A test problem for visual investigation of high-dimensional multi-objective search

An inherent problem in multiobjective optimization is that the visual observation of solution vectors with four or more objectives is infeasible, which brings major difficulties for algorithmic design, examination, and development. This paper presents a test problem, called the Rectangle problem, to aid the visual investigation of high-dimensional multiobjective search. Key features of the Rectangle problem are that the Pareto optimal solutions 1) lie in a rectangle in the two-variable decision space and 2) are similar (in the sense of Euclidean geometry) to their images in the four-dimensional objective space. In this case, it is easy to examine the behavior of objective vectors in terms of both convergence and diversity, by observing their proximity to the optimal rectangle and their distribution in the rectangle, respectively, in the decision space. Fifteen algorithms are investigated. Underperformance of Pareto-based algorithms as well as most state-of-the-art many-objective algorithms indicates that the proposed problem not only is a good tool to help visually understand the behavior of multiobjective search in a high-dimensional objective space but also can be used as a challenging benchmark function to test algorithms' ability in balancing the convergence and diversity of solutions

Resilient network dimensioning for optical grid/clouds using relocation

In this paper we address the problem of dimensioning infrastructure, comprising both network and server resources, for large-scale decentralized distributed systems such as grids or clouds. We will provide an overview of our work in this area, and in particular focus on how to design the resulting grid/cloud to be resilient against network link and/or server site failures. To this end, we will exploit relocation: under failure conditions, a request may be sent to an alternate destination than the one under failure-free conditions. We will provide a comprehensive overview of related work in this area, and focus in some detail on our own most recent work. The latter comprises a case study where traffic has a known origin, but we assume a degree of freedom as to where its end up being processed, which is typically the case for e. g., grid applications of the bag-of-tasks (BoT) type or for providing cloud services. In particular, we will provide in this paper a new integer linear programming (ILP) formulation to solve the resilient grid/cloud dimensioning problem using failure-dependent backup routes. Our algorithm will simultaneously decide on server and network capacity. We find that in the anycast routing problem we address, the benefit of using failure-dependent (FD) rerouting is limited compared to failure-independent (FID) backup routing. We confirm our earlier findings in terms of network capacity savings achieved by relocation compared to not exploiting relocation (order of 6-10% in the current case studies)

Synthesis of Parametric Programs using Genetic Programming and Model Checking

Formal methods apply algorithms based on mathematical principles to enhance the reliability of systems. It would only be natural to try to progress from verification, model checking or testing a system against its formal specification into constructing it automatically. Classical algorithmic synthesis theory provides interesting algorithms but also alarming high complexity and undecidability results. The use of genetic programming, in combination with model checking and testing, provides a powerful heuristic to synthesize programs. The method is not completely automatic, as it is fine tuned by a user that sets up the specification and parameters. It also does not guarantee to always succeed and converge towards a solution that satisfies all the required properties. However, we applied it successfully on quite nontrivial examples and managed to find solutions to hard programming challenges, as well as to improve and to correct code. We describe here several versions of our method for synthesizing sequential and concurrent systems.Comment: In Proceedings INFINITY 2013, arXiv:1402.661

Denoising Autoencoders for fast Combinatorial Black Box Optimization

Estimation of Distribution Algorithms (EDAs) require flexible probability models that can be efficiently learned and sampled. Autoencoders (AE) are generative stochastic networks with these desired properties. We integrate a special type of AE, the Denoising Autoencoder (DAE), into an EDA and evaluate the performance of DAE-EDA on several combinatorial optimization problems with a single objective. We asses the number of fitness evaluations as well as the required CPU times. We compare the results to the performance to the Bayesian Optimization Algorithm (BOA) and RBM-EDA, another EDA which is based on a generative neural network which has proven competitive with BOA. For the considered problem instances, DAE-EDA is considerably faster than BOA and RBM-EDA, sometimes by orders of magnitude. The number of fitness evaluations is higher than for BOA, but competitive with RBM-EDA. These results show that DAEs can be useful tools for problems with low but non-negligible fitness evaluation costs.Comment: corrected typos and small inconsistencie