Mehrdad Mahdavi

An improved harmony search algorithm for solving optimization problems

This paper develops an Improved harmony search (IHS) algorithm for solving optimization problems. IHS employs a novel method for generating new solution vectors that enhances accuracy and convergence rate of harmony search (HS) algorithm. In this paper the impacts of constant parameters on harmony search algorithm are discussed and a strategy for tuning these parameters is presented. The IHS algorithm has been successfully applied to various benchmarking and standard engineering optimization problems. Numerical results reveal that the proposed algorithm can find better solutions when compared to HS and other heuristic or deterministic methods and is a powerful search algorithm for various engineering optimization problems.

Global-best harmony search

Harmony search (HS) is a new meta-heuristic optimization method imitating the music improvisation process where musicians improvise their instruments’ pitches searching for a perfect state of harmony. A new variant of HS, called global-best harmony search (GHS), is proposed in this paper where concepts from swarm intelligence are borrowed to enhance the performance of HS. The performance of the GHS is investigated and compared with HS and a recently developed variation of HS. The experiments conducted show that the GHS generally outperformed the other approaches when applied to ten benchmark problems. The effect of noise on the performance of the three HS variants is investigated and a scalability study is conducted. The effect of the GHS parameters is analyzed. Finally, the three HS variants are compared on several Integer Programming test problems. The results show that the three approaches seem to be an efficient alternative for solving Integer Programming problems. 2007 Elsevier Inc. All rights reserved.

Harmony search based algorithms for bandwidth-delay-constrained least-cost multicast routing

The advent of various real-time multimedia applications in high-speed networks creates a need for quality of service (QoS) based multicast routing. Two important QoS constraints are the bandwidth constraint and the end-to-end delay constraint. The QoS based multicast routing problem is a known NP-complete problem that depends on (1) bounded end-to-end delay and link bandwidth along the paths from the source to each destination, and (2) minimum cost of the multicast tree. In this paper, we presents novel centralized algorithms to solve the bandwidth-delay-constrained least-cost multicast routing problem based on the harmony search (HS) algorithm. Our first algorithm uses modified Prufer number as Steiner tree representation that is called HSPR. Prufer number has poor locality and heritability in evolutionary search, so, we describe a new representation, node parent index (NPI) representation, for representing trees and describe harmony operations accord to this representation. Our second algorithm is based on NPI representation that is called HSNPI, an empirical study to determine the impacts of different parameters of the HSNPI algorithm on the solution quality and convergence behavior was performed. We evaluate the performance and efficiency of our proposed methods with a GA-based algorithm and a modified version of the bounded shortest multicast algorithm (BSMA). Simulation results on randomly generated networks and real topologies indicate that HSNPI algorithm that we proposed has overcome other three algorithms on a variety of random generated networks considering average tree cost.

Harmony K-means algorithm for document clustering

Fast and high quality document clustering is a crucial task in organizing information, search engine results, enhancing web crawling, and information retrieval or filtering. Recent studies have shown that the most commonly used partition-based clustering algorithm, the K-means algorithm, is more suitable for large datasets. However, the K-means algorithm can generate a local optimal solution. In this paper we propose a novel Harmony K-means Algorithm (HKA) that deals with document clustering based on Harmony Search (HS) optimization method. It is proved by means of finite Markov chain theory that the HKA converges to the global optimum. To demonstrate the effectiveness and speed of HKA, we have applied HKA algorithms on some standard datasets. We also compare the HKA with other meta-heuristic and model-based document clustering approaches. Experimental results reveal that the HKA algorithm converges to the best known optimum faster than other methods and the quality of clusters are comparable.

Novel meta-heuristic algorithms for clustering web documents

Clustering the web documents is one of the most important approaches for mining and extracting knowledge from the web. Recently, one of the most attractive trends in clustering the high dimensional web pages has been tilt toward the learning and optimization approaches. In this paper, we propose novel hybrid harmony search (HS) based algorithms for clustering the web documents that finds a globally optimal partition of them into a specified number of clusters. By modeling clustering as an optimization problem, first, we propose a pure harmony search-based clustering algorithm that finds near global optimal clusters within a reasonable time. Then, we hybridize K-means and harmony clustering in two ways to achieve better clustering. Experimental results reveal that the proposed algorithms can find better clusters when compared to similar methods and also illustrate the robustness of the hybrid clustering algorithms.

Efficient stochastic algorithms for document clustering

Clustering has become an increasingly important and highly complicated research area for targeting useful and relevant information in modern application domains such as the World Wide Web. Recent studies have shown that the most commonly used partitioning-based clustering algorithm, the K-means algorithm, is more suitable for large datasets. However, the K-means algorithm may generate a local optimal clustering. In this paper, we present novel document clustering algorithms based on the Harmony Search (HS) optimization method. By modeling clustering as an optimization problem, we first propose a pure HS based clustering algorithm that finds near-optimal clusters within a reasonable time. Then, harmony clustering is integrated with the K-means algorithm in three ways to achieve better clustering by combining the explorative power of HS with the refining power of the K-means. Contrary to the localized searching property of K-means algorithm, the proposed algorithms perform a globalized search in the entire solution space. Additionally, the proposed algorithms improve K-means by making it less dependent on the initial parameters such as randomly chosen initial cluster centers, therefore, making it more stable. The behavior of the proposed algorithm is theoretically analyzed by modeling its population variance as a Markov chain. We also conduct an empirical study to determine the impacts of various parameters on the quality of clusters and convergence behavior of the algorithms. In the experiments, we apply the proposed algorithms along with K-means and a Genetic Algorithm (GA) based clustering algorithm on five different document datasets. Experimental results reveal that the proposed algorithms can find better clusters and the quality of clusters is comparable based on F-measure, Entropy, Purity, and Average Distance of Documents to the Cluster Centroid (ADDC).

Matrix Factorization with Explicit Trust and Distrust Side Information for Improved Social Recommendation

With the advent of online social networks, recommender systems have became crucial for the success of many online applications/services due to their significance role in tailoring these applications to user-specific needs or preferences. Despite their increasing popularity, in general, recommender systems suffer from data sparsity and cold-start problems. To alleviate these issues, in recent years, there has been an upsurge of interest in exploiting social information such as trust relations among users along with the rating data to improve the performance of recommender systems. The main motivation for exploiting trust information in the recommendation process stems from the observation that the ideas we are exposed to and the choices we make are significantly influenced by our social context. However, in large user communities, in addition to trust relations, distrust relations also exist between users. For instance, in Epinions, the concepts of personal “web of trust” and personal “block list” allow users to categorize their friends based on the quality of reviews into trusted and distrusted friends, respectively. Hence, it will be interesting to incorporate this new source of information in recommendation as well. In contrast to the incorporation of trust information in recommendation which is thriving, the potential of explicitly incorporating distrust relations is almost unexplored. In this article, we propose a matrix factorization-based model for recommendation in social rating networks that properly incorporates both trust and distrust relationships aiming to improve the quality of recommendations and mitigate the data sparsity and cold-start users issues. Through experiments on the Epinions dataset, we show that our new algorithm outperforms its standard trust-enhanced or distrust-enhanced counterparts with respect to accuracy, thereby demonstrating the positive effect that incorporation of explicit distrust information can have on recommender systems.

Web page clustering using Harmony Search optimization

Clustering has become an increasingly important task in modern application domains. Targeting useful and relevant information on the World Wide Web is a topical and highly complicated research area. Clustering techniques have been applied to categorize documents on Web and extracting knowledge from the Web. In this paper we propose novel clustering algorithms based on harmony search (HS) optimization method that deals with Web document clustering. By modeling clustering as an optimization problem, first, we propose a pure HS based clustering algorithm that finds near global optimal clusters within a reasonable time. Then we hybridize K-means and harmony clustering to achieve better clustering. Experimental results on five different data sets reveal that the proposed algorithms can find better clusters when compared to similar methods and the quality of clusters is comparable. Also proposed algorithms converge to the best known optimum faster than other methods.

Hybridization of K-Means and Harmony Search Methods for Web Page Clustering

Clustering is currently one of the most crucial techniques for dealing with massive amount of heterogeneous information on the web, which is beyond human beingpsilas capacity to digest. Recent studies have shown that the most commonly used partitioning-based clustering algorithm, the K-means algorithm, is more suitable for large datasets. However, the K-means algorithm can generate a local optimal solution. In this paper we present novel harmony search clustering algorithms that deal with documents clustering based on harmony search optimization method. By modeling clustering as an optimization problem, first, we propose a pure harmony search based clustering algorithm that finds near global optimal clusters within a reasonable time. Contrary to the localized searching of the K-means algorithm, the harmony search clustering algorithm performs a globalized search in the entire solution space. Then harmony clustering is integrated with the K-means algorithm in three ways to achieve better clustering. The proposed algorithms improve the K-means algorithm by making it less dependent on the initial parameters such as randomly chosen initial cluster centers, hence more stable. In the experiments we conducted, we applied the proposed algorithms, K-means clustering algorithm on five different document datasets. Experimental results reveal that the proposed algorithms can find better clusters when compared to K-means and the quality of clusters is comparable and converge to the best known optimum faster than it.

Robust Ensemble Clustering by Matrix Completion

Data clustering is an important task and has found applications in numerous real-world problems. Since no single clustering algorithm is able to identify all different types of cluster shapes and structures, ensemble clustering was proposed to combine different partitions of the same data generated by multiple clustering algorithms. The key idea of most ensemble clustering algorithms is to find a partition that is consistent with most of the available partitions of the input data. One problem with these algorithms is their inability to handle uncertain data pairs, i.e. data pairs for which about half of the partitions put them into the same cluster and the other half do the opposite. When the number of uncertain data pairs is large, they can mislead the ensemble clustering algorithm in generating the final partition. To overcome this limitation, we propose an ensemble clustering approach based on the technique of matrix completion. The proposed algorithm constructs a partially observed similarity matrix based on the data pairs whose cluster memberships are agreed upon by most of the clustering algorithms in the ensemble. It then deploys the matrix completion algorithm to complete the similarity matrix. The final data partition is computed by applying an efficient spectral clustering algorithm to the completed matrix. Our empirical studies with multiple real-world datasets show that the proposed algorithm performs significantly better than the state-of-the-art algorithms for ensemble clustering.