recognizing the importance of influence and recognition in the academic community. However, it is essential to note that this criterion may be unfair to recent papers that have yet to have time to accumulate a large number of citations. Therefore, the QA4 criterion described below is introduced to deal with this situation.

The fourth quality evaluation criterion (QA4) deals with the issue of fairness about recent works that may have yet to receive many citations in QA3. It analyzes articles from the last five years, considering their potential relevance, and makes the following classification:

• Articles with at least one citation are considered to be of "high" relevance;

• Articles without citations that have potential relevance are considered of "medium" relevance.

The potential relevance that classifies the article as a medium is the following:

• The article may be innovative or present new approaches that the academic community has not widely recognized;

• The article may contain promising results or valuable insights that have not yet been fully explored or disseminated;

• The paper may address emerging issues or challenges that must be fully understood or appreciated.

C. Search Processes and Results Obtained

This phase presents the results of the research carried out in digital libraries, considering specific configurations for each library according to its peculiarities.

Table I shows the digital libraries used, the search commands, and the number of articles, journals, or conferences obtained.

TABLE I
DIGITAL LIBRARIES, SEARCH COMMANDS AND NUMBER OF ARTICLES OBTAINED.

Digital Library	Search command	Number of articles obtained
Web of Science	(AB=(elastic optical network) OR AB=(elastic optical networks) ) AND (AB=(routing and spectrum assignment) OR AB=(spectrum assignment and routing) AND (AB=(algorithm)))	390
Scopus	( ABS ( "elastic optical network" OR "elastic optical networks" ) AND ABS ( "routing and spectrum assignment" OR "spectrum assignment and routing" ) AND ABS ( "algorithm" ) )	133
Springer Link	("elastic optical network" OR "elastic optical networks") AND ("routing and spectrum assignment" OR "spectrum assignment and routing") AND ("algorithm")	56
IEEE Xplore	(("Abstract":"elastic optical network" OR "Abstract":"elastic optical networks") AND ("Abstract":"routing and spectrum assignment" OR "Abstract":"spectrum assignment and routing") AND ("Abstract":"algorithm"))	55
ScienceDirect	("elastic optical network" OR "elastic optical networks") AND ("routing and spectrum assignment" OR "spectrum assignment and routing") AND ("algorithm"))	25
ACM Digital Library	[[Abstract: "elastic optical network"] OR [Abstract: "elastic optical networks"]] AND [[Abstract: "routing and spectrum assignment"] OR [Abstract: "spectrum assignment and routing"]] AND [Abstract: "algorithm"]	0

Table I shows that 659 articles are found, with the majority, 390 (59.2%), coming from the Web of Science library. The Scopus library returns 133 (20.2%), the second-highest number of studies. The Springer Link and IEEE Xplore libraries brings similar numbers of articles, 56 (8.5%) for the first and 55 (8.3%) for the second. The ScienceDirect library contributes with only 25 (3.8%) articles, and the ACM Digital Library returns no articles.

1) Analysis of Results and Application of Quality Criteria: The first analysis of the articles consists of applying the quality criteria, which indicates the final list of primary studies considered in this systematic review. In this stage, the inclusion and exclusion criteria, except criterion E6, is applied to all the studies identified by evaluating titles, keywords and abstracts. However, it should be noted that, when any doubt arises regarding the inclusion or not of a given study, the recommendation is to include it in this phase, leaving the decision to the final selection. Exclusion criterion E6 is applied after analyzing the content of the remaining articles.

After applying the inclusion and exclusion criteria, 40 articles remain. Table II shows the number of articles selected after applying the criteria mentioned earlier.

TABLE II
NUMBER OF SELECTED ARTICLES.

Digital Library	Number of selected articles
Web of Science	22
Scopus	12
Springer Link	5
IEEE Xplore	0
ScienceDirect	1
ACM Digital Library	0

The final list of articles selected for this systematic review is presented in Table III. It informs the year of publication and the respective references used throughout the text.

TABLE III
LIST OF SELECTED ARTICLES.

Year	Reference
2023	Hernández-Chulde [38], Petale [5], Zou [12], Tanaka [39], Selva Kunar [31], Ge [40], Wang [41], Agarwal [42]
2022	Lourenço [43], Hajipour [13], Ziazet [14], Xu [44], Zhu [45], Halder [46], Cheng [47]
2021	Dinarte [10], Li [48], Masayuki [49]
2020	Jashvantbhai Pandy [21], Lezama [28], Rodrigues [15], Alves [50]
2019	Salani [22], Xuan [29], Chen [16], Zhang [51], Chen [52], Luo [53], Lv [54]
2018	Barbosa [32], Luo [55]
2017	Wang [30], Luo [56], Xuan [57], Xuan [58]
2015	Nagły [59], Markowski [60]
2013	Gong [11]
2011	Christodoulopoulos [7]
2010	Christodoulopoulos [61]

Fig. 4 shows the distribution of selected articles by year of publication. It is observed that no articles published in 2024 is found. Of the 40 articles selected, 29 were published between 2019 and 2023. These articles represent 72.5% of the total selected. It is also noted that the year with the highest number of publications is 2023, which shows the topicality and relevance of the topic.

Fig. 4
Distribution of the number of selected articles published per year.

Next, analyses related to the research questions are carried out.

2) Analysis of the Selected Articles Regarding the Main Research Question: The main research question is, "Where is computational intelligence used in the RSA problem in elastic optical networks?". The first information that can be extracted is that 34 of the 40 articles work on the RSA problem, and only six work on spectrum allocation. The articles referring only to spectrum allocation are [²⁹], [⁵], [⁴⁵], [⁴⁶], [⁵¹] and [⁵⁹]. The other articles deal with the RSA.

Studies [⁵] and [⁴⁶] consider the effect of crosstalk interference on spectrum allocation, seeking to minimize it. While Petale and Subramanian [⁵] use a deep neural network on demand of dynamic traffic, Halder et al. [⁴⁶] use a genetic algorithm to allocate spectrum in a static traffic scenario. Zhu et al. [⁴⁵] proposed using a deep neural network with reinforcement learning for spectrum allocation for advance booking requests. The work proposed by Zhang et al. [⁵¹] uses a genetic algorithm for spectrum allocation in network failure scenarios, also considering the optical signal-to-noise ratio of the signal. A multi-objective algorithm has been proposed by Xuan et al. [²⁹] to optimize spectrum allocation in elastic optical networks, aiming to minimize power consumption, total spectrum occupancy, and maximum frequency spectrum utilization rate. The technique used is a PSO and DE-based modification of the GWO algorithm.

IV. DISCUSSION

How the RSA problem is solved in EONs impacts network control and resource management, influencing spectral efficiency, the probability of request blocking, and the network’s flexibility in reconfiguration for failure management. Artificial neural networks and reinforcement learning techniques have stood out in this area, which includes the following sub-problems: traffic prediction, resource allocation, performance monitoring of physical layer link and signal, estimation of QoT in the lightpath, and failure management in optical networks [¹], [⁶].

Failures in optical networks can severely degrade communication. Therefore, detecting and localizing failures is essential for maintaining optical networks and enhancing survivability [¹]. Survivable RMLSA (S-RMLSA) is fundamental in EONs to ensure network survivability under failures. S-RMLSA identifies suitable working and protection routes for source-destination pairs while allocating adaptive modulation levels and appropriate frequency resources to these paths. Most machine learning applications in network monitoring and survivability tasks comprise supervised learning techniques, which stand out in artificial neural networks, decision trees and random forests [¹], [²].

The main challenges for applying CI in optical networks include [¹], [²], [⁶], [⁶²]:

• Data Availability and Quality: The lack of quality datasets to train machine learning models limits the development and validation of CI solutions, especially in dynamic environments.

• Real-Time Processing: The need for fast responses makes implementing CI in optical networks that operate at high speeds challenging.

• Scalability: As networks increase in size and complexity, CI solutions must be scalable to handle the growing demand for data and connections.

• Integration with Legacy Systems: Integrating CI into existing infrastructures presents compatibility challenges and requires careful adaptation.

• Robustness and Generalization: CI models must be robust to operate under varying network conditions and avoid overfitting problems, compromising performance on new data.

• Complexity of Problems: Many routing and resource allocation problems are computationally intensive, challenging the effectiveness of CI methods in optical networks.

A. Related Works

This subsection refers to works that address topics related to the treatises in this article. Here, the similarities and differences between the published works and this SLR are pointed out.

Gu et al. [¹] presents a comprehensive review of the application of machine learning techniques in optical networks. It discusses machine learning applications in control and management, resource allocation, and network survivability. The paper also discusses challenges and future innovations in using machine learning in optical networks. Regarding the problem of RSA, the article briefly discusses the application of reinforcement learning as a tool for the solution. The articles cited by him are [⁵²], [⁶³].

Zhang et al. [²] provides a comprehensive overview of the use of machine learning techniques in routing and resource allocation in optical networks. The article discusses application scenarios of machine learning techniques such as broadcast quality estimation, traffic estimation, and crosstalk prediction. Also, the paper analyzes machine learning-enabled algorithms to solve these problems. Furthermore, the paper highlights future research directions to enhance routing and resource allocation in multidimensional optical networks and satellite optical networks through the use of machine learning techniques. Regarding the application of machine learning in the RSA problem, the authors cite the following articles: [²], [⁵²], [⁵³], [⁶⁴], [⁶⁵].

Villa et al. [⁶] present a systematic study to identify and organize the machine learning techniques applied to solve problems related to the functioning and operation of optical networks. The main objective is to provide a comprehensive overview of the machine learning techniques used in this context, identify gaps and trends in the research area, and suggest directions for future research that can fill these gaps. It is concluded that machine learning techniques are mainly used for resource management, network monitoring, fault management, and traffic prediction of an optical network. Regarding the application of machine learning in the RSA problem, the authors cite the following articles: [²²], [⁶⁶], [⁶⁷].

It is verified that the related works [¹], [²], [⁶] focus on something other than the issues raised in this article. From the related works, only seven of them, [⁵²], [⁵³], [⁶³]-[⁶⁷] cover the theme of this SLR; of which only works [⁵²], [⁵³] have been selected in this article.

B. Analysis of the Selected Articles Regarding Secondary Research Questions

Secondary question 1 is, "What computational intelligence techniques are used in the RSA problem in elastic optical networks?" Table IV shows which techniques are used in the RSA problem, the number of occurrences, and the respective articles.

TABLE IV
COMPUTATIONAL INTELLIGENCE TECHNIQUES USED BY EACH SELECTED ARTICLE IN THE RSA PROBLEM.

Line	Technique	Number of articles	References
1	GA	11	[10], [11], [40], [42], [46], [51], [54]-[58]
2	ANN and RL	11	[12], [14], [16], [38], [39], [44], [45], [48], [49], [52], [53]
3	ANN	5	[5], [13], [15], [41], [47]
4	SA	3	[7], [59], [61]
5	GA and PSO	1	[50]
6	TS	1	[60]
7	Random forests	1	[22]
8	GWO	1	[29]
9	KNN	1	[21]
10	ACO	1	[30]
11	ACO and DE	1	[28]
12	ANN and fuzzy system	1	[43]
13	Fuzzy system	1	[32]
14	IWO	1	[31]

According to Table IV, it can be seen that the artificial neural network technique is the most used in the RSA problem in the selected studies. Regarding spectrum allocation, there are only 17 occurrences (lines 2, 3, and 12). It is also noteworthy that, within this number, on 11 occasions, neural networks have been used in conjunction with reinforcement learning and once used with a fuzzy logic system. The genetic algorithm comes next and is present in 12 articles (lines 1 and 5), and in one of them, the technique is used in conjunction with optimization by the ant colony. Simulated annealing is applied in 3 articles. The other techniques are used on two or one occasion.

The ways how artificial neural networks are applied each of the 17 articles are:

• [³⁸]: The DRL agent is used to represent the network’s current state to compute the quality of the optical path. The state of the network comprises the source and destination of the request, the required number of slots, the current spectrum utilization determined by the tuple formed by the position of the first available slot block, the average size of the available slot blocks, the number of available slots, and finally the maximum latency tolerated by the request;

• [⁵]: The paper uses a DNN to estimate the litcore threshold, which is the maximum allowable number of adjacent cores that can be occupied, in such a way that crosstalk is within the tolerance threshold to ensure the quality of transmission (QoT) and avoid unwanted interference between adjacent channels. The values obtained by the neural network are used in the proposed algorithm, SWARM (Spectrum-Wastage-Avoidance-based Resource Allocation), which considers a combination of litcore thresholds, spectrum wastage, crosstalk constraints, and the trade-off between spectrum utilization and crosstalk tolerance to perform an efficient allocation of resources in elastic optical networks based on MCF (Multicore fiber).

• [¹²]: The DRL agent determines whether a lightpath request should be fulfilled according to the policies and network state representation provided by the DNN. The algorithm determines the route, modulation format, and start time of the lightpath by considering the nonlinear effects of the physical layer.

• [³⁹]: The agent decides the route and spectrum to be used considering the network information represented in the neural network, as well as pre-and post-processing techniques, which improve the performance of the algorithm.

• [⁴¹]: The paper proposes the Reinforcement Matrix-Based Genetic Routing Analysis. This approach combines elements of genetic optimization with reinforcement learning for spectrum routing and allocation in elastic optical networks.

• [⁴³]: The paper uses a deep neural network (DNN) model for analyzing network failures, integrating it with the fuzzy inference system. This DNN model trained with the fuzzy system is used to protect and restore traffic affected by network failures, contributing to improving network survivability in failure scenarios.

• [¹³]: An ANN is employed to learn and adjust Control Parameters (CPs) based on the blocking rates of the request classes, to perform routing, modulation and spectrum allocation (RMSA) according to the priorities of the classes of service in multiclass elastic optical networks.

• [¹⁴]: The proposed algorithm uses DRL to solve the RMSA problem in elastic optical networks. It utilizes convolutional neural networks (CNN) to represent the state of the network and DNN to learn decision policy.

• [⁴⁴]: The algorithm uses graph convolutional neural networks (GCN) for the extraction of features from the network topology and recurrent neural networks (RNN) to aggregate link-level features to path-level. The agent then chooses the path between the K routes and allocates the spectrum by the first-fit algorithm.

• [⁴⁵]: The designed DRL algorithm is based on the idea of dual DNN structures of the Deep Q-learning Network (DQN) algorithm, i.e., the evaluation network and the target network. When a resource allocation request arrives, the DRL agent interacts with the network environment, and the spectrum resource matrix extracted by the control plane is entered as state. The algorithm determines the position of the available time-frequency block to be allocated.

• [⁴⁷]: The proposal employs long short-term memory (LSTM) to learn and optimize spectrum routing and allocation strategies. Through LSTM, the proposed algorithm can accumulate operational experience and improve operations over time, resulting in more effective routing and spectrum allocation strategies.

• [⁴⁸]: It proposes an inter-domain service framework that uses multiple cooperative deep reinforcement learning agents for network automation in multi-domain environments. Each agent is responsible for making local decisions to improve the efficiency and quality of service within their domain. DRL agents share a restricted amount of information, allowing them to make decisions in a distributed and cooperative manner. The algorithm chooses the RSA heuristic adaptively.

• [⁴⁹]: It uses a CNN to map the network, and the agent uses a mask to choose a route in a set of K shorter paths. Also, it determines the slots to be allocated. The mask favors the outermost slots to avoid network fragmentation.

• [¹⁵]: The proposed approach uses CNN to extract and select network characteristics and, thus, infer the value of the guard band that will serve for the routing, modulation level, and spectrum allocation (RMLSA) algorithm to select the spectrum for the lightpath.

• [¹⁶]: A DNN stores the network state for each of the K candidate routes. The agent chooses one of the K routes, the modulation format. Spectrum allocation is done by first-fit.

• [⁵²]: The algorithm uses a DNN to parameterize the policies and to represent the network considering each of the K pre-selected routes. The agent chooses the route and frequency slots for the lightpath request.

• [⁵³]: The current state of each frequency slot in the network determines the current state. The worker and the protection agent decide the route, modulation level, and spectrum to be allocated. The goal is to maximize the cost-effectiveness of the entire network with survivability (WCES).

Secondary question 2 is "What network parameters are used in RSA algorithms?". The network parameters are categorized, and the five categories that appeared the most, in descending order, are the following: spectral occupation (33.9%), type of traffic (20.6%), route (12.1%), network topology (9.7%) and signal quality (7.3%). These categories, together, correspond to more than 83% of the parameters used. The parameters related to the spectrum mainly involve spectrum availability and fragmentation. Such characteristics correlate with the available slots’ continuity and contiguity along the candidate route(s).

Regarding traffic, the primary feature is the demand for required frequency slots and the duration. The latter refers to dynamic traffic. The type of traffic considered in each article is shown in Table V. It shows that 87.5% of the articles consider only dynamic traffic, 10% of the articles consider static traffic and only 2.5% consider both forms of traffic. In the dynamic traffic scenario, there are 15 of the 17 neural network works and 11 of the 12 articles with genetic algorithms. As for static traffic, 2 of the 4 works use the simulated annealing technique.

TABLE V
TYPE OF TRAFFIC CONSIDERED IN EACH ARTICLE.

Type of traffic	Number of articles	References
Dynamic	35	[5], [10]-[16], [21], [22], [25], [28]-[32], [38]-[40], [42]-[44], [46]- [57], [59]
Static	4	[7], [41], [58], [61]
Dynamic and static	1	[45]

For the route consideration, the algorithms mainly take into account the distance and the number of candidate routes [⁷], [¹⁰]-[¹²], [²²], [²⁹], [⁴²], [⁴⁹], [⁵²], [⁵⁴], [⁵⁶]-[⁵⁸]. Signal quality is mainly investigated by the optical signal-to-noise ratio of the lightpath and the bit error rate of the connection [¹²], [¹³], [³²], [⁴¹], [⁴²], [⁵⁰]-[⁵²], [⁵⁶].

Secondary question 3 is "How do you decide between the R-SA and SA-R approach in the RSA solution?". The only selected article that addresses the issue as mentioned earlier is the study by Dinarte et al. [¹⁰]. The paper proposes a hybrid approach to order the selection, named Hybrid Routing and Spectrum Assignment (HRSA), which uses a genetic algorithm to decide between spectrum assignment strategies as a function of routing or routing as a function of candidate spectral bands precomputed by criteria of spectrum assignment algorithms. HRSA selects the most appropriate RSA strategy (R-SA or SA-R) for each source and destination pair in the network based on the criteria established during the readiness assessment. Still, Dinarte et al. highlight the differences between the two approaches, emphasizing that the R-SA strategy prioritizes reducing network occupancy by using shortest routes first. In contrast, the SA-R strategy emphasizes load distribution and a more efficient spectrum organization.

C. Concluding Remarks on the Selected Papers

In addition to the research questions, the number of topologies analyzed in each selected article is also verified. It is found that 15 of the 40 articles used only one topology, and another 15 used two topologies in their studies. That is, 75% of the total articles apply their algorithms in only one or two topologies. Five articles consider three topologies, three articles use four topologies, one article uses five topologies and one article does not mention the topology.

D. Points of Attention

Some points are found that need attention. The first tackles the order of handling the RSA problem. That is, whether it will be performed in the routing and spectrum assignment sequence (R-SA) or the spectrum assignment and routing sequence (SA-R). Although, as already mentioned throughout this article, Dinarte et al. [¹⁰] propose a way to decide between R-SA and SA-R for each pair of nodes in the network through the use of a genetic algorithm. It is found that there are still situations to be explored. It can be said that the decision criterion between the R-SA and SA-R approaches can be dynamic and consider the current parameters of the network, differently from what is proposed by Dinarte et al. [¹⁰].

Another point to be explored is how the choice between the R-SA and SA-R approaches impacts network design. Elastic optical network design scenarios can be investigated when considering fixed R-SA, SA-R, or HRSA and comparing the resulting topology, cost, and equipment allocation. Once HRSA provides an additional allocation alternative, would it be possible to design more cost-effective elastic optical networks than if we applied only R-SA or SA-R?

V. CONCLUSIONS

This work systematically reviews the literature on the applications of computational intelligence techniques in the RSA problem. Six search engines are used, and 659 articles are obtained. After analyzing the inclusion/exclusion criteria and the quality criteria, 40 articles are selected for analysis.

We find that, although there are many studies with applications of computational intelligence techniques in the problem of RSA in elastic optical networks, there are still points that need to be better studied. Notably, only one article among those selected considered the importance of solving the RSA problem by changing the order of the two subproblems.

At the end of this SLR, it is verified that the combinatorial and complex nature of the RSA problem in elastic optical networks makes many categories of intelligent algorithms able to contribute with reasonable solutions. It is also noted that machine learning techniques have stood out in this field currently. Combining this with the possibilities of studies mentioned above, it is also recommended to explore the application of computational intelligence in the problem of RSA in elastic optical networks for several existing topology scenarios and the design scenario of new networks.

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Publication Dates

• Publication in this collection
  07 Apr 2025
• Date of issue
  2025

History

• Received
  12 Aug 2024
• Reviewed
  20 Aug 2024
• Accepted
  30 Jan 2025