Combinatorial optimization and metaheuristics

Today, combinatorial optimization is one of the youngest and most active areas of discrete mathematics. It is a branch of optimization in applied mathematics and computer science, related to operational research, algorithm theory and computational complexity theory. It sits at the intersection of several fields, including artificial intelligence, mathematics and software engineering. Its increasing interest arises for the fact that a large number of scientific and industrial problems can be formulated as abstract combinatorial optimization problems, through graphs and/or (integer) linear programs. Some of these problems have polynomial-time (“efficient”) algorithms, while most of them are NP-hard, i.e. it is not proved that they can be solved in polynomial-time. Mainly, it means that it is not possible to guarantee that an exact solution to the problem can be found and one has to settle for an approximate solution with known performance guarantees. Indeed, the goal of approximate methods is to find “quickly” (reasonable run-times), with “high” probability, provable “good” solutions (low error from the real optimal solution). In the last 20 years, a new kind of algorithm commonly called metaheuristics have emerged in this class, which basically try to combine heuristics in high level frameworks aimed at efficiently and effectively exploring the search space. This report briefly outlines the components, concepts, advantages and disadvantages of different metaheuristic approaches from a conceptual point of view, in order to analyze their similarities and differences. The two very significant forces of intensification and diversification, that mainly determine the behavior of a metaheuristic, will be pointed out. The report concludes by exploring the importance of hybridization and integration methods

Hybrid Swarm Intelligence Method for Post Clustering Content Based Image Retrieval

AbstractContent Based Image Retrieval is one of the most promising method for image retrieval where searching and retrieving images from large scale image database is a critical task. In Content Based Image Retrieval many visual feature like color, shape, and texture are extracted in order to match query image with stored database images. Matching the query image with each image of large scale database results in large number of disc scans which in turns slows down the systems performance.The proposed work suggested an approach for post clustering Content Based Image Retrieval, in which the database images are clustered into optimized clusters for further retrieval process. Various clustering algorithms are implemented and results are compared. Among all, it is found that hybrid ACPSO algorithm performs better over basic algorithms like k-means, ACO, PSO etc. Hybrid ACPSO has the capability to produce good cluster initialization and form global clustering.This paper discusses work-in-progress where we have implemented till clustering module and intermediate results are produced. These resulted clusters will further be used for effective Content Based Image Retrieval

A comparison of general-purpose optimization algorithms forfinding optimal approximate experimental designs

Several common general purpose optimization algorithms are compared for findingA- and D-optimal designs for different types of statistical models of varying complexity,including high dimensional models with five and more factors. The algorithms of interestinclude exact methods, such as the interior point method, the Nelder–Mead method, theactive set method, the sequential quadratic programming, and metaheuristic algorithms,such as particle swarm optimization, simulated annealing and genetic algorithms.Several simulations are performed, which provide general recommendations on theutility and performance of each method, including hybridized versions of metaheuristicalgorithms for finding optimal experimental designs. A key result is that general-purposeoptimization algorithms, both exact methods and metaheuristic algorithms, perform wellfor finding optimal approximate experimental designs

Bat-Cluster: A Bat Algorithm-based Automated Graph Clustering Approach

Defining the correct number of clusters is one of the most fundamental tasks in graph clustering. When it comes to large graphs, this task becomes more challenging because of the lack of prior information. This paper presents an approach to solve this problem based on the Bat Algorithm, one of the most promising swarm intelligence based algorithms. We chose to call our solution, “Bat-Cluster (BC).” This approach allows an automation of graph clustering based on a balance between global and local search processes. The simulation of four benchmark graphs of different sizes shows that our proposed algorithm is efficient and can provide higher precision and exceed some best-known values

Towards Optimized K Means Clustering using Nature-inspired Algorithms for Software Bug Prediction

In today s software development environment the necessity for providing quality software products has undoubtedly remained the largest difficulty As a result early software bug prediction in the development phase is critical for lowering maintenance costs and improving overall software performance Clustering is a well-known unsupervised method for data classification and finding related patterns hidden in dataset

On the use of biased-randomized algorithms for solving non-smooth optimization problems

Soft constraints are quite common in real-life applications. For example, in freight transportation, the fleet size can be enlarged by outsourcing part of the distribution service and some deliveries to customers can be postponed as well; in inventory management, it is possible to consider stock-outs generated by unexpected demands; and in manufacturing processes and project management, it is frequent that some deadlines cannot be met due to delays in critical steps of the supply chain. However, capacity-, size-, and time-related limitations are included in many optimization problems as hard constraints, while it would be usually more realistic to consider them as soft ones, i.e., they can be violated to some extent by incurring a penalty cost. Most of the times, this penalty cost will be nonlinear and even noncontinuous, which might transform the objective function into a non-smooth one. Despite its many practical applications, non-smooth optimization problems are quite challenging, especially when the underlying optimization problem is NP-hard in nature. In this paper, we propose the use of biased-randomized algorithms as an effective methodology to cope with NP-hard and non-smooth optimization problems in many practical applications. Biased-randomized algorithms extend constructive heuristics by introducing a nonuniform randomization pattern into them. Hence, they can be used to explore promising areas of the solution space without the limitations of gradient-based approaches, which assume the existence of smooth objective functions. Moreover, biased-randomized algorithms can be easily parallelized, thus employing short computing times while exploring a large number of promising regions. This paper discusses these concepts in detail, reviews existing work in different application areas, and highlights current trends and open research lines