SOMS: SurrOgate MultiStart algorithm for use with nonlinear programming for global optimization

SOMS is a general surrogate-based multistart algorithm, which is used in combination with any local optimizer to find global optima for computationally expensive functions with multiple local minima. SOMS differs from previous multistart methods in that a surrogate approximation is used by the multistart algorithm to help reduce the number of function evaluations necessary to identify the most promising points from which to start each nonlinear programming local search. SOMS’s numerical results are compared with four well-known methods, namely, Multi-Level Single Linkage (MLSL), MATLAB’s MultiStart, MATLAB’s GlobalSearch, and GLOBAL. In addition, we propose a class of wavy test functions that mimic the wavy nature of objective functions arising in many black-box simulations. Extensive comparisons of algorithms on the wavy testfunctions and on earlier standard global-optimization test functions are done for a total of 19 different test problems. The numerical results indicate that SOMS performs favorably in comparison to alternative methods and does especially well on wavy functions when the number of function evaluations allowed is limited.

SOP: Parallel surrogate global optimization with Pareto center selection for computationally expensive single objective problems

This paper presents a parallel surrogate-based global optimization method for computationally expensive objective functions that is more effective for larger numbers of processors. To reach this goal, we integrated concepts from multi-objective optimization and tabu search into, single objective, surrogate optimization. Our proposed derivative-free algorithm, called SOP, uses non-dominated sorting of points for which the expensive function has been previously evaluated. The two objectives are the expensive function value of the point and the minimum distance of the point to previously evaluated points. Based on the results of non-dominated sorting, P points from the sorted fronts are selected as centers from which many candidate points are generated by random perturbations. Based on surrogate approximation, the best candidate point is subsequently selected for expensive evaluation for each of the P centers, with simultaneous computation on P processors. Centers that previously did not generate good solutions are tabu with a given tenure. We show almost sure convergence of this algorithm under some conditions. The performance of SOP is compared with two RBF based methods. The test results show that SOP is an efficient method that can reduce time required to find a good near optimal solution. In a number of cases the efficiency of SOP is so good that SOP with 8 processors found an accurate answer in less wall-clock time than the other algorithms did with 32 processors.

Global Optimization with Sparse and Local Gaussian Process Models

We present a novel surrogate model-based global optimization framework allowing a large number of function evaluations. The method, called SpLEGO, is based on a multi-scale expected improvement (EI) framework relying on both sparse and local Gaussian process (GP) models. First, a bi-objective approach relying on a global sparse GP model is used to determine potential next sampling regions. Local GP models are then constructed within each selected region. The method subsequently employs the standard expected improvement criterion to deal with the exploration-exploitation trade-off within selected local models, leading to a decision on where to perform the next function evaluation(s). The potential of our approach is demonstrated using the so-called Sparse Pseudo-input GP as a global model. The algorithm is tested on four benchmark problems, whose number of starting points ranges from 102 to 104. Our results show that SpLEGO is effective and capable of solving problems with large number of starting points, and it even provides significant advantages when compared with state-of-the-art EI algorithms.

Differentiating the Multipoint Expected Improvement for Optimal Batch Design

This work deals with parallel optimization of expensive objective functions which are modelled as sample realizations of Gaussian processes. The study is formalized as a Bayesian optimization problem, or continuous multi-armed bandit problem, where a batch of q > 0 arms is pulled in parallel at each iteration. Several algorithms have been developed for choosing batches by trading off exploitation and exploration. As of today, the maximum Expected Improvement (EI) and Upper Confidence Bound (UCB) selection rules appear as the most prominent approaches for batch selection. Here, we build upon recent work on the multipoint Expected Improvement criterion, for which an analytic expansion relying on Tallis’ formula was recently established. The computational burden of this selection rule being still an issue in application, we derive a closed-form expression for the gradient of the multipoint Expected Improvement, which aims at facilitating its maximization using gradient-based ascent algorithms. Substantial computational savings are shown in application. In addition, our algorithms are tested numerically and compared to state-of-the-art UCB-based batchsequential algorithms. Combining starting designs relying on UCB with gradient-based EI local optimization finally appears as a sound option for batch design in distributed Gaussian Process optimization.

Nonparametric location estimators in the randomized complete block design

Several tests for the comparison of different groups in the randomized complete block design exist. However, there is a lack of robust estimators for the location difference between one group and all the others on the original scale. The relative marginal effects are commonly used in this situation, but they are more difficult to interpret and use by less experienced people because of the different scale. In this paper two nonparametric estimators for the comparison of one group against the others in the randomized complete block design will be presented. Theoretical results such as asymptotic normality, consistency, translation invariance, scale preservation, unbiasedness, and median unbiasedness are derived. The finite sample behavior of these estimators is derived by simulations of different scenarios. In addition, possible confidence intervals with these estimators are discussed and their behavior derived also by simulations.

An Avron rule for fragments of R-mingle

Axiomatic bases of admissible rules are obtained for fragments of the substructural logic R-mingle. In particular, it is shown that a ‘modus-ponens-like’ rule introduced by Arnon Avron forms a basis for the admissible rules of its implication and implication–fusion fragments, while a basis for the admissible rules of the full multiplicative fragment requires an additional countably infinite set of rules. Indeed, this latter case provides an example of a three-valued logic with a finitely axiomatizable consequence relation that has no finite basis for its admissible rules.

The Complexity of Non-Iterated Probabilistic Justification Logic

The logic PJ is a probabilistic logic defined by adding (noniterated) probability operators to the basic justification logic J. In this paper we establish upper and lower bounds for the complexity of the derivability problem in the logic PJ. The main result of the paper is that the complexity of the derivability problem in PJ remains the same as the complexity of the derivability problem in the underlying logic J, which is π[p/2] -complete. This implies that the probability operators do not increase the complexity of the logic, although they arguably enrich the expressiveness of the language.

Probabilistic Justification Logic

We present a probabilistic justification logic, PPJ, to study rational belief, degrees of belief and justifications. We establish soundness and completeness for PPJ and show that its satisfiability problem is decidable. In the last part we use PPJ to provide a solution to the lottery paradox.

Information-Centric Content Retrieval for Delay-Tolerant Networks

The shift from host-centric to information-centric networking (ICN) promises seamless communication in mobile networks. However, most existing works either consider well-connected networks with high node density or introduce modifications to {ICN} message processing for delay-tolerant Networking (DTN). In this work, we present agent-based content retrieval, which provides information-centric {DTN} support as an application module without modifications to {ICN} message processing. This enables flexible interoperability in changing environments. If no content source can be found via wireless multi-hop routing, requesters may exploit the mobility of neighbor nodes (called agents) by delegating content retrieval to them. Agents that receive a delegation and move closer to content sources can retrieve data and return it back to requesters. We show that agent-based content retrieval may be even more efficient in scenarios where multi-hop communication is possible. Furthermore, we show that broadcast communication may not be necessarily the best option since dynamic unicast requests have little overhead and can better exploit short contact times between nodes (no broadcast delays required for duplicate suppression).

Dynamic Unicast: Information-Centric Multi-hop Routing for Mobile Ad-hoc Networks

Abstract Information-centric networking (ICN) offers new perspectives on mobile ad-hoc communication because routing is based on names but not on endpoint identifiers. Since every content object has a unique name and is signed, authentic content can be stored and cached by any node. If connectivity to a content source breaks, it is not necessarily required to build a new path to the same source but content can also be retrieved from a closer node that provides the same content copy. For example, in case of collisions, retransmissions do not need to be performed over the entire path but due to caching only over the link where the collision occurred. Furthermore, multiple requests can be aggregated to improve scalability of wireless multi-hop communication. In this work, we base our investigations on Content-Centric Networking (CCN), which is a popular {ICN} architecture. While related works in wireless {CCN} communication are based on broadcast communication exclusively, we show that this is not needed for efficient mobile ad-hoc communication. With Dynamic Unicast requesters can build unicast paths to content sources after they have been identified via broadcast. We have implemented Dynamic Unicast in CCNx, which provides a reference implementation of the {CCN} concepts, and performed extensive evaluations in diverse mobile scenarios using NS3-DCE, the direct code execution framework for the {NS3} network simulator. Our evaluations show that Dynamic Unicast can result in more efficient communication than broadcast communication, but still supports all {CCN} advantages such as caching, scalability and implicit content discovery.

Signature, positive Hopf plumbing and the Coxeter transformation

By a theorem of A'Campo, the eigenvalues of certain Coxeter transformations are positive real or lie on the unit circle. By optimally bounding the signature of tree-like positive Hopf plumbings from below by the genus, we prove that at least two thirds of them lie on the unit circle. In contrast, we show that for divide links, the signature cannot be linearly bounded from below by the genus.

A unified approach to architecture conformance checking

Architectural decisions can be interpreted as structural and behavioral constraints that must be enforced in order to guarantee overarching qualities in a system. Enforcing those constraints in a fully automated way is often challenging and not well supported by current tools. Current approaches for checking architecture conformance either lack in usability or offer poor options for adaptation. To overcome this problem we analyze the current state of practice and propose an approach based on an extensible, declarative and empirically-grounded specification language. This solution aims at reducing the overall cost of setting up and maintaining an architectural conformance monitoring environment by decoupling the conceptual representation of a user-defined rule from its technical specification prescribed by the underlying analysis tools. By using a declarative language, we are able to write tool-agnostic rules that are simple enough to be understood by untrained stakeholders and, at the same time, can be can be automatically processed by a conformance checking validator. Besides addressing the issue of cost, we also investigate opportunities for increasing the value of conformance checking results by assisting the user towards the full alignment of the implementation with respect to its architecture. In particular, we show the benefits of providing actionable results by introducing a technique which automatically selects the optimal repairing solutions by means of simulation and profit-based quantification. We perform various case studies to show how our approach can be successfully adopted to support truly diverse industrial projects. We also investigate the dynamics involved in choosing and adopting a new automated conformance checking solution within an industrial context. Our approach reduces the cost of conformance checking by avoiding the need for an explicit management of the involved validation tools. The user can define rules using a convenient high-level DSL which automatically adapts to emerging analysis requirements. Increased usability and modular customization ensure lower costs and a shorter feedback loop.

A Proof-Theoretic Analysis of Theories for Stratified Inductive Definitions

In this article we study subsystems SIDᵥ of the theory ID₁ in which fixed point induction is restricted to properly stratified formulas.

Gradient-domain Path Tracing

We introduce gradient-domain rendering for Monte Carlo image synthesis.While previous gradient-domain Metropolis Light Transport sought to distribute more samples in areas of high gradients, we show, in contrast, that estimating image gradients is also possible using standard (non-Metropolis) Monte Carlo algorithms, and furthermore, that even without changing the sample distribution, this often leads to significant error reduction. This broadens the applicability of gradient rendering considerably. To gain insight into the conditions under which gradient-domain sampling is beneficial, we present a frequency analysis that compares Monte Carlo sampling of gradients followed by Poisson reconstruction to traditional Monte Carlo sampling. Finally, we describe Gradient-Domain Path Tracing (G-PT), a relatively simple modification of the standard path tracing algorithm that can yield far superior results.