### Chair: Xin-She Yang

 437 Comparison of Constraint-Handling Techniques for Metaheuristic Optimization [abstract]Abstract: Most engineering design problems have highly nonlinear constraints and the proper handling of such constraints can be important to ensure solution quality. There are many different ways of handling constraints and different algorithms for optimization problems, which makes it difficult to choose for users. This paper compare six different constraint-handling techniques such as penalty methods, barrier functions, $\epsilon$-constrained method, feasibility criteria and stochastic ranking. The pressure vessel design problem is solved by the flower pollination algorithm, and results show that stochastic ranking and $\epsilon$-constrained method are most effective for this type of design optimization. Xing-Shi He, Qin-Wei Fan and Xin-She Yang 231 Dynamic Partitioning of Evolving Graph Streams using Nature-inspired Heuristics [abstract]Abstract: Detecting communities of interconnected nodes is a frequently addressed problem in situation that be modeled as a graph. A common practical example is this arising from Social Networks. Anyway, detecting an optimal partition in a network is an extremely complex and highly time-consuming task. This way, the development and application of meta-heuristic solvers emerges as a promising alternative for dealing with these problems. The research presented in this paper deals with the optimal partitioning of graph instances, in the special cases in which connections among nodes change dynamically along the time horizon. This specific case of networks is less addressed in the literature than its counterparts. For efficiently solving such problem, we have modeled and implements a set of meta-heuristic solvers, all of them inspired by different processes and phenomena observed in Nature. Concretely, considered approaches are Water Cycle Algorithm, Bat Algorithm, Firefly Algorithm and Particle Swarm Optimization. All these methods have been adapted for properly dealing with this discrete and dynamic problem, using a reformulated expression for the well-known modularity formula as fitness function. A thorough experimentation has been carried out over a set of 12 synthetically generated dynamic graph instances, with the main goal of concluding which of the aforementioned solvers is the most appropriate one to deal with this challenging problem. Statistical tests have been conducted with the obtained results for rigorously concluding the Bat Algorithm and Firefly Algorithm outperform the rest of methods in terms of Normalized Mutual Information with respect to the true partition of the graph. Eneko Osaba, Miren Nekane Bilbao, Andres Iglesias, Javier Del Ser, Akemi Galvez-Tomida, Iztok Jr. Fister and Iztok Fister 317 Bat Algorithm for Kernel Computation in Fractal Image Reconstruction [abstract]Abstract: Computer reconstruction of digital images is an important problem in many areas such as image processing, computer vision, medical imaging, sensor systems, robotics, and many others. A very popular approach in that regard is the use of different kernels for various morphological image processing operations such as dilation, erosion, blurring, sharpening, and so on. In this paper, we extend this idea to the reconstruction of digital fractal images. Our proposal is based on a new affine kernel particularly tailored for fractal images. The kernel computes the difference between the source and the reconstructed fractal images, leading to a difficult nonlinear constrained continuous optimization problem, solved by using a powerful nature-inspired metaheuristics for global optimization called the bat algorithm. An illustrative example is used to analyze the performance of this approach. Our experiments show that the method performs quite well but there is also room for further improvement. We conclude that this approach is promising and that it could be a very useful technique for efficient fractal image reconstruction. Akemi Galvez-Tomida, Eneko Osaba, Javier Del Ser and Andres Iglesias Prieto 107 Heuristic Rules for Coordinated Resources Allocation and Optimization in Distributed Computing [abstract]Abstract: In this paper, we consider heuristic rules for resources utilization optimization in distributed computing environments. Existing modern job-flow execution mechanics impose many restrictions for the resources allocation procedures. Grid, cloud and hybrid computing services operate in heterogeneous and usually geographically distributed computing environments. Emerging virtual organizations and incorporated economic models allow users and resource owners to compete for suitable allocations based on market principles and fair scheduling policies. Subject to these features a set of heuristic rules for coordinated compact scheduling are proposed to select resources depending on how they fit a particular job execution and requirements. Dedicated simulation experiment studies integral job flow characteristics optimization when these rules are applied to conservative backfilling scheduling procedure. Victor Toporkov and Dmitry Yemelyanov 37 Nonsmooth Newton’s Method: Some Structure Exploitation [abstract]Abstract: We investigate real asymmetric linear systems arising in the search direction generation in a nonsmooth Newton’s method. This applies to constrained optimisation problems via reformulation of the necessary conditions into an equivalent nonlinear and nonsmooth system of equations. We propose a strategy to exploit the problem structure. First, based on the sub-blocks of the original matrix, some variables are selected and ruled out for a posteriori recovering; then, a smaller and symmetric linear system is generated; eventually, from the solution of the latter, the remaining variables are obtained. We prove the method is applicable if the original linear system is well-posed. We propose and discuss different selection strategies. Finally, numerical examples are presented to compare this method with the direct approach without exploitation, for full and sparse matrices, in a wide range of problem size. Alberto De Marchi and Matthias Gerdts