Application of reduced-set pareto-lipschitzian optimization to truss optimization

In this paper, a recently proposed global Lipschitz optimization algorithm Pareto-Lipschitzian Optimization with Reduced-set (PLOR) is further developed, investigated and applied to truss optimization problems. Partition patterns of the PLOR algorithm are similar to those of DIviding RECTangles (DIRECT), which was widely applied to different real-life problems. However here a set of all Lipschitz constants is reduced to just two: the maximal and the minimal ones. In such a way the PLOR approach is independent of any user-defined parameters and balances equally local and global search during the optimization process. An expanded list of other well-known DIRECT-type algorithms is used in investigation and experimental comparison using the standard test problems and truss optimization problems. The experimental investigation shows that the PLOR algorithm gives very competitive results to other DIRECT-type algorithms using standard test problems and performs pretty well on real truss optimization problems

Dynamics of the Nemunas River delta front during the period 1910-2005

Abstract An analysis of changes in the coastline of the Nemunas River delta front was undertaken with GIS based on cartographic material representing a 95 year period. Delta development was analysed comparing two time periods : 1910-1958 and 1958-2005. Quantitative indicators of land area determined during the study indicate that land in the northern part of the Nemunas delta front decreased more than 2.1 times in the 1958-2005 period, compared to the previous 1910-1958 period. The main reasons for the decrease of sediment accumulation are a decrease Nemunas River runoff, and a similar decrease of sediment particulates, due to anthropogenic activity and natural factors a rise in the water levels of the Baltic Sea and the Curonian Lagoon, as well as land subsidence in the Nemunas delta region

On parallel Branch and Bound frameworks for Global Optimization

Branch and Bound (B&B) algorithms are known to exhibit an irregularity of the search tree. Therefore, developing a parallel approach for this kind of algorithms is a challenge. The efficiency of a B&B algorithm depends on the chosen Branching, Bounding, Selection, Rejection, and Termination rules. The question we investigate is how the chosen platform consisting of programming language, used libraries, or skeletons influences programming effort and algorithm performance. Selection rule and data management structures are usually hidden to programmers for frameworks with a high level of abstraction, as well as the load balancing strategy, when the algorithm is run in parallel. We investigate the question by implementing a multidimensional Global Optimization B&B algorithm with the help of three frameworks with a different level of abstraction (from more to less): Bobpp, Threading Building Blocks (TBB), and a customized Pthread implementation. The following has been found. The Bobpp implementation is easy to code, but exhibits the poorest scalability. On the contrast, the TBB and Pthread implementations scale almost linearly on the used platform. The TBB approach shows a slightly better productivity

Greed Is Good: Exploration and Exploitation Trade-offs in Bayesian Optimisation

The performance of acquisition functions for Bayesian optimisation to locate the global optimum of continuous functions is investigated in terms of the Pareto front between exploration and exploitation. We show that Expected Improvement (EI) and the Upper Confidence Bound (UCB) always select solutions to be expensively evaluated on the Pareto front, but Probability of Improvement is not guaranteed to do so and Weighted Expected Improvement does so only for a restricted range of weights. We introduce two novel ϵ-greedy acquisition functions. Extensive empirical evaluation of these together with random search, purely exploratory, and purely exploitative search on 10 benchmark problems in 1 to 10 dimensions shows that ϵ-greedy algorithms are generally at least as effective as conventional acquisition functions (e.g. EI and UCB), particularly with a limited budget. In higher dimensions ϵ-greedy approaches are shown to have improved performance over conventional approaches. These results are borne out on a real world computational fluid dynamics optimisation problem and a robotics active learning problem. Our analysis and experiments suggest that the most effective strategy, particularly in higher dimensions, is to be mostly greedy, occasionally selecting a random exploratory solution

Planar methods and grossone for the Conjugate Gradient breakdown in nonlinear programming

This paper deals with an analysis of the Conjugate Gradient (CG) method (Hestenes and Stiefel in J Res Nat Bur Stand 49:409-436, 1952), in the presence of degenerates on indefinite linear systems. Several approaches have been proposed in the literature to issue the latter drawback in optimization frameworks, including reformulating the original linear system or recurring to approximately solving it. All the proposed alternatives seem to rely on algebraic considerations, and basically pursue the idea of improving numerical efficiency. In this regard, here we sketch two separate analyses for the possible CG degeneracy. First, we start detailing a more standard algebraic viewpoint of the problem, suggested by planar methods. Then, another algebraic perspective is detailed, relying on a novel recently proposed theory, which includes an additional number, namely grossone. The use of grossone allows to work numerically with infinities and infinitesimals. The results obtained using the two proposed approaches perfectly match, showing that grossone may represent a fruitful and promising tool to be exploited within Nonlinear Programming

Pooled testing with replication as a mass testing strategy for the COVID-19 pandemics

During the COVID-19 pandemic it is essential to test as many people as possible, in order to detect early outbreaks of the infection. Present testing solutions are based on the extraction of RNA from patients using oropharyngeal and nasopharyngeal swabs, and then testing with real-time PCR for the presence of specific RNA filaments identifying the virus. This approach is limited by the availability of reactants, trained technicians and laboratories. One of the ways to speed up the testing procedures is a group testing, where the swabs of multiple patients are grouped together and tested. In this paper we propose to use the group testing technique in conjunction with an advanced replication scheme in which each patient is allocated in two or more groups to reduce the total numbers of tests and to allow testing of even larger numbers of people. Under mild assumptions, a 13 × average reduction of tests can be achieved compared to individual testing without delay in time. © 2021, The Author(s)