A new multi-document summarisation approach using saplings growing-up optimisation algorithms: Simultaneously optimised coverage and diversity

Abstract

Automatic text summarisation is obtaining a subset that accurately represents the main text. A quality summary should contain the maximum amount of information while avoiding redundant information. Redundancy is a severe deficiency that causes unnecessary repetition of information within sentences and should not occur in summarisation studies. Although many optimisation-based text summarisation methods have been proposed in recent years, there exists a lack of research on the simultaneous optimisation of scope and redundancy. In this context, this study presents an approach in which maximum coverage and minimum redundancy, which form the two key features of a rich summary, are modelled as optimisation targets. In optimisation-based text summarisation studies, different conflicting objectives are generally weighted or formulated and transformed into single-objective problems. However, this transformation can directly affect the quality of the solution. In this study, the optimisation goals are met simultaneously without transformation or formulation. In addition, the multi-objective saplings growing-up algorithm (MO-SGuA) is implemented and modified for text summarisation. The presented approach, called Pareto optimal, achieves an optimal solution with simultaneous optimisation. Experimentation with the MO-SGuA method was tested using open-access (document understanding conference; DUC) data sets. Performance success of the MO-SGuA approach was calculated using the recall-oriented understudy for gisting evaluation (ROUGE) metrics and then compared with the competitive practices used in the literature. Testing achieved a 26.6% summarisation result for the ROUGE-2 metric and 65.96% for ROUGE-L, which represents an improvement of 11.17% and 20.54%, respectively. The experimental results showed that good-quality summaries were achieved using the proposed approach.

Keywords

Content coverage document summarisation document understanding conference information diversity multi-criteria optimisation multi-document summarisation optimisation model recall-oriented understudy for gisting evaluation saplings growing-up algorithm

1. Introduction

The development of information and communication technologies has led to an exponential increase in electronic information generated each day. This ease of access to text collection has resulted in consumers being confronted with a significant amount of online information. As a result, digital data sizes are growing, and automated summarisation systems are used to cope with the large amounts of data amounts of data flow. Therefore, today’s readers face an increased need for effective text summarisation systems to convert text into short summaries [1 –4]. However, it is challenging to create a single text document that meets the reader’s needs satisfactorily within a set topic within a limited period. Document summarisation systems are used to provide a solution to this problem. Automated document summarisation is used to obtain a more compact version of a textual document while preserving its fundamental features. With automated multi-document summarising systems, the aim is to create close-to-ideal summaries of documents to realise a quicker overall review of text-based information [5 –8].

Various approaches produce different types of abstracts, such as abstractive-based and extractive-based. Abstractive summaries are obtained by re-representing information presented in the text to be summarised. Therefore, the summaries obtained are independent of the input texts. Abstractive summarisation systems aim to understand the document linguistically and conceptually and then re-express the document in a more limited dimension based on maximum scope and consistency. Extractive summarisation, conversely, selects a subset of the input documents to create a summary. Therefore, extractive summarisation is carried out without re-expression or interpretation in summary based on the input documentation. Extractive summarising systems have proven quite favoured due to their simplicity and low cost as per abstractive summarisation systems. However, it is challenging to predict which sentences in the text will be used in abstractive systems and how they will be reinterpreted later. This is a significant disadvantage compared to subtractive summarisation systems [5,9 –12].

Depending on the count of text documents, an abstract can be single-document or multi-documentary, that is, single-document abstraction focuses on a shorter representation of a single-document, while multi-document abstraction focuses on obtaining abstracts from a set of documents. A single-document summary can be considered as a simplification of the multi-document summary system, whereas a multi-document summarisation system can be used to illustrate the outline of data held in with a diverse of texts [13 –15].

According to the summary contents, abstracts are classified as query-based or comprehensive. While query-based summaries perform according to user queries, generic summaries focus on obtaining the underlying notions of the reference documentation out of reference to foreign information or guidance [16,17].

In addition, document summarisation can be performed in two different ways: supervised and unsupervised. Selecting meaningful sentences in supervised summarisation methods is offered as a classification issue by separating units in the documents to be summarised according to whether they are included in the summary. Unsupervised methods often score sentences in documents using a set of predefined definitions and properties. Supervised methods need a significant volume of data, while unsupervised techniques require no educational data [2,5,13,14,18]. Promising results are obtained by transferring learning using pre-trained word embeddings within the scope of supervised learning [19].

This study introduces an extractive generic summarisation system using a multi-objective mission derived from maximum coverage and minimum redundancy values from the original documents. Document summarisation has been represented as an optimisation problem. The selected algorithm is the saplings growing-up algorithm (SGuA), which has not been used in previous studies on document summarisation. The optimisation problem is addressed in the research by the multi-objective saplings growing-up algorithm (MO-SGuA).

In this work, only sentences with the highest coverage value were excluded from the whole document while determining units to be chosen for the abstract. At the same time, to expand the diversity of sentences and concepts utilised for creating the summary, a redundancy parameter was simultaneously minimised. For this purpose, two objective functions were formed through modelling. A few previous studies in the literature have achieved summarisation using concurrent optimisation. In addition, there are many studies introduced as multi-objective optimisation. However, the fitness functions of these studies contain a single mathematically unified objective. Furthermore, in these studies, more than one factor is combined mathematically. Therefore, our presented study differs from the previous ones regarding its innovative perspective and the values it reports.

The remainder of the work is planned as follows: Section 2 discusses related works in document summarisation. Then, section 3 explains the motivation and objectives of this study, and the next section information is given about the problem discussed in this study. While Section 5 contains information about the SGuA used, the experimental studies performed are described in detail in Chapter 6. Finally, in Section 7, detailed information about the study results is given.

2. Related works

The sentence weighting phase is the critical step of the extractive summarisation technique, and researchers continue working to improve sentence sorting to increase the standard of the abstract. Text summarisation is a field of study for which popularity is increasing daily. Summarisation was previously conducted using statistical tools; however, this offers poor performance in terms of sentence selection. Therefore, in the last 20 years, researchers have considered the document summarisation problem as an optimisation problem [20,21].

In the context of multi-document summary, it aims to minimise the relationship between sentences in summary creation based on various documents and obtain a good summary with maximum coverage. Researchers have focused on optimisation algorithms such as genetic algorithm (GA), particle swarm optimisation (PSO), harmony search (HS), differential evolution (DE) and cat swarm optimisation (CSO) for both single- and multi-document summarisation [22]. In addition, many researchers have conducted single-/multi-objective optimisation studies that consider features such as coverage and/or redundancy to obtain high-quality summaries [23]. While coverage states the essential concepts and subjects in a document to be summarised and included in the summary, redundancy aims to avoid the repetition of similar concepts and subjects. It is considered an NP-hard-type problem to find the most appropriate summary for the purposes above.

Therefore, researchers have employed various methods to obtain appropriate solutions such as population-based [5,24], swarm intelligence [22,25], artificial bee colony [22,23] and ant colony and cuckoo search [20]. All criteria in single-objective optimisation approaches are weighted to obtain a one-dimensional function. Weights are determined from a purely subjective perspective, which directly and significantly influences the optimisation result. Zhao and Tang [26] proposed a query-based, GA-based hashing approach to achieve length, scope, informativeness and redundancy.

Kogilavani and Balasubramanie [27] provided a feature-based multi-generic summariser using GA. Similar documents are grouped using a clustering algorithm, and meaningful sentences for each cluster are determined according to specific criteria. Maximum length, coverage, informativeness and minimum redundancy are targeted in selecting the best sentences. In the study of Huang et al. [28], a multi-objective optimisation problem used information coverage, significance, redundancy and text coherence. Aliguliyev [29] used the PSO algorithm for text clustering to produce a rich summary and proposed a generic, multi-document summarisation method by optimising the similarities of the clusters. Nandhini and Balasundaram [30] used the DE algorithm to create an easy-to-understand textual summary. Lozano et al. [31] proposed an algorithm to provide an extractive summation from multiple documents that optimise the coverage and redundancy variables through binary optimisation.

Alguliyev et al. [13] optimised three features by focusing on the Boolean programming problem solved by a DE algorithm. Mirshojaei and Masoomi [32] used cuckoo search optimisation algorithm (CSOA) to improve the performance of extractive-based text summarisation. Rautray et al. [33] proposed a corpus-based generic and single-document method to obtain cohesion and coverage values of sentences in summary through the use of the statistical properties of each sentence. Goleman et al. [34] introduced a new multi-document summarisation approach that simultaneously optimised coverage, diversity and coherence parameters.

Unlike previous studies, Saleh et al. [35] realised a real multi-purpose function definition that utilised the non-dominated sorting genetic algorithm-II (NSGA-II) optimisation model for extractive summarisation. Sanchez-Gomez et al. [36] mentioned the lack of multi-objective optimisation approaches and presented an extractive multi-document summarisation approach. John et al. [5] provided a generic, extractive summary in a population-based optimisation approach that performed optimisation separately according to three determined objective functions. As a result, common sentences found in three separate abstracts were selected and a final summary was prepared.

Table 1 includes related studies, single- or multi-document summary, single/multi-criteria objective function information, applied algorithm and criteria to be optimised. Most of the related works shown in Table 1 utilised the document understanding conference (DUC) data set and evaluated their approach using recall-oriented understudy for gisting evaluation (ROUGE) metrics with coverage, redundancy, length, coherence and significance, the most commonly used criteria. Optimisation-based document summarisation approaches present specific time-consuming performance problems and no further formulation. They also differ from each other in terms of primary objectives such as redundancy reduction, coverage and maximising diversity. In this study, appropriate and sufficient formulation analyses were conducted to achieve high-quality, rich abstracts focused on multiple purposes. In addition, simultaneous optimisation of different semantic objectives was employed, such as coverage and diversity. The formulation was achieved in which the most appropriate sentences were identified from the main text.

Table 1.

Optimisation approach used in document summarisation.

Work	Optimisation information
Work	Multi-objective	Simultaneous	Algorithm	Criterion/objective
Zhao and Tang [26]	No	No	GA	length, coverage, informativeness andredundancy
Kogilavani andBalasubramanie [27]	No	No	GA	length, coverage, informativeness andredundancy
Huang et al. [28]	Yes	No	–	Coverage, significance, redundancy andcoherence
Aliguliyev [29]	No	No	PSO	Clustering
Nandhini and Balasundaram [30]	No	No	DE	Informative and cohesion
Lozano et al. [31]	No	No	CHC Greedy	Coverage and redundancy reduction
Alguliyev et al. [13]	No	No	DE	Relevance, redundancy and length
Mirshojaei and Masoomi [32]	No	No	CSOA	–
Rautray et al. [33]	No	No	DE, PSO	Redundant reducing and maximisingrelevancy
Goleman et al. [34]	No	No	SaDE	Coverage, diversity and coherence
Saleh et al. [35]	Yes	Yes	NSGA-II	Coverage and redundancy reduction
Sanchez-Gomez et al. [36]	Yes	Yes	ABC	Coverage and redundancy reduction
John et al. [5]	Yes	No	–	Coverage and redundancy reduction

GA: genetic algorithm; PSO: particle swarm optimisation; CSOA: cuckoo search optimisation algorithm; NSGA-II: Non-dominated Sorting Genetic Algorithm-II; CHC: Cross-generational elitist selection, Heterogeneous recombination, Cataclysmic mutation; SaDE: Self-Adaptive Differential Evolution; ABC: Artificial Bee Colony; DE: Differential evolution.Bold expressions in the Simultaneous column indicate real simultaneous optimization studies.

3. Motivation and objectives

This study introduces an extractive generic summarisation system using a multi-objective mission derived from maximum coverage and minimum redundancy values from the original documents. Document summarisation has been represented as an optimisation problem. The selected algorithm is the SGuA, which has not been used in previous studies on document summarisation. The optimisation problem is addressed in the research by the MO-SGuA.

There are many extractive text summarisation studies in the literature. Some of these studies are summarisation studies based on optimisation. However, these optimisation-based studies are not real-time simultaneous text summarisation studies except [35,36].

MO-SGuA focuses on measuring the summary value of each candidate sentence and how much residual information it contains. It does this by simultaneously optimising the goals represented with rich content and minimum repetition. However, these two criteria contradict each other. For this reason, some of the researchers have tried to combine the optimised objectives at different times. Another group of researchers opted to optimise the conflicting criteria by formulating them mathematically or by weighting the objectives. However, in this case, too, the optimisation performance leads to results that are highly dependent on the weighting or mathematical formulation of the objective function. This is a non-multi-objective approach and has a limiting and guiding effect on the solution set.

Within the scope of the proposed approach, it is aimed to isolate the different conflicting objectives from the formulation forms of the researchers. We also aimed to determine the sentences that make up the summary without restrictions. Candidate sentences are selected over an optimal result set obtained by optimisation. In cases where a candidate solution outweighs the other solutions for all objectives, the solution is considered to have more optimal values than the others.

The SGuA has a good level of robustness and high computational efficiency. It draws its strength from the ability to generate stable initial populations without randomising. For this reason, SGuA has been used in this study to solve the simultaneous optimisation model. The purpose of using SGuA and real concurrent formulation and the regular starting population is to investigate the overall effect of these two concepts on text summarisation performance.

We aimed to take the multi-objective studies in the field a step further.

A Pruning step was applied for the first time in this study. The quality of the solution was improved by pruning the branches on the sapling stem. First, existing branches (candidate summary sentences) are grouped in pairs, and then the branch that is weakest in the pair is pruned.

This is the first study in which an SGuA-based approach has been designed and applied for a multi-document summary. In addition, comparisons were made with other studies in the field.

4. Problem definition

In this section, document summarisation is transformed into an optimisation problem.

4.1. Similarity-based sentence scoring

Vector space model (VSM) is the most common method used to represent sentences. Each term represents a dimension in the feature vector space. Assume that D = {d₁, d₂,…,d_N} document set is decomposed into S = {S₁, S₂,…,S_n} sentences. Here, N is the number of documents and n is the number of sentences, while s_i is the ith sentence in S. Set T = {t_1, t_2,,,, t_m} represents all terms in S, S_i ₌ [wi₁, wi₂,…, wi_m]. The weight w_ik is associated with the term t_k in a sentence s_i and can be calculated using the term frequency inverse-sentence-frequency scheme (t_f_isf). This is a combination of tf and isf, where t_f holds the number of times a term appears in a sentence, while isf keeps track of how many sentences in the document collection contain the term [9,37].

Local term weighting: tf_ik = m_ik/m_i, where m_ik is the frequency of occurrence of the term t_k in the sentence si, and m_i is the number of terms in the sentence s_i.

Global term weighting: isf = log(n/n_k), where n is the total number of sentences in the document, n_k is the number of sentences where the term t_k appears, and m is the number of different terms.

Each s_i sentence is positioned as a point in the m-dimensional vector space

w_{i k} = t f_{i k} . \log (\frac{n}{n_{k}})

(1)

where W_ik is the weight of the term t_k in the sentence s_i (Figure 1).

Figure 1.

Graphical illustration of preprocessing and sentence scoring stages.

The centre of gravity of the main document and the candidate can be represented as a summary vector. The overall content of the D document collection can be summarised by the average weight of the term m in T. This can be achieved with an average vector calculation

o_{k} = \frac{1}{n} \sum_{i = 1}^{n} w_{i j}, k = 1, 2, \dots, m

(2)

with cosine similarity between S_i = [wi₁, wi₂,…, wi_m] and S_j =[wj₁, wj₂,…, wjm] clauses

s i m_{c o s} (s i, s j) = \frac{\sum_{k = 1}^{m} w_{i k} w_{j k}}{\sqrt{\sum_{k = 1}^{m} w_{i k}^{2} * \sum_{k = 1}^{m} w_{j k}^{2}}}, i, j = 1, \dots, n

(3)

4.2. Formulation of the optimisation problem

This section presents a multi-objective optimisation for the problem of multi-document summarisation and then explains the strategies adopted to resolve this optimisation problem (Figure 2).

Figure 2.

Graphical illustration of the optimisation problem.

In this study, the summary belonging to the sentence set S = {s₁, s₂,…, s_n} should have the maximum coverage and minimum redundancy possible. Coverage means that the summary produced includes as many subtopics as possible. However, focusing only on sentences with the highest coverage values to cover all subtopics can result in the repetition of subtopics in summary. Therefore, within the scope of this study, a second objective was needed to ensure minimal subtopic repetition because a rich summary should cover all subtopics as much as possible and should include as few repetitions as possible. For this reason, this study’s focus was not only on coverage but simultaneousness and with minimal redundancy backups. A simultaneous summary of these qualities reflects the quality of the summary.

4.2.1. Maximised coverage

The coverage value of the summary reflects the extent to which it covers the content in the original documents. Umam et al. [30] stated that the coverage calculation should consider content similarities between the candidate summary document and the main document. By calculating the similarity between each sentence in summary and the main content of the original document, the importance of each summary sentence in the original document can be assessed. Sanchez-Gomez et al. [36] stated that the average weights of the document terms or the centre of gravity of the document reflect the main content of the document set. To calculate the coverage value of the summary, equation (4) was applied

s u m m a r y_{c o v e r a g e} (x) = \sum_{i = 1}^{n} \frac{sim (s_{i}, o) . x_{i}}{n}

(4)

where x_i∈ {0,1}, and the binary solution vector of the summary is x = (x₁, x₂,…, x_n).

4.2.2. Minimum redundancy

The minimum redundancy value of a summary relates to the diversity of sentences in summary and is obtained by calculating the similarities between sentences that make up the abstract. The higher the total sentence similarity of the summary, the lower the diversity. However, a high level of diversity is required to produce a quality summary [34]. In other words, low diversity has the potential to provide a weak summary because the redundant text may well contain valid and useful information. For a good summary, similarity values between sentences forming the summary held to a minimum. In calculating the redundancy value of a summary, equation (5) is applied

s u m m a r y_{redundancy} (x) = \frac{1}{(\sum_{i = 1}^{n - 1} \sum_{j = i + 1}^{n} sim (s_{i}, s_{j}) u_{i} u_{j}) \sum_{i = 1}^{n} X_{i}}

(5)

u_{i}, u_{j} \in {0, 1}, i, j = 1, \dots, n

(5)

Simultaneous optimisations of different objectives such as maximum coverage and minimum redundancy and multi-document text summarisation problem formulation are as follows

m a x f (x) = {f_{c o v e r a g e} (x), f_{r e d u n d a n c y} (x)}

(6)

x_{i} \in {0, 1}, i = 1, \dots, n

(7)

5. Proposed MO-SGuA

The MO-SGuA is presented in this section. Before explaining the details of the approach presented, the SGuA will be mentioned. Pruning, mutation and repair operators will be explained afterward.

Artificial techniques inspired by nature can provide a solution that is considered close to the optimal level in a reasonable amount of time. Karcı [39,40] proposed an effective optimisation algorithm inspired by natural events like planting and growing seedlings.

The SGuA has a good level of robustness and high computational efficiency. It draws its strength from the ability to generate regular initial populations without randomising. For this reason, SGuA has been used in this study to solve the simultaneous optimisation model. Detailed information on SGuA can be found in studies by Saleh et al. [35] and Sanchez-Gomez et al. [36].

5.1. Text preprocessing

Stop-words were removed before the operation of raw documents. In this way, the workload of the operation was decreased. Only terms with certain content are included in the process. In addition, specific representative changes in this study were applied between the words forming the texts to be summarised using a different perspective. Finally, changes were made in words, taking into account the relationship between the terms in the document/s and the n-grammes. Briefly, a novelty method was developed, unlike well-known text-preprocessing tools.

The method suggested that the terms in the raw document have been converted into uncombined forms. Thus, the relationships between words can be determined correctly despite their suffixes. This change was applied using C# in .NET platform.

Algorithm 1.

Pseudocode of word conversions applied.

1.	Input	(Texts from the DUC data sets are presented as input data to the algorithm)
2.	Preparation	(Matrix and variables to be used are defined and initial values assigned)
3.	Sentence vectorised	(Input paragraph separated to obtain sentence vectors)
4.	Word vectorised	(Word vectors are created from sentence vectors)
5.	All alternatives	(The most appropriate word selected from alternative words list (n-gramme))
6.	Best alternatives	(The most suitable alternative is selected from all alternative words)
7.	Change word vector	(Replace with the most appropriate alternative found in word vectors)
8.	Loop	(Repeat until word vector size)
9.	Create output text	(Combine words in word vector according to sentence vector order after all operations ended)

5.2. Main steps of MO-SGuA

In multi-purpose optimisation problems modelled for document summarisation, the vast majority of researchers reduce the problem to single-purpose optimisation using fixed and variable-weighted goal functions. These solutions are not multi-purpose problems conducted simultaneously, and few studies on the subject use this format. However, such methods can present decision-makers with certain disadvantages, such as poorly modelling the problem, producing a single solution, and limiting Algorithm 2.

Algorithm 2.

Proposed Multi-Objective Saplings Growing-up Algorithm.

1. t←0 // Initial time

2. SowingSapling(G(t)) // Initial garden (solution)

3. Whilet <= Maximum Cycle do

4. G1(t)←mating_operation(G(t))

5. G2(t)←mix&develop_operation (G1(t)) // *2

6. G3(t)←pruning_operation (G2(t))

7. G4(t)←mutation_operation (G3(t))

8. ComputeObjectiveFunction((G4(t))

9. Select_best_solution via_pareto() // Pareto Front

10. G(t + l)←Selection(G4(t)/2)

11. t ←t + i

12. end while

13. Repair

14.create summary

First, the initial state is created (Initial garden). Then, the initial population generation step is carried out as recommended in the original SGuA. At this stage, the sentences in the document collection are selected by creating a regular initial population (Line 2). The initial garden is non-randomised and uniform by the nature of SGuA.

After creating the objective function and uniform initial solution, the main steps of Algorithm 2 are repeated with a specified value measure (Lines 3–12).

During the pairing phase, new saplings (Line 4) are produced in the form of a global search using existing information among the existing summary solutions. The number of solutions does not change in this operator.

In the proposed MO-SGuA, the mix and develop operator improves the solution quality of matching seedlings (Line 5). This operator uses the Euclidean distance between the S_i and S_j seedlings. In this case, the number of solutions doubles [38 –40].

The next step is the pruning phase (Line 6), used first in this study. At this stage, the branches on the sapling trunk are pruned to increase the solution quality. Existing branches (sentences in the candidate summary) are grouped in pairs. Afterward, weak branches are pruned depending on the amount of the original document content of the sentences. At this stage, new branches (sentences) are not added to the binary solution vector (x = (x₁, x₂,…, x_n)) of the summary.

As specified in Section 6.3 (Line 7), the mutation operator is performed. The number of solutions does not change in this operator. By adding or subtracting sentences from the summary binary solution vector (x = (x₁, x₂,…,x_n)).

New members are selected if a goal value is minimised (deterioration) and another goal value is increased (improved). The solution will be chosen only if it dominates the original, that is, it heals some goals without worsening others. The best solutions are determined and selected from the solutions obtained in Line 9. This process primarily sorts and selects solutions according to the dominance relationships in Pareto sets. At the end of the cycle, the colony size returns to its original size. If there is an overflow outside of the permitted word limits (Line 13), the repair operator is applied as specified in Section 6.3. Then the next cycle begins.

5.3. Pruning operator

A Pruning step was applied for the first time in this study. In this stage, the quality of the solution was improved by pruning the branches on the sapling stem. First, existing branches (candidate summary sentences) are grouped in pairs, and then the weakest branch in the pair is pruned. The amount of the sentences covering the original document content is decisive at this stage, and new branches (sentences) are not added to the binary solution vector (x = (x₁, x₂,…, x_n)) of the summary. Pruning is a local search, so there is no change in the number of solutions. The pruning steps are as stated in Algorithm 3.

Algorithm 3.

Pruning algorithm.

1. summary_size = 100|| 200|| 400

2.for i = 1 to len(solution_matrix) do

3. sentence_indices = get_sentence_indices (i.solution)

4. While candidate_summary_size > summary_size

5. j = random(sentence_indices)

6. sentence_indices.remove(j)

7. k = random(sentence_indices)

8. sentence_indices.remove(k)

9. if

sim (s_{j}, o) \geq sim (s_{k}, o)

10. candidate_solution[k]= 0

11. else

12. candidate_solution[j]= 0

13. end if

14. end while

15. end for

5.4. Mutation operator

Summary mutations are applied by making changes with a mutation operator regarding whether or not sentences are included in the summary. Here, the probability of mutation is controlled by pm. Unique random ri ~ [0,1] variable is generated for each sentence. If the condition (ri ≤ pm) is met, it is decided whether or not a sentence will be included in the summary according to equation (8)

sim (S_{i}, o) \geq \frac{1}{n} \sum_{j = 1}^{n} sim (s_{j}, o)

(8)

Algorithm 4.

Mutation algorithm.

1. p_m = 0.1

2. for j = 1 to n do

3. ri~ [0,1]

4. if

(ri \leq pm)

and

(sim (S_{i}, o) \geq \frac{1}{n} \sum_{j = 1}^{n} sim (s_{j}, o))

5. x_j = 1 //corresponding bit in the binary representation of the summary

6. else

7. x_j = 0

8. end if

9.end for

5.5. Pareto-optimal front

To resolve the optimisation problem, adaptations were applied to the SGuA. In many cases, a single optimal solution cannot be found in very limited decision problems. Instead, there is a set of alternative solutions for at least one purpose with more appropriate values than other solutions. These alternative solutions are known as Pareto-optimal solutions [5,28]. Using this approach, solutions are compared to achieve the Pareto-optimum cluster (Figure 3). If a solution suppresses other solutions for all purposes, then that solution is considered better than the others, with the solution having more optimum values than others.

Figure 3.

Pareto-optimal set.

5.6. Repair operator

Each cycle is checked at the end to ensure that the generated summary remains within the previously determined summary limits. Equation (9) is applied in order to check if the word length limitation has been violated

subject to L - ε \leq \sum_{i = 1}^{n} l_{i} \leq L + ε

(9)

where ϵ is the tolerance coefficient of the summary length, which is the length of the sentence $S$ , and L is the desired summary size. If the created summary has a size below the specified limit, it is discarded based on the proposed approach. However, where the size exceeds the limit, the summary is not discarded, and the Repair operator modifies the summary to provide a more rich summary.

Regarding the quality of the abstract, the main determinant is which sentence (s) will be issued. Sentences should be similar, and a threshold (δ) value should be determined. Throughout the experimental processes, the value was chosen as δ = 0.3. Binary sentence groups with a similarity above this value are candidate sentences to be deleted from the summary, as throwing one or two similar sentences will only reduce the coverage value of the summary by a minimum amount (rich summary carries max Coverage value, see Section 4.1). The similarity between the sentence repair and Sj is calculated according to equation (3)

s i m_{c o s} (s i, s j) \geq δ

(10)

Here, if the condition specified in i ≠ j and the Si Sj∈ summary in equation (10) is met, then the repair operator is run. It was then determined which of the similar sentences should be omitted, here $s i m_{c o s} (o^{s u m}, o)$ is the similarity of the summary in the sentence Si, and $s i m_{c o s} (o^{s u m - s_{i}}, o)$ is the similarity of the summary in which there is no sentence. Thus, the effect of sentence Si on the summary is determined. Finally, the process continues as specified in Algorithm 5. It is weighted with a coefficient of 10 to strengthen the effect of S_i and S_j sentences on summary quality.

Algorithm 5.

Repair algorithm.

1. while

(s u m m a r y_length > L + ε)

2. for i = 0 to n do

3. for j = 1 to n do

4. if

s i, s j \in Summary and i! = j a n d s i m_{c o s} (s i, s j) \geq δ

scor e_s i = s i m_{c o s} (s i, o) + ((s i m_{c o s} (o^{s u m}, o) - s i m_{c o s} (o^{s u m - s_{i}}, o)) *

scor e_s i = s i m_{c o s} (s j, o) + ((s i m_{c o s} (o^{s u m}, o) - s i m_{c o s} (o^{s u m - s_{i}}, o)) *

7. if

s c o r e_s i \geq s c o r e_s j

8. remove Sj

9. else

10. remove Si

11. end if

12. end if

13. end for

14. end for

15. end

6. Experimental works

The experimental processes of the presented approach have been executing out using Python. In the preprocessing phase, using C# tags, meaningless words called unwanted characters are removed. In addition, a maximum of 1000 cycles and 20 repetitions were performed during the experimental processes.

6.1. Description of data sets

A data set called DUC was used to check the accuracy of the proposed approach. These data sets are provided by the National Institute of Standards and Technology (NIST). DUC is a summary data set of news articles on different topics. There are different versions of this data set, and each version contains a different number of news articles. The texts in the data set and the summaries corresponding to these components were created manually. Multiple document summaries, which have several documents for each news topic and include target summaries compiled considering each document on that topic, can also be used in DUC. With these aspects, it was created as a basic data set. Performance results for most studies were obtained using DUC data, which can be used in both abstractive and subtractive summarisation studies [17,36,41]. The very popular DUC dataset is used in 70% of text summarization studies [42]. Within the scope of the study, the DUC-2002 data set was used to make a fair comparison with previous studies. In addition, summaries can be found in the data set created by two different evaluators by determining a limit of 100, 200 and 400 words. The properties of the DUC data set are presented in Table 2 [43,44].

Table 2.

Properties of the DUC-2002 data set.

Property
Number of clusters in the data set	59
Number of text per cluster	~10
Number of text in the data set	567
Length of summaries	200 and 400 words

DUC: document understanding conference.

6.2. Performance metrics

ROUGE was used to measure the performance of the proposed multi-purpose SGuA method. This toolkit is based on n-gramme. ROUGE measurements take values between 0 and 1. The higher the value, the closer the content is to the model summary, and in this case, the automatic summarisation is considered better and more informative. The ROUGE-N metric evaluates the number of n-grammes shared between the proposed and model summaries

ROUGE - N = \frac{\sum_{C \in {R e f e r e n c e S u m m a r i e s} g r a m_{n} \in S} \sum c o u n t_{m a t c h} (g r a m_{n})}{\sum_{C \in {R e f e r e n c e S u m m a r i e s} g r a m_{n} \in S} \sum Count (g r a m_{n})}

(11)

where value n in the formula is equal to the length of n-gramme $g r a m_{n}$ , and $c o u n t_{m a t c h}$ ( $g r a m_{n}$ ) is the maximum number of n-grammes intersecting in the draft summary and the reference summary. Similarly, the ROUGE-L metric calculates the longest common word string in the two lowest word sequence values. Equations (12)–(14) include two-word strings, where X and Y are given to reach a calculation related to the value of ROUGE-L [45]

R_{l c s} = \frac{L C S (X, Y)}{m}

(12)

P_{l c s} = \frac{L C S (X, Y)}{n}

(13)

F_{l c s} = \frac{(1 + β^{2}) R_{l c s} P_{l c s}}{R_{l c s} + β^{2} P_{l c s}}

(14)

Also in this study, range and a coefficient of variation-type distribution statistic are as follows

R a n g e = R o u g e_{b e s t} - R o u g e_{w o r s t}

(15)

C V = \frac{R a n g e}{R o u g e_{a v e r a g e}} \cdot 100

(16)

ROUGE-1.5.5 was applied using Py-ROUGE throughout the experiments.

6.3. Results

The performance of MO-SGuA presented within the scope of the study was evaluated with ROUGE criteria. The related tables show the mean, range and CV scores for each subject and the average values for all subjects (ROUGE-2, ROUGE-L). The proposed MO-SGuA approach reported reasonably good performance data and was then compared with similar competitive methods. Tests used 200-word abstracts, as shown in Tables 3 and 4, to be appropriate with competitive summarisation approaches. The values were then compared to those reported for Adaptive DE [46], NSGA-II [35] and MOABC [36] using the DUC-2002 data set. NSGA-II and MOABC were two multi-objective approaches in the literature, with the researchers having found no other multi-objective methods.

Table 3.

Comparison of MO-SGuA with state-of-the-arts for ROUGE-2.

Document topic	Summary for 200-words (ROUGE-2)
	Adaptive DE			NSGA-II			MOABC			Proposed MO-SGuA
	Avg.	Range	CV	Avg.	Range	CV	Avg.	Range	CV	Avg.	Range	CV
D061j	0.266	0.290	109.02	0.306	0.263	85.95	0.365	0.093	25.43	0.3186	0.1359	42.649
D062j	0.188	0.275	146.28	0.200	0.422	211.0	0.342	0.023	6.60	0.4483	0.1394	31.098
D063j	0.245	0.208	84.90	0.275	0.279	101.45	0.272	0.005	1.84	0.3876	0.6435	16.601
D064j	0.194	0.280	144.33	0.233	0.256	152.79	0.308	0.009	2.83	0.4531	0.1081	23.85
D065j	0.144	0.209	145.14	0.182	0.208	114.29	0.198	0.026	13.32	0.2215	0.1777	80.25
D066j	0.201	0.257	127.86	0.181	0.245	135.36	0.290	0.019	6.54	0.4294	0.1106	25.75
D067f	0.239	0.235	98.33	0.260	0.298	114.62	0.356	0.005	1.39	0.402	0.320	79.6
D068f	0.491	0.284	78.21	0.496	0.281	56.65	0.444	0.084	18.83	0.5362	0.2048	38.05
D069f	0.184	0.166	90.22	0.232	0.239	103.02	0.240	0.008	3.15	0.314	0.0854	27.2
D070f	0.224	0.260	116.07	0.262	0.215	82.03	0.305	0.002	0.76	0.4478	0.1407	31.436
Avg	0.238	0.256	114.04	0.263	0.280	115.72	0.312	0.027	8.07	0.395	0.2066	39.648

MO-SGuA: multi-objective saplings growing-up algorithm; ROUGE: recall-oriented understudy for gisting evaluation; NSGA-II: non-dominated sorting genetic algorithm-II. DE: Differential evolution; MOABC: multi-objective artificial bee colony; CV: coefficient of variation. Bold values indicate the overall best performance.

Table 4.

Comparison of MO-SGuA with state-of-the-arts for ROUGE-L.

Document topic	Summary for 200-words (ROUGE-L)
	Adaptive DE			NSGA-II			MOABC			Proposed MO-SGuA
	Avg.	Range	CV	Avg.	Range	CV	Avg.	Range	CV	Avg.	Range	CV
D061j	0.542	0.208	38.38	0.554	0.205	37.00	0.590	0.056	9.46	0.5608	0.0821	14.64
D062j	0.473	0.239	50.53	0.481	0.306	63.62	0.536	0.017	3.26	0.6145	0.1100	17.90
D063j	0.493	0.156	31.64	0.528	0.171	32.39	0.509	0.050	9.74	0.6012	0.0738	12.28
D064j	0.462	0.235	50.87	0.488	0.287	58.81	0.495	0.011	2.19	0.6399	0.1121	17.51
D065j	0.431	0.141	32.71	0.457	0.174	38.07	0.464	0.057	12.29	0.4536	0.1637	36.08
D066j	0.455	0.196	43.08	0.441	0.149	33.79	0.519	0.007	1.36	0.6194	0.0642	10.36
D067f	0.509	0.232	45.58	0.529	0.244	46.12	0.580	0.012	2.15	0.6189	0.199	32.15
D068f	0.666	0.226	33.93	0.626	0.226	36.10	0.639	0.071	11.09	0.7124	0.1878	26.36
D069f	0.454	0.135	29.74	0.476	0.191	40.13	0.554	0.010	1.81	0.566	0.08	14.13
D070f	0.496	0.173	34.88	0.513	0.158	30.80	0.515	0.005	0.90	0.6166	0.1304	21.15
Avg	0.498	0.194	39.13	0.509	0.211	41.68	0.540	0.03	5.425	0.6003	0.1203	20.256

According to the values reported in Table 3, the proposed MO-SGuA approach outperformed the other methods. Adaptive DE, NSGA-II and MOABC were shown to have been exceeded by the proposed MO-SGuA in the average scores for all topics (except for MOABC’s D061). Another observation from Table 3 is that, compared to Adaptive DE and NSGA-II, 8 out of 10 documents were shown to have better scores in terms of range scores for the MO-SGuA approach. Similarly, in terms of CV scores, much better values were obtained for MO-SGuA when compared to both Adaptive DE and NSGA-II, and superior results were obtained across all subjects. These results show that the suggested MO-SGuA is much more consistent and reliable than the Adaptive DE and NSGA-II methods. Furthermore, the highest average score across all subjects was achieved by the proposed MO-SGuA method, according to the values reported, with the second-best values in the range and CV types.

In Figure 4, the average ROUGE-2 scores obtained according to the subjects in the DUC data set are schematised. As shown in Figure 4, the highest values were achieved across all subjects using the proposed MO-SGuA approach.

Figure 4.

Comparison of performance values of methods in terms of ROUGE-2 (ROUGEavg) scores.

In Table 4, it can be seen that 8 out of the 10 highest ROUGE average scores were achieved by the proposed MO-SGuA method. Furthermore, in terms of $ROUG E_{R a n g e}$ and CV scores, much more robust and consistent values were obtained from the MO-SGuA method over both the Adaptive DE and NSGA-II methods. Overall, the comparative test results obtained from the ROUGE-L score type after ROUGE-2 confirmed the performance of the proposed MO-SGuA approach.

In Table 4, the highest average values were achieved with the proposed MO-SGuA approach. In 8 out of the 10 scores reported, the Range and CV scores for the proposed MO-SGuA approach were much better than the Adaptive DE and NSGA-II methods. These values confirm the consistency and robustness of the proposed MO-SGuA approach for ROUGE-L.

In Figure 5, the average ROUGE-L scores obtained according to the subjects in the DUC data set are schematised. As shown in Figure 5, the proposed MO-SGuA approach achieved the highest ROUGE-L values across all subjects, except for D061j and D065j.

Figure 5.

Comparison of performance values of methods in terms of ROUGE-L (ROUGEavg) scores.

In Table 5, the percentage values for the ROUGE metric average changed for all 10 subjects in terms of their ROUGE-2 and ROUGE-L scores. The proposed MO-SGuA approach surpassed both the Adaptive DE and NSGA-II methods in all measurement types with a general evaluation. The MOABC approach improved of 26.6% for ROUGE-2 and an improvement of 11.17% for ROUGE-L. Also, Table 5 shows that the proposed MO-SGuA approach achieved the most robust and consistent values (based on ROUGE mean and CV scores), surpassing both the Adaptive DE and NSGA-II after MOABC.

Table 5.

Comparison of the proposed approach with other models.

Other models	MO-SGuA (%)
	ROUGE-2			ROUGE-L
	Avg.	Range	CV	Avg.	Range	CV
Adaptive DE	+65.96	+23.91	+187.63	+20.54	+61.26	+93.18
NSGA-II	+50.19	+35.52	+191.87	+17.94	+75.39	+105.77
MOABC	+26.60	−86.93	–79.65	+11.17	−75.06	−73.22

7. Conclusion

The presented model is an innovative optimisation-based and unsupervised document summarisation system. Within the scope of the study, MO-SGuA was modelled for the first time and brought to the literature. The experimentation results proved very satisfactory for almost all types of metrics. The proposed approach obtained much better results than Adaptive DE, which may be explained by the multi-document summary problem being represented better with multi-objective optimisation due to its nature. Simultaneous multi-objective optimisation used for text summarisation, other than NSGA-II and MOABC, has not been found elsewhere in the literature. The researchers of this study believe that the superior performance of the proposed MO-SGuA, compared to the NSGA-II and MOABC methods, can be explained by MO-SGuA’s ability to create a regular initial population without randomisation.

In multi-objective optimisation problems, researchers generally use fixed and variable weight goal functions to reduce problems to a single-objective state to obtain a solution. However, these methods present certain disadvantages to the decision-maker, such as modelling the problem inadequately, producing a single solution and limiting the options. The architecture of the proposed method is unaffected by these same issues, as explained in detail in the relevant sections of the paper.

While determining which sentences to include in the abstract, those with the highest relationship scores (Maximum Coverage) are selected. While there can be a tendency to include only the most common subtopics, such a summary cannot be considered rich. Therefore, in this study, minimum concept overlaps (Minimum redundancy) of the sentences that form the abstract is considered an additional goal. Subtopic repetitions that have adverse effects on system performance were minimised via modelling. Within the scope of this study, Maximum Coverage and Minimum redundancy values are optimised simultaneously. Generally, goals are weighted down to a single goal function in multi-objective optimisation problems, with only a few studies opting for exclusion.

In multi-purpose problems, goals often conflict with each other and there is usually no single solution that can optimise all objectives. Within the scope of this study, Pareto-optimal front was preferred since there is no single solution that will improve both the maximum conflicting coverage and minimum relationship parameters. As a result, better results have been reported compared to competitive methods. Furthermore, within the scope of the study, the choices between suitable solutions were successfully made by using Pareto optimal to represent the entire solution space. Therefore, the researchers believe that the presented approach will encourage other researchers to utilise the Pareto optimal in optimisation-based text summarisation studies.

For the first time, SGuA has been enriched with the Pruning operator, a local search, within the model’s scope presented in this study. The solution was improved by cutting the branches on the sapling stem (sentences in the candidate summary). Furthermore, by trying different mathematical text representation methods, new text summarisation studies are planned for the future with MO-SGuA, which has shown to be more assertive with the Pruning operator.

Footnotes

Funding

The author(s) received no financial support for the research, authorship and/or publication of this article.

ORCID iD

Cengiz Hark

References

Grant

. Extractive multi-document summarization of news articles. Linköping: Department of Computer and Information Science, Linköping University, 2019.

Hark

Uçkan

Seyyarer

et al. Metin Özetlemesi için Düğüm Merkezliklerine Dayalı Denetimsiz Bir Yaklaşım [An unsupervised approach based on node centralization for text summarization]. Bitlis Eren Üniv Fen Bilim Derg 2019; 8(3): 1109–1118.

Uçkan

Hark

Karci

et al. SSC: clustering of Turkish texts by spectral graph partitioning. J Polytech 2021; 24: 1433–1444.

Maciej

Serda

. Synteza i aktywność biologiczna nowych analogów tiosemikarbazonowych chelatorów żelaza. Uniw śląski 2013; 343–354.

John

Premjith

Wilscy

. Extractive multi-document summarization using population-based multicriteria optimization. Expert Syst Appl 2017; 86: 385–397.

Hark

Uckan

Seyyarer

et al. Extractive text summarization via graph entropy Çizge Entropi ile Çikarici Metin Özetleme. In: 2019 international artificial intelligence and data processing symposium (IDAP), Malatya, 21–22 September2019.

Uçkan

Hark

Seyyarer

et al. AğırlıklandırılmışÇizgelerde Tf-Idf ve Eigen Ayrışımı Kullanarak Metin Sınıflandırma. Bitlis Eren Üniv Fen Bilim Derg 2019; 8: 1349–1362.

Hark

Seyyarer

Uçkan

et al. Doğal dil işleme yaklaşimlari ile yapisal olmayan dökümanlarin benzerliği. In: 2017 international artificial intelligence and data processing symposium (IDAP), Malatya, 16–17 September2017.

Belwal

Rai

Gupta

. Text summarization using topic-based vector space model and semantic measure. Inform Process Manag 2021; 58(3): 102536.

10.

Mani

. Advances in automatic text summarization. Cambridge, MA: MIT Press, 1999.

11.

Goyal

Ferrara

. Graph embedding techniques, applications, and performance: a survey. Knowl-Based Syst 2018; 151: 78–94.

12.

Zhang

Zhou

et al. FAR-ASS: Fact-aware reinforced abstractive sentence summarization. Inform Process Manag 2021; 58(3): 102478.

13.

Alguliyev

Aliguliyev

Isazade

. An unsupervised approach to generating generic summaries of documents. Appl Soft Comput J 2015; 34: 236–250.

14.

Uçkan

Karcı

. Extractive multi-document text summarization based on graph independent sets. Egypt Inform J 2020: 21: 145–157.

15.

Mutlu

Sezer

Akcayol

. Candidate sentence selection for extractive text summarization. Inform Process Manag 2020; 57(6): 102359.

16.

Carbonell

Goldstein

. The use of MMR, diversity-based reranking for reordering documents and producing summaries. SIGIR 1998; 98: 335–336.

17.

Hark

Karcı

. Karcı summarization: a simple and effective approach for automatic text summarization using Karcı entropy. Inform Process Manag 2020; 57(3): 102187.

18.

Alguliyev

Aliguliyev

Isazade

. A new similarity measure and mathematical model for text summarization. Probl Inf Technol 2015; 6(1): 42–53.

19.

Lamsiyah

El Mahdaouy

Ouatik

SEA

et al. Unsupervised extractive multi-document summarization method based on transfer learning from BERT multi-task fine-tuning. J Inf Sci. Epub ahead of print 15 February 2021. DOI: 10.1177/0165551521990616.

20.

Rautray

Balabantaray

. Cat swarm optimization based evolutionary framework for multi document summarization. Physica A 2017; 477: 174–186.

21.

Verma

. MCRMR: maximum coverage and relevancy with minimal redundancy based multi-document summarization. Expert Syst Appl 2019; 120: 43–56.

22.

Alguliev

Aliguliyev

Hajirahimova

et al. MCMR: maximum coverage and minimum redundant text summarization model. Expert Syst Appl 2011; 38(12): 14514–14522.

23.

Qaroush

Farha

Ghanem

et al. An efficient single document Arabic text summarization using a combination of statistical and semantic features. J King Saud Univ Comput Inf Sci 2021; 33: 677–692.

24.

Alguliev

Aliguliyev

Isazade

. Multiple documents summarization based on evolutionary optimization algorithm. Expert Syst Appl 2013; 40(5): 1675–1689.

25.

Alguliev

Aliguliyev

Isazade

. MR&MR-sum: maximum relevance and minimum redundancy document summarization model. Int J Inf Technol Decis Mak 2013; 12(3): 361–393.

26.

Zhao

Tang

. Query-focused summarization based on genetic algorithm. In: 2010 international conference on measuring technology and mechatronics automation, Changsha, China, 13–14 March2010, vol. 2, pp. 968–971. New York: IEEE.

27.

Kogilavani

Balasubramanie

. Clustering based optimal summary generation using genetic algorithm. In: Proceedings of the 2010 international conference on communication and computational intelligence (INCOCCI), Erode, India, 27–29 December2010, pp. 324–329. New York: IEEE.

28.

Huang

Wei

et al. Modeling document summarization as multi-objective optimization. In: 2010 third international symposium on intelligent information technology and security informatics, Jian, China, 2–4 April2010, pp. 382–386. New York: IEEE.

29.

Aliguliyev

. Clustering techniques and discrete particle swarm optimization algorithm for multi-document summarization. Comput Intell 2010; 26(4): 420–448.

30.

Nandhini

Balasundaram

. Extracting easy to understand summary using differential evolution algorithm. Swarm Evol Comput 2014; 16: 19–27.

31.

Lozano

Rodríguez

Herrera-Viedma

. A new memetic algorithm for multi-document summarization based on CHC algorithm and Greedy search. Mex Int Conf Artif Intell 2014; 8856(1): 15.

32.

Mirshojaei

Masoomi

. Text summarization using Cuckoo Search Optimization algorithm. J Comput Robot 2015; 8(2): 19–24.

33.

Rautray

Balabantaray

Bhardwaj

. Document summarization using sentence features. Int J Inf Retr Res 2015; 5(1): 36–47.

34.

Goleman

Boyatzis

Mckee . Coverage, diversity, and coherence optimization for multi-document summarization. J Chem Inf Model 2019; 53(9): 1689–1699.

35.

Saleh

Kadhim

Bara’a

. A genetic based optimization model for extractive multi-document text summarization. Iraqi J Sci 2015; 56(2B): 1489–1498.

36.

Sanchez-Gomez

Vega-Rodríguez

Pérez

. Extractive multi-document text summarization using a multi-objective artificial bee colony optimization approach. Knowl-Based Syst 2018; 159: 1–8.

37.

Tomer

Kumar

. Multi-document extractive text summarization based on firefly algorithm. J King Saud Univ Comput Inf Sci. Epub ahead of print 24 April 2021. DOI: 10.1016/j.jksuci.2021.04.004.

38.

Karci

. Natural inspired computational intelligence method: Saplings Growing Up algorithm. In: 2007 IEEE international conference on computational cybernetics, Gammarth, Tunisia, 19–21 October2007, pp. 221–226. New York: IEEE.

39.

Karci

. Theory of Saplings growing up algorithm. In: Beliczynski

Dzielinski

Iwanowski

et al. (eds) Adaptive and natural computing algorithms. Berlin: Springer, 2007, pp. 450–460.

40.

Karci

Alatas

. Thinking capability of Saplings Growing Up algorithm. In: Intelligent data engineering and automated Learning (IDEAL), Burgos, 20–23 September2006, pp. 386–393. Berlin: Springer.

41.

Verma

. A novel approach for text summarization using optimal combination of sentence scoring methods. Sādhanā 2019; 44(5): 110.

42.

Widyassari

Rustad

Shidik

et al. Review of automatic text summarization techniques & methods. J King Saud Univ Comput Inf Sci 2022; 34: 1029–1046.

43.

Document Understanding Conferences (DUC-2002), 2002. http://duc.nist.gov (accessed 1 March 2021).

44.

Bidoki

Moosavi

Fakhrahmad

. A semantic approach to extractive multi-document summarization: applying sentence expansion for tuning of conceptual densities. Inform Process Manag 2020; 57(6): 102341.

45.

Lin

. ROUGE: a package for automatic evaluation of summaries. In: Proceedings of the workshop on text summarization branches out (WAS 2004), 2004, pp. 25–26, https://aclanthology.org/W04-1013.pdf

46.

Alguliev

Aliguliyev

Mehdiyev

. Sentence selection for generic document summarization using an adaptive differential evolution algorithm. Swarm Evol Comput 2011; 1(4): 213–222.