Multi-Objective Ant Colony Optimization (MOACO) Approach for Multi-Document Text Summarization ^†

Abstract

The demand for creating automatic text summarization methods has significantly emerged as a result of the web’s explosive growth in textual data and the challenge of finding re-quired information within this massive volume of data. Multi-document text summarizing (MDTS) is an effective method for creating summaries by grouping texts that are relevant to a similar subject. With the aid of optimization methods, this strategy can be optimized. The majority of optimization algorithms used in the scientific literature are single-objective ones, but more recently, multi-objective optimization (MOO) techniques have been created, and their findings have outperformed those of single-objective methods. Metaheuristics-based techniques are also increasingly being used effectively in the study of MOO. The MDTS issue is therefore solved by the Multi-Objective Ant Colony Optimization (MOACO) method. This multi-objective metaheuristic algorithm is based on the Pareto optimization. Recall-Oriented Understudy for Gisting Evaluation (ROUGE) metrics have been used to assess the outcomes of experiments using Document Understanding Conferences (DUC) datasets. Additionally, they have consistently outperformed other referenced summarizer systems.

1. Introduction

On the Internet, a tremendous amount of knowledge has recently been provided as a result of numerous scientific and engineering sectors. One of the most difficult challenges for researchers in this specific instance is to find the necessary information in the vast collection of data. For this reason, in the past 10 years, there has been an increasing trend for summarization systems. On the Internet, there is still a lot of crucial information available in written form. Text summarization systems may be useful in locating the most crucial textual information rapidly in the modern day because of the tremendous volume of textual information that users obtain every day. As a result, automatic text summarization has been included in various text processing tools, including “decision support systems, search engines, and medical information process systems [1].” It is currently a major challenge in the field of natural language processing as well.

Text summarizing is a technique that aims to summarize and extract the most important data from a document or paper [2]. Text summarizing may be categorized as single or multi-document summarization depending on how many documents are simultaneously analyzed and summarized. A different category of document summary methodology is known as extractive or abstractive summarization.

While the information in the text is rephrased in abstractive summarizing, the main aim of extractive summarization is to extract the most essential lines from documents and combine them into a summary [3]. Multi-document approaches combine the textual content of a large collection of documents. One of the most common techniques for creating summaries manually is extractive multi-document text summarizing. In the scientific literature, multi-objective optimization has outperformed single-objective optimization for extractive multi-document text summarization (MDTS).

New methods have been developed in this emerging field as the MOO methodologies have improved in various ways. To provide high-quality multi-document text summaries, the main goal of this paper was to design a language-autonomous summarizer system. This paper suggests a heuristic approach for multi-objective problems based on “Pareto Ant Colony Optimization (P-ACO).” This approach transforms the multi-objective optimization challenge into an ant colony optimization issue, and it uses several ant colonies to examine the solution space and find progressively better non-dominated sets of MDTS. To test this technique and demonstrate the advantages of using numerous pheromone matrices and various ant colonies in multi-objective challenges, an experimental model and many modifications are performed.

In this study, the effectiveness of MDTS was analyzed by widely used DUC benchmark datasets and compared to some of the finest methods recently proposed. These data sets were selected because, compared to other DUC datasets, their source text had a more complex structure. The performance criteria of our suggested generic summarizer show the value of PACMO while also demonstrating the proposed algorithm’s high efficacy when compared to other algorithms previously in use in the area of summarization. The results indicate that our system could outperform some of the well-liked methods that are being developed for the challenge of MDTS.

The structure of this paper is as follows: Section 2 reviews the literature on the issue of multi-document text summarizing. The suggested framework for the Pareto Ant Colony Optimization (P-ACO) hypothesis is described in Section 3. The approach used for issue description and solution for determining MDTS designs using P-ACO is described in Section 4. An experimental proposal is shown in Section 5 along with test results to evaluate the suggested approach. Section 6 concludes the paper.

2. Related Works

Multi-document summarization is an optimization problem that necessitates the synchronized optimization of many objective functions. Two important goals focused on in the related work are diversity and content coverage. Any automatic text-summarizing system has some difficulties in producing high-quality summaries. Two clear optimization models have used content coverage and content diversity, both considering a sentence extraction-based generic text summarization model design directed towards more semantic measures. Some difficulties are identified, i.e., content coverage with text similarity by extrapolating the first criterion. These methods postulate that text similarity can be divided into three different levels of the optimization procedure. Firstly, to achieve global optimization, the candidate summary should overlap with the summary of the document collection. Secondly, to achieve less global optimization, candidate summary sentences should cover the document collection’s summary. The third level of optimization is comfortable with local optimization; the candidate summary’s coverage of conditions should be similar to that of the document collection. The coverage model is stated as a multi-objective optimization (MOO) problem and is united with a proposed model. To exploit the evolutionary algorithm’s strengths, heuristic perturbation and heuristic local repair operators are used (Kadhim and Saleh, 2018) [4]. The proposed model was approved by the document sets provided by (DUC2002), and it was compared to other state-of-the-art techniques. The ROUGE toolkit was the metric used to estimate the performance of the suggested task.

Multi-document summarization (MDS) is a successful method that creates a summary by grouping data from numerous papers that are related to the same topic. MDS is limited when extraction and abstraction methods are combined, but still, it is a complex research issue. The MDS use a unique hybrid structure called HEATS that was established to produce an efficient summary using the RNN-LSTMCNN deep learning design for an abstractive summary and the N-Gram model for an extractive summary (Lakshmi and Rani, 2021) [5]. The proposed system performance was assessed using benchmark datasets, and when measured in terms of ROUGE scores, it was found to be quite competitive with that of the existing systems.

To automatically build the summaries from a document collection that encloses the necessary information while minimizing extraneous details, extractive multi-document text summarizing techniques are used (Pérez, 2020) [6]. Generally, single-objective optimization techniques are used, but recently, multi-objective techniques have been produced; these have enhanced the existing single-objective outcomes. In the area of MOO, decom- position-based methods are increasingly being used with success. For example, to resolve the extractive MDTS challenge, a (MOABC/D) was proposed. Due to the advantage of using multi-core architectures, the MOABC/D method was designed in an asynchronous parallel design. Experiments have been run using DUC datasets and the results have been prolonged using (ROUGE) metrics.

Multi-modal summarization methods have been used in the significant advancement of communication technologies in the past few years. Multi-modal summarization has mainly been concentrated on text and images in the majority of earlier studies. To construct a multi-modal summary that includes text, photos, and videos, it has been suggested that unique extractive multi-objective optimization-based approaches are used (Jangra, 2020) [7]. To produce a successful multi-modal output, important objectives such as cross-modal redundancy, cross-modal similarity, and intra-modal salience, which are concurrently optimized in an MOO algorithm, are used. The proposed approach has been thoroughly examined for several methods and has demonstrated improved performance over cutting-edge methods.

In 2021, Mojrian proposed the unique MDTS method known as MTSQIGA, which arranges a summary by choosing significant passages from a collection of source documents. The suggested basic summarizer presents extractive summarizing as a binary optimization method that, to find the optimum solutions, uses a modified “quantum-inspired genetic algorithm (QIGA)” (Mojrian, 2021) [8]. This method’s objective function is essential to optimizing the linear combination of factors that make up the six sentence score measures. The proposed system was designed using ROUGE standard metrics, on benchmark datasets from DUC 2005 and 2007. It also displays the potential effectiveness of our proposed technique in testing the QIGA intext summarization tasks.

The most common technique for organizing an information is, automated text summarization (Moosavi, 2022) [9]. In extractive summarizing, the text’s most important phrases are selected and serve as the best summary. The MOO issue was solved and an appropriate MDTS was created utilizing a language-independent, semantic-aware method based on the harmony search algorithm. The objective function is learned by using an additional set of reference summaries, and after training, the function produces the best summaries it is capable of. It enlarges the sentences by utilizing a creative technique meant to concentrate the intellectual density in the sentences on important issues. Additionally, this paper presented a revolutionary clustering technique for identifying important issues and removing duplicates. A sentence placement approach based on the Hamiltonian shortest path was developed to produce intelligible summaries. The experiments are focused on DUC datasets.

Information coverage and diversity are two competing goal functions that are used to categorize the text-summarizing work as a MOO challenge (Jung, 2017) [10]. The resulting solutions offer summaries that ensure that the original content is fully covered while also guaranteeing the diversity of the sentence used within the summary. An evolutionary multi-objective optimization strategy named MS-EMO is proposed for MDTS. The results of our initial test show that the proposed method for generating automatic summaries utilizing the ROUGE assessment metric and the DUC dataset works as intended.

3. Proposed Framework

3.1. Text Preprocessing

Before executing the algorithm, the input texts from the document collection must be preprocessed [6]. Lemmatization and stemming methods are two examples of preprocessing methods used in the Natural Language Processing (NLP) domain to standardize the text [11]. Word stemming creates an approximate version of the fundamental form, which is known as a stem, whereas lemmatization substitutes or eliminates the suffix of a word to acquire the basic form, which is known as a lemma. The Porter stemming algorithm is the best method for word normalization in the English language, according to Toman et al. [11]. It is the method most used in the extractive MDTS field. As a result, word stemming is utilized in this study through the subsequent preprocessing phases:

• Sentence Segmentation: The objective of separating each sentence in the document collection is to determine its beginning and end.
• Word Tokenization: The phrases’ words are retrieved one by one. Any exclamation, question, and other marks are removed from the text.
• Stop Word Removal: Stop words, which include “prepositions, conjunctions, articles, possessives, pronouns, and others,” are frequently used words that have no particular meaning. As a result, these lines are removed from the sentences. A list of 598 stop words in the English language is contained in the ROUGE tool.
• Word Stemming: The roots of the remaining words are then retrieved using the Porter stemming technique, which allows words with the same lexical root to be processed as a single word. As one of the most frequently used and expanded algorithms, the Porter stemming algorithm has emerged as the industry standard for word conflation for information retrieval across a wide range of languages.

3.2. Word Embedding

The meanings of phrases and a variety of complex semantic phenomena, including polysemy, can have a negative influence on similarity analyses. Researchers’ interest in word embedding techniques has been significantly increased by the new word2vec algorithm designed by Google. The semantic similarity on the word level can be effectively reflected by word embedding approaches. The textual form of each word can be transformed into a numerical semantic vector using word2vec.

The word2vec model can be trained locally or globally, somewhat like the statistical thesauri generated in information retrieval. The global model can train the general meanings of words using the complete collection of both relevant and irrelevant materials, but it is incapable of properly reflecting the actual meanings of words. As a result, in the global model, word meaning ambiguities are more obvious. On the other hand, the local training strategy places a strong emphasis on the only relevant material. As a result, the variety of concepts provided in the collection of documents being summarized is smaller than in the whole set of documents. The local model can create semantic vectors that are more biased toward local concepts and less ambiguous. The locally trained system can be thought of as a context-aware strategy that could perform well enough to solve word sense ambiguity. For estimating the semantic similarity between words, the locally trained word2vec model can be used. A standard similarity metric, such as Cosine similarity, can be applied to quickly estimate it.

$$\cos \theta =\frac{A\cdot B}{‖A‖‖B‖}=\frac{\sum _{i=1}^n{A}_i{B}_i}{\sqrt{\sum _{i=1}^n{A}_i^2}\sqrt{\sum _{i=1}^n{B}_i^2}}$$

(1)

3.3. Redundancy Reduction

After the clusters have been constructed, the pairwise similarities of each cluster’s phrases are determined. When two phrases are too similar, the one with the lowest TR score is removed from the cluster. It produces the least amount of information overlap among the sentences in each cluster. Consequently, certain clusters may become extremely sparse. Members of such clusters are relocated to the clusters closest to them when those clusters are eliminated. Less significant clusters disintegrate, whereas those linked to the most significant principles persist.

3.4. Multi-Objective Ant Colony Optimization (MOACO)

Ant colonies work together to solve complex discrete optimization problems using meta-heuristics; this is named Ant Colony Optimization (ACO).

The ability to smell and deposit a chemical compound known as pheromone/odor allows real ants to interact with each other. When ants leave the colony to search for food, they move randomly, but they choose whether or not to follow a pheromone trail when they do. They spread their pheromone along the route if they choose to do so. An ant is more likely to pick one way over another depending on the intensity of the pheromones it can sense across the pathways. The stronger the odor that is prevalent across a path, the more likely it is that an ant will select that way. The amount of odor on a trail gradually exhausts over time. Ants use all alternative routes equally before the colony decides which one leads closest to the food source, leaving pheromones behind along the way. The ant that covers the shortest distance in a single trip returns food to the colony earliest. Since the “new” odor has not dissipated and is more interesting to those ants looking for a food source, the minimum distance would provide the maximum odor strength at that time.

In ACO, an artificial pheromone (t) is distributed over the vertices of a network that artificial ant colonies (A) walk through. A starting condition/vertex represents the nest, and an end condition/vertex provides the food. Probabilistically, the ant will choose which node to travel toward depending on how much pheromone has been spread throughout the chosen vertex and its surrounding vertices. Pheromone Matrix (PM), which includes pheromones linked with each vertex, is the primary method through which ants deposit and sense pheromones. The goal functions and constraints used to solve the problem serve as a representation of it. An ant spreads a certain quantity of pheromone increment over each vertex of the path it has taken. This odor increment quantity depends on how effectively the identified path performs. Since the amount of pheromone on every vertex can decline with time, just like in real ant colonies, low-performing pathways become gradually neglected. The ants analyze the problem constraints each time they have to decide which vertex to visit next to confirm that the corresponding pathways are realistic.

The main aim of optimization for problems with multiple objective functions is to identify a total Pareto Optimal Set (POS) of solutions, which includes all non-dominated design solutions. In the specific instance of a multi-objective minimization problem with two results, namely R_X and R_Y, R_X prevails over R_Y if and only if no objective achieved by R_X is higher than the equivalent objective achieved by R_Y, and at least one objective achieved by R_X is less than that achieved by RY. In mathematics, two factors are assumed to be G₁ and G₂, R_X > R_Y where (G^X₁ ≤ G^Y₁) ⋀ (G^X₂ ≤ G^Y₂), and (G^X₁ < G^Y₁) ⋁ (G^X₂ < G^Y₂) where G^X₁, G^X₂ G^Y₁, and G^Y₂, represent the coefficients of the objective functions that the two solutions, correspondingly, achieved. If none of the solutions in a group of solutions, often known as a Pareto Set, dominate it, the solution is said to be non-dominated within the group. The group’s preferred option set (POS) is a subclass of options that are mostly non-dominated responses to the difficulties facing the group. If the group encompasses the whole objective function, the POS will contain all feasible options for resolving the issue.

As shown in the Figure 1, the proposed multi-objective ACO, a continuous search space is used and it is necessary to initialize the pheromone trail network to finish the problem description. Pareto ACO (P-ACO) for multi-objective challenges is a heuristic approach that employs artificial ants to continually search across the solution space in favor of increasingly better sets of solutions. There is no guarantee that all of the feasible solutions will be explored, and without this guarantee, the completeness and effectiveness of the resultant POS cannot be guaranteed. Numerous ant colonies are used sequentially to examine the optimum solution and find increasingly better solutions to the issue. Every ant in a colony is permitted to explore the network in search of a solution, resulting in a collection of solutions known as the Pareto set of the colony. The POS of the colony is a set of non-dominated solutions for the group that has been discovered by comparing the solutions inside the group with one another. For the succeeding colony to further explore the solutions found by the current colony, ants in the colonial power then leave behind pheromones along the pathways that correlate to their findings. Moreover, the pheromone consistently flows in all directions across each of the nodes.

4. The Proposed Multi-Objective Ant Colony Optimization Framework

4.1. Problem Representation

The issue being resolved includes selecting the best resource options possible within a multi-document text to concurrently reduce a summary’s overall cost and lead time. A summary with M activities (x₁, x₂, …, x_z, …, x_M), representing M phases of the processes involved in the design and distribution of the optimization of multiple documents, each with several resource options xz, y (y = 0, 1, 2,...., M_z), where “M_z is the total number of resource options available to activity xz”, is to be considered. The total summary cost is calculated as follows:

$$S=\sum _{z=1}^M\left({\lambda }_z{\Sigma }_{y=1}^{Mz}{w}_{z{y}^{b}zy}\right)$$

(2)

If W_zy is the cost that x_z,y, the y^th resource selection, and node Z added, respectively, if option x_zy is assigned to carry out operation x_z, then the decision variable b_{zy = 1} alternatively equals 0. ξ, representing the important term. The average demand per unit of time at activity x_z is known as λ_z. The average demands per unit time of downstream activities connected to stage x_z are added to determine the average demand per u at any stage, x_z. Requests per time interval, which are the overall average time needs of the clients, are recognized for the execution phases.

N nodes may be used to describe individual activities in the text summarization, and each node has several sub-nodes that can be used as resource alternatives [12]. R = {r(xz, xf)} connections could be used to indicate the relationships of priority between activities. Since there is a connection r(x_z, x_f) indicating that activity x_z’s output feeds into activity x_f, x_z should follow the preceding x_f.

Nodes have a demand and supply connection; thus, an activity at one node never starts until all of its inputs are accessible, or until all immediately preceding operations have been performed. An assembly node is an illustration of one such node where processing is delayed until the arrival of all methods. As a result, the sum of the sequencing lead time at the node plus the extended execution lead time for all input components represents the overall lead time at the node, i.e.,

$$T{P}_z=\sum _{y=1}^{Mz}{P}_{zy}{b}_{zy}+\mathit{max}\left(T{P}_f\right)x_f\in Dz$$

(3)

where TPz is the total lead time for node z, and TP_f is the total lead time for the node. Z is the processing of the y^th option selection, Dz is the group of nodes that node z receives 32 inputs from, x_f ∈ D_z if t(x_f, x_z) ∈ T, and TP_f is the total lead time for node f. There are no 33 previous input nodes for the nodes reflecting sourcing operations. In Equation (3) the second derivative would be 0.

The overall lead time for the execution of tasks to the target would be equal to the cumulative lead time at a delivery node, xt, TPt. The delivery node serves as the network’s last node when there is only one product running to a single destination. As a result, the cumulative lead-time at node M represents the overall text summarization delay.

$$TP=T{P}_M$$

(4)

There will be more than one delivery node in a network with various items and delivery destinations, each with its own total lead time. The lead time of the system could be determined by averaging these.

$$TP=\frac{1}{G}{\Sigma }_{x_t\in T}\left(T{P}_t\right)$$

(5)

where D denotes the collection of delivery nodes in the network and M denotes their number. Therefore, the total lead time of the complete network might be determined by using the longest lead time among delivery nodes or by averaging the lead times of delivery nodes weighted by the significance of client groups, depending on issues [12]. There may be more than two main goals for the entire problem if, in a generalized case, each product destination lead-time was specified individually as an aim.

The issue is therefore specified by two objective functions represented by Equations (2) and (5) and several constraints, supposing that the resources have an unlimited capacity.

$${\displaystyle {\sum }_{y=1}^{Mz}}{P}_{zy}{b}_{zy}+\mathit{max}\left(T{P}_f\right)-T{P}_z=0\hspace{1em}\hspace{1em}\hspace{1em}\forall z\in M$$

(6)

$$b_{zy}=\left\{\begin{array}{c} 1 if y is selected.\\ 0 otherwise z\in M\end{array}\right.$$

(7)

$${\sum }_{y=1}^{Mz}{b}_{zy}=1\hspace{1em}\hspace{1em}\hspace{1em}\forall z\in M$$

(8)

Constraints represented by Equations (6) and (7) establish that the lead time interactions between modules are so accurate 8 that usually a single resource feature is chosen for each activity, i.e., a single sourcing policy is considered, and 7 that the decision for a resource option depends on whether the resource is recognized to outperform the resulting operation.

4.2. Pheromone Representation

When using P-ACMO, it is important to consider the issue as a graph in which ants move about to find the answers, to describe the pheromone and its depositing and evaporating processes, and to choose how to utilize the pheromone to influence the ants’ behavior.

The MDTS, which is used by ants in P-ACMO, is made up of a collection of nodes that describe various activities, each with a set of sub-nodes that reflect resource availability, and a set of connections that show the relationships of precedence between the nodes. Ants can move between network activities, including sourcing, supplying, and delivering ones, while picking up a selection of goods at each node. This is the case if they choose the components for a particular application, distribute those components to factories for the production of sub-assemblies and the storage of goods, and then provide those finalized goods to customers. Once an ant Er has completed its tour of the whole network, it produces a Multi-Text Summarization (MTS) that simply becomes a sequence of resource actions performed at the tasks.

$$MT{S}_{E_r}=\left(x_{1y_1},x_{2y_2},x_{zyz}\dots \cdot x_{MyM}\right)$$

(9)

where x_zyz is the source option selected over stage x_z in the MTS.

The desire of ants to maintain a specific path is described by the pheromone. The desire of ants to select each of their source options at each network node is expressed by the issue under consideration. Therefore, it is represented as a U = {σ_zy} pheromone matrix, with each element indicating a possible opportunity at a network node.

$$U=\left\{{\sigma }_{zy}\right\}=\left({\sigma }_{11}{\sigma }_{12}\dots {\sigma }_{1M1},{\sigma }_{21},{\sigma }_{22,\dots \dots ..{\sigma }_{2M2\dots \dots .}}\right)$$

(10)

where σ_zy corresponds to the resource x_zy in terms of a pheromone element. The proportions of the components in U are significantly changed to simulate pheromone deposition and evaporation, either via a process of evaporation at particular times or via amplification by ants depending on the performances of the MTSs created by ants.

An evaporation factor of ρ is used where σ_zy ← (1 − ρ) σ_zy in the case of the former. The factor considers the range between (0, 1). When it comes to the latter, the increment of σ_zy, ∆σ_zy, corresponding to each resource x_z,y chosen by a supply chain design MTS_E produced by an agent E_r, is determined depending upon the accuracy of MTS_E.

$$\Delta {\sigma }_{zy}=\frac{1}{v}\left[{\left(\frac{\pi }{s_E}\right)}^2+{\left(\frac{\partial }{T{P}_E}\right)}^2\right]\forall x_{zy}\in MT{s}_E$$

(11)

where “V” is the total number of ants in a colony, π and ∂ are parameters that balance the value of the cost and time, and SAq and TPAq denote the cost of the learning outcomes and the lead time of MTSEr. For the equivalent components of the resources that the MTS does not accept, the increase is 0. Regarding [13], the proportion of pheromone updates is directly related to both goals rather than being measured against a separate performance metric that is particular to a certain situation.

According to the probabilistic decision rule, when an ant goes through a network, it chooses a resource out of each node; this indicates that the chance that the ant will select resource x_z,y to conduct activity x_z is represented by the following:

$$J_{X_{z,y}}=\frac{{\left[{\sigma }_{zy}\right]}^{\gamma }{\left[{\eta }_{zy}\right]}^{\delta }}{\Sigma X_{z^F,Y^F}\in M{X}_{z,y}{\left[{\sigma }_z{F}_{y}F\right]}^{\gamma }{\left[{\eta }_z{F}_{y}F\right]}^{\delta }}$$

(12)

where η_zy represents the heuristic value determined by η_zy = $\frac{1}{w_{zy}}$, γ and δ are factors that have ranges between 0 and 1 to equalize the importance of the ant’s tendency to follow the route with the strongest odor and to seek out other paths, and Mx_zy is the neighborhood of possibilities when the ant is at a certain place.

$$x_{z,y^{\prime }}M{x}_{z,y}=\left\{\left.Z_{z^F,y^F}\right|z=z^{\prime },1\le y^{\prime }\le M_z\right\}$$

(13)

Alternately, two identical-sized pheromone matrices that represent one goal function each could be employed. As a result, based on each of the related objectives, a separate update is made to the cost-related matrix UW and the time-related matrix UP. This technique is defined as the Multi-Pheromone Multi-Objective Method (MPM), as opposed to the Single-Pheromone Multi-Objective (SPM) approach that uses only one matrix. The cost-related matrix improvements for MPM are calculated via the following:

$$\mathbf{\Delta }{\mathit{\sigma }}_{\mathit{z}\mathit{y}}^{\mathit{w}}=\frac{\mathbf{1}}{{\mathit{s}}_{{\mathit{E}}_{\mathit{r}}}}$$

(14)

and the matrix of time-related data is calculated via the following:

$$\mathit{\Delta }{\mathit{\sigma }}_{\mathit{z}\mathit{y}}^{\mathit{P}}=\frac{\mathbf{1}}{{\mathit{T}\mathit{P}}_{{\mathit{E}}_{\mathit{r}}}}$$

(15)

Unlike [14,15,16,17,18], the amount of pheromone update depends on how well the solution achieves all the criteria instead of being supplied as a specific value. The heuristic value is also divided.

$${\mathit{\eta }}_{\mathit{z}\mathit{y}}^{\mathit{w}}=\frac{\mathbf{1}}{{\mathit{w}}_{\mathit{z}\mathit{y}}}$$

(16)

$${\mathit{\eta }}_{\mathit{z}\mathit{y}}^{\mathit{P}}=\frac{\mathbf{1}}{{\mathit{T}\mathit{P}}_{\mathit{z}\mathit{y}}}$$

(17)

4.3. The Solution Representation Algorithm

The suggested technique makes use of many colonies. The process begins by creating H ant colonies, Ho, each of which has K ants, Xk, where k = {1, 2, …, K}. Then, individually, the colonists are utilized to traverse the system. Every ant in a colony travels across the network’s nodes individually, selecting the best resources on each one using the probability decision rule indicated by Equation (12). According to Equation (12), the likelihood of every optional resource being selected for a specific ant on a certain node I is computed, and the source is assigned while considering the necessary probability distributions. The resource combination that results after the ant has explored every node is known as an SCD, and its effectiveness is evaluated by Equation (2) and in terms of absolute cost and lead time Equation (5).

The collection of SCDs created by every ant in the colonies is then analyzed using statistics to find non-dominated SCDs within the colony, which are then combined to form the Pareto Optimal Set of the colony. Then, using Equation (11) or (14), ants that produce the colony’s non-dominated SCDs are permitted to add pheromone enhancements to the pheromone matrices Equation (15). Before the emergence of the following colony of ants, a consistent flow rate is likewise provided to all components of the pheromone matrix or matrices. The network is then traversed by the following colony, utilizing the pheromone matrix produced by the preceding colony. The resulting POS is used as the optimal decision; after, this procedure is repeated until the last colony has finished the excursions. The pheromone updates, in this case, are made possible by allowing all ants that have produced SCDs in the colony’s current non-dominated set to do so.

5. Experimental Results and Discussion

The datasets involved, the experimental conditions, the performance metrics and the metrics of analysis, as well as the outcomes achieved, are all included in this section. Finally, to achieve optimum results for the proposed summarization framework, it has been evaluated by comparing it with a few other document summarization frameworks that have been previously developed. Users experimented to determine the impact of various aspects of the suggested optimization technique. This section discusses these experiments and gives the findings. The proposed ant colony optimization algorithm evaluates the accuracy of the suggested result using the ROUGE scores using DUC datasets. The accuracy graph of the proposed work is shown in Figure 2. The detailed ROUGE evaluation strategy is represented below in Section 5.2.

5.1. Dataset Description

An annual conference sequence called the Document Understanding Conference (DUC) is focused on testing automated text summarizing tools. The National Institute of Standards and Technology (NIST) hosts this series of conferences to advance automatic text summarizing research and allow scholars to take part in an esteemed scientific conference.

The DUC conference published the DUC 2005, DUC 2006, and DUC 2007 datasets in 2005, 2006, and 2007, correspondingly. They are three of the most common open benchmark datasets for multi-document summarization that are particularly provided for determining multi-document summarization systems. All datasets were scored using the ROUGE evaluation and had various kinds of common summaries. The proposed research performed several experiments using the benchmark DUC 2005, DUC 2006, and DUC 2007 datasets to analyze the effectiveness of our summarization method. They each include 50, 50, and 50 topics. There are topic descriptions for each topic, as well as document sets of 25 to 50, 35, and 30 news sections, correspondingly. Each topic’s reference summaries are required to be 200 to 300 words in length.

Each document refers to a news report from a different news organization, like The Associated Press, New York Times, or The Wall Street Journal [19]. The reference summaries constructed by human evaluators in these datasets for the evaluation of the MDTS are probably 250 words in length. These are the open benchmark datasets for MDTS that are used the most frequently and are explicitly provided for system evaluation. Hence, the summary produced by the algorithm must have a range of 250 to 300 words to be evaluated using the effectively open reference summaries. It is crucial to acknowledge that the primary function of datasets is query-focused text summarization, meaning that each subject is linked to a question that embodies the information demand. Our summary system, however, uses a standardized summary strategy. As a result, in all of our trials, users produce the final summary without getting the dataset’s query into factor. The different subsets of the DUC 2005, DUC 2006 and DUC 2007 datasets are briefly described in

Table 1. An overview of the Different DUC datasets.

Feature Description	DUC 2005	DUC 2006	DUC 2007
Number of Topics	50	50	50
Number of documents per topic	25 to 50	35	30
Total number of documents	1682	1130	1150
Data source	TREC	AQUAINT	AQUAINT
Reference summary length	200 words	250 words	300 words

.

5.2. ROUGH Evaluation Metrics

The most popular technique for analyzing text summarization challenges, ROUGE (Recall-Oriented Understudy for Gisting Evaluation) toolkit version 2.0 [20], was used to examine the effectiveness of our suggested method. DUC chose ROUGE as the authorized assessment technique to gauge the caliber of summaries produced by the system. The ROUGE toolset counts the number of overlapping units, like N-grams, among the 2a framework-generated summary and a collection of reference summaries to determine the accuracy of the created summary. Due to their being selected as the authorized measures in the DUC 2007 dataset, we employed two systematic evaluation measures included in the ROUGE tools, mainly ROUGE-A and ROUGE-B, for all tests to examine our summarization method and compare it to a few of the most cutting-edge approaches.

The ROUGE-A and ROUGE-B algorithms analyze the bigram and unigram intersect between the reference summaries produced by humans and the system, correspondingly.

According to Lin (2004) [21], these two measures are a special instance of ROUGE-Z and may be computed by the following ROUGE-Z equations:

$$ROUGE-Z=\frac{{\Sigma }_{0\in Rsumm}{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\Sigma }_{z-gram\in 0\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}}Coun{t}_{match}\left(Z-gram\right)}{{\Sigma }_{0\in Rsumm}{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\Sigma }_{z-gram\in 0\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}} Count\left(Z-gram\right)}$$

(18)

where Z denotes the size of the Z-gram, Count match (Z-gram) denotes the total amount of matching Z-grams that may co-occur in a system-generated summary and a collection of reference summaries, and Count (Z-gram) denotes the number of Z-grams that can co-occur in the reference summaries. ROUGE-Z is a recall-oriented metric since the denominator of Equation (18) is the total number of N-grams that appear in the reference summaries.

Based on the specified evaluation metrics (ROUGE-A, ROUGE-B, and ROUGE-Z), the ROUGE Scores toolbox reports findings in the form of precision, recall, and F1-score. To evaluate the performance of our proposed approach with several advanced approaches that have produced the most effective outcomes on the DUC 2005, DUC 2006, and DUC 2007 datasets, this paper will use the F-score, which is the harmonic average of the precision and recall.

Table 2. ROUGE Scores ratings of our proposed methods on DUC 2005, DUC 2006 and DUC 2007.

t Metrics	DUC 2005			DUC 2006			DUC 2007
	Rough-A	Rough-B	Rough-Z	Rough-A	Rough-B	Rough-Z	Rough-A	Rough-B	Rough-Z
Recall	0.401	0.089	0.136	0.451	0.1	0.175	0.527	0.110	0.157
Precision	0.395	0.081	0.140	0.463	0.156	0.169	0.5	0.097	0.155
F-Score	0.408	0.085	0.143	0.468	0.113	0.178	0.523	0.099	0.156

represents the evaluation findings of our proposed summarization technique developed using the dynamic population size and third objective function based on DUC 2005, DUC 2006 and DUC 2007. The goal function, together with the dynamic population size, suggests greater performance based on the findings of the tests conducted on DUC datasets. We have analyzed the solution using different DUC datasets to validate its quality. The outcomes of our DUC 2005, DUC 2006 and DUC 2007 tests using the goal function and various population sizes are shown in Table 2.

5.3. MOACO with Baselines Evaluation Metrics

In the experiments, we evaluate our proposed method with several baselines, like the DUC NIST baseline, the average ROUGE scores and the median scores of all DUC participating frameworks, many extractive baselines, and several modern abstractive MDS techniques. The sentences with the highest scores are extracted to provide a summary using the extractive baselines centroid [16], which assesses sentences based on the centroid of texts; sentences are sorted using a graph-ranking system created by TextRank [17], which creates a representation of each sentence as a graph; using the idea of eigenvector significance in a graph’s visualization of sentences, LexPageRank [18] calculates sentence salience rankings; MultiMR extracts a topic-focused summary from several papers using the multi-modality manifold-ranking technique; and Sub-modular maximizes sub-modular functionalities while adhering to a budget restriction to accomplish summarization.

The algorithms proposed in [20,21] are implemented, respectively, by Submodular1 and Submodular2. The multi-document summarizing method is the basis for all of the aforementioned extractive baselines. The most recent abstractive baselines are MDS, a sparse-coding method built on a unified optimization framework that uses compression; TextSumm, an abstractive technique that involves sentence fusion and text-based global optimization; as well as PSM, an abstraction-based MDS architecture that produces novel phrases by selecting and integrating noun and verb phrase combinations.

Table 3. The efficiency results of our proposed MOACO on DUC 2006.

System	ROUGH-A	ROUGH-B	ROUGH-Z
D-ACO	0.795	0.409	0.121
MACS	0.804	0.415	0.130
ABC	0.815	0.456	0.139
MOACO	0.829	0.459	0.147
ABC	0.815	0.456	0.139
MOACO	0.829	0.459	0.147

’s results for the DUC 2006 datasets demonstrate how well our system performs in comparison to MOACO on ROUGE-A, while outperforming the three baselines on ROUGE-B and ROUGE-Z. The results in

Table 4. The efficiency results of our proposed MOACO on DUC 2007.

System	ROUGH-A	ROUGH-B	ROUGH-Z
D-ACO	0.831	0.493	0.163
MACS	0.876	0.502	0.175
ABC	0.883	0.525	0.179
MOACO	0.915	0.531	0.185

demonstrate that, on the DUC 2007 datasets, our system exceeds the three baselines. Furthermore, our approach works much better on both datasets than the three baselines using the Pyramid metric. The outcomes illustrate how words and instances are used to describe document content, as well as the efficiency of our suggested model for summarizing. The performance of our system continuously compares to that of the baseline system on both datasets, proving the value of MOACO approaches.

The ROUGE scores were examined using the DUC 2007 datasets, and the findings are shown in Figure 2 along with a comparison of their performance to that of developed and previous methods.

According to the DUC 2007 dataset’s summary performance and accuracy metrics, the proposed system provides the highest ROUGE scores; these are essential to the original text among several existing and suggested frameworks, with ROUGE-A scores of 51.07, ROUGE-B scores of 30.15, and ROUGE-Z scores of 51.42, accordingly. The aforementioned experimental findings on the benchmark DUC 2007 datasets for multi-documents on “ROUGE-A, ROUGE-B, and ROUGE-L” demonstrate that the proposed approach outperforms the most recent summarization models (ATS) in terms of the semantic and syntactic structure.

5.4. Convergence Analysis based on MOACO

In this section, several algorithms are chosen for comparison. Additionally, several scale test scenarios are used to evaluate how these algorithms’ convergence analyses per- form. The aim is to quantify the number of algorithmic maximum fitness evaluations across various scale test cases. Following that, we examine how well the algorithm performed following convergence. The test cases include ROUGE-A; ROUGE-B and ROUGE-Z, and the test algorithms include D-ACO, MACS, ABC, MOACO, and so on. The number of fitness evaluations is represented by the x-axis in Figure 3a,b. The number of fitness examinations grows along with the problem’s size. The ROUGE value is shown on the y-axis. The figure illustrates how each algorithm’s location of convergence increases as the size of the test cases increases.

5.5. Case Study

To further ensure the performance of our strategy, we compared it to various approaches using DUC 2007. Table 2 provides the findings of this comparison. The table demonstrates that, when compared to other solutions, our suggested solution performs more effectively based on ROUGE-A, ROUGE-A, and ROUGE-Z evaluations. As demonstrated by the findings in Table 3, our suggested summarizer (MOACO) performs better than all other approaches recently presented for multi-document text summarization using the DUC 2005, DUC 2006, and DUC 2007 datasets. This is because it enhances other state-of-the-art methods based on all three-evaluation metrics, such as ROUGE-A, ROUGE-B, and ROUGE-Z. The findings also show an improved ROUGE-A and ROUGE-Z ranking measure performance for our solution using DUC 2007. Based on the analysis, this performance is connected to several aspects of our system.

To maximize the coverage of essential and relevant data offered in the document collection, MOACO first took into consideration both sentence-to-document and sentence-to-topic similarities. Analyzing cosine similarity in the summary also reduces the number of candidate sentences that contain redundant information. Additionally, by taking into account cosine similarity, it also takes into account all of the concepts addressed by the source cluster, as well as common proper nouns in sentences from each document; this is another basis for choosing phrases that are more important and educational. Second, compared to previous methods, the weighted combination of sentence scoring measures utilized in the proposed ACO’s objective function has a substantial impact on the production of quality extract summaries. The most efficient and most scalable meta-heuristic evolutionary technique, the proposed MOACO with modified quantum measurement and an adaptive quantum rotation gate, is mainly responsible for the best outcomes.

6. Conclusions

In this paper, the Pareto-optimal solution-based multi-objective optimization technique was proposed for developing the MDTS. In our method, extractive summarization is proposed as an optimization issue, and the global optimum solution is found by combining a Pareto-based optimal solution with an ant colony optimization strategy. This improves the efficiency and speed of our suggested system. This paper used the DUC 2007 benchmark datasets, which provide state-of-the-art outcomes, to test our summarization method. In terms of ROUGE-A, ROUGE-B, and ROUGE-Z, we have contrasted our strategy with some of the most cutting-edge summarization systems now in use. The comparison’s findings show that our solution achieved better performance than any other strategy in terms of practically every ROUGE assessment indicator. A well-tuned MOACO may offer promising outcomes in comparison to many other evolutionary algorithms in the field of text summarization, as this work also illustrates. In terms of producing labels for efficient summaries, the suggested model performs well.