Tournament versus Fitness Uniform Selection

In evolutionary algorithms a critical parameter that must be tuned is that of selection pressure. If it is set too low then the rate of convergence towards the optimum is likely to be slow. Alternatively if the selection pressure is set too high the system is likely to become stuck in a local optimum due to a loss of diversity in the population. The recent Fitness Uniform Selection Scheme (FUSS) is a conceptually simple but somewhat radical approach to addressing this problem - rather than biasing the selection towards higher fitness, FUSS biases selection towards sparsely populated fitness levels. In this paper we compare the relative performance of FUSS with the well known tournament selection scheme on a range of problems.Comment: 10 pages, 8 figure

On a quantum-classical correspondence: from graphs to manifolds

We establish conditions for which graph Laplacians $\Delta_{\lambda,\epsilon}$ on compact, boundaryless, smooth submanifolds $\mathcal{M}$ of Euclidean space are semiclassical pseudodifferential operators ($\Psi$DOs): essentially, that the graph Laplacian's kernel bandwidth ($\textit{bias term}$) $\sqrt{\epsilon}$ decays faster than the semiclassical parameter $h$, $\textit{i.e.}$, $h \gg \sqrt{\epsilon}$ and we compute the symbol. Coupling this with Egorov's theorem and coherent states $\psi_h$ localized at $(x_0, \xi_0) \in T^*\mathcal{M}$, we show that with $U_{\lambda,\epsilon}^t := e^{-i t \sqrt{\Delta}_{\lambda,\epsilon}}$ spectrally defined, the (co-)geodesic flow $\Gamma^t$ on $T^*\mathcal{M}$ is approximated by $\langle U_{\lambda,\epsilon}^{-t} \operatorname{Op}_h(a) U_{\lambda,\epsilon}^t \psi_h, \psi_h \rangle = a \circ \Gamma^t(x_0, \xi_0) + O(h)$. Then, we turn to the discrete setting: for $\Delta_{\lambda,\epsilon,N}$ a normalized graph Laplacian defined on a set of $N$ points $x_1, \ldots, x_N$ sampled $\textit{i.i.d.}$ from a probability distribution with smooth density, we establish Bernstein-type lower bounds on the probability that $||U_{\lambda,\epsilon,N}^t[u] - U_{\lambda,\epsilon}^t[u]||_{L^{\infty}} \leq \delta$ with $U_{\lambda,\epsilon,N}^t := e^{-i t \sqrt{\Delta}_{\lambda,\epsilon,N}}$. We apply this to coherent states to show that the geodesic flow on $\mathcal{M}$ can be approximated by matrix dynamics on the discrete sample set, namely that $\textit{with high probability}$, $c_{t,N}^{-1} \sum_{j=1}^N |U_{\lambda,\epsilon,N}^t[\psi_h](x_j)|^2 u(x_j) = u(x_t) + O(h)$ for $c_{t,N} := \sum_{j=1}^N |U_{\lambda,\epsilon,N}^t[\psi_h](x_j)|^2$ and $x_t$ the projection of $\Gamma^t(x_0, \xi_0)$ onto $\mathcal{M}$.Comment: This is a companion paper to "Manifold learning via quantum dynamics

Message-Passing Algorithms for Quadratic Programming Formulations of MAP Estimation

Computing maximum a posteriori (MAP) estimation in graphical models is an important inference problem with many applications. We present message-passing algorithms for quadratic programming (QP) formulations of MAP estimation for pairwise Markov random fields. In particular, we use the concave-convex procedure (CCCP) to obtain a locally optimal algorithm for the non-convex QP formulation. A similar technique is used to derive a globally convergent algorithm for the convex QP relaxation of MAP. We also show that a recently developed expectation-maximization (EM) algorithm for the QP formulation of MAP can be derived from the CCCP perspective. Experiments on synthetic and real-world problems confirm that our new approach is competitive with max-product and its variations. Compared with CPLEX, we achieve more than an order-of-magnitude speedup in solving optimally the convex QP relaxation

Distributed constraint optimization with structured resource constraints

Distributed constraint optimization (DCOP) provides a framework for coordinated decision making by a team of agents. Often, during the decision making, capacity constraints on agents ’ resource consumption must be taken into account. To address such scenarios, an extension of DCOP- Resource Constrained DCOP- has been proposed. However, certain type of resources have an additional structure associated with them and exploiting it can result in more efficient algorithms than possible with a general framework. An example of these are distribution networks, where the flow of a commodity from sources to sinks is limited by the flow capacity of edges. We present a new model of structured resource constraints that exploits the acyclicity and the flow conservation property of distribution networks. We show how this model can be used in efficient algorithms for finding the optimal flow configuration in distribution networks, an essential problem in managing power distribution networks. Experiments demonstrate the efficiency and scalability of our approach on publicly available benchmarks and compare favorably against a specialized solver for this task. Our results extend significantly the effectiveness of distributed constraint optimization for practical multi-agent settings

Design and Validation of a Context-Aware Publish-Subscribe Model

A system is said to be context-aware if it can extract, interpret and use contextual information to adapt its functionality and enhance its utility. Context awareness allows the application to gain sensitivity for many environmental parameters that are beyond the reach of conventional systems. Human factors related to context include information about the user (knowledge of habits, emotional state), the user’s social environment (co-location of others, social interaction, group dynamics), and the user’s tasks (spontaneous activity, engaged tasks, general goals). With access to this contextual information, there are many exciting possibilities for applications involving direct human interaction. Software modelling is one of the first steps in the life cycle of a software system. Software models can lead to the discovery of errors in a system, which is useful as the early discovery of such flaws can enable the designers to update the inexpensive system model. By not using system models before the development of the full scale system, we risk the discovery of major problems later on in the life cycle, which will be more expensive to fix. Validation of any software system is an essential part of the development life cycle. The validation of context-aware systems is especially challenging as the input range of the system is loosely defined. But despite this it is very important to validate context-aware systems thoroughly because it is possible that a subset of possible inputs to the system can be part of a failure-critical user interaction. Modeling and validation are important activities in the development or enhancement of all software systems. While software modelling helps check the properties of the systems before actual development, software validation is essential for ensuring the quality of the software based on the original software requirements. This thesis focuses on the modeling and the validation of formal case study design models for context-aware systems based on the event based and publish-subscribe pattern. The study validates formal case study design models against relevant properties using a model checker

Resource constrained deep reinforcement learning

In urban environments, supply resources have to be constantly matched to the "right" locations (where customer demand is present) so as to improve quality of life. For instance, ambulances have to be matched to base stations regularly so as to reduce response time for emergency incidents in EMS (Emergency Management Systems); vehicles (cars, bikes, scooters etc.) have to be matched to docking stations so as to reduce lost demand in shared mobility systems. Such problem domains are challenging owing to the demand uncertainty, combinatorial action spaces (due to allocation) and constraints on allocation of resources (e.g., total resources, minimum and maximum number of resources at locations and regions). Existing systems typically employ myopic and greedy optimization approaches to optimize allocation of supply resources to locations. Such approaches typically are unable to handle surges or variances in demand patterns well. Recent research has demonstrated the ability of Deep RL methods in adapting well to highly uncertain environments. However, existing Deep RL methods are unable to handle combinatorial action spaces and constraints on allocation of resources. To that end, we have developed three approaches on top of the well known actor critic approach, DDPG (Deep Deterministic Policy Gradient) that are able to handle constraints on resource allocation. More importantly, we demonstrate that they are able to outperform leading approaches on simulators validated on semi-real and real data sets