Anatomy of the attraction basins: Breaking with the intuition

olving combinatorial optimization problems efficiently requires the development of algorithms that consider the specific properties of the problems. In this sense, local search algorithms are designed over a neighborhood structure that partially accounts for these properties. Considering a neighborhood, the space is usually interpreted as a natural landscape, with valleys and mountains. Under this perception, it is commonly believed that, if maximizing, the solutions located in the slopes of the same mountain belong to the same attraction basin, with the peaks of the mountains being the local optima. Unfortunately, this is a widespread erroneous visualization of a combinatorial landscape. Thus, our aim is to clarify this aspect, providing a detailed analysis of, first, the existence of plateaus where the local optima are involved, and second, the properties that define the topology of the attraction basins, picturing a reliable visualization of the landscapes. Some of the features explored in this article have never been examined before. Hence, new findings about the structure of the attraction basins are shown. The study is focused on instances of permutation-based combinatorial optimization problems considering the 2-exchange and the insert neighborhoods. As a consequence of this work, we break away from the extended belief about the anatomy of attraction basins

Characterising the rankings produced by combinatorial optimisation problems and finding their intersections

The aim of this paper is to introduce the concept of intersection between combinatorial optimisation problems. We take into account that most algorithms, in their machinery, do not consider the exact objective function values of the solutions, but only a comparison between them. In this sense, if the solutions of an instance of a combinatorial optimisation problem are sorted into their objective function values, we can see the instances as (partial) rankings of the solutions of the search space. Working with specific problems, particularly, the linear ordering problem and the symmetric and asymmetric traveling salesman problem, we show that they can not generate the whole set of (partial) rankings of the solutions of the search space, but just a subset. First, we characterise the set of (partial) rankings each problem can generate. Secondly, we study the intersections between these problems: those rankings which can be generated by both the linear ordering problem and the symmetric/asymmetric traveling salesman problem, respectively. The fact of finding large intersections between problems can be useful in order to transfer heuristics from one problem to another, or to define heuristics that can be useful for more than one problem

New Knowledge about the Elementary Landscape Decomposition for Solving the Quadratic Assignment Problem

Previous works have shown that studying the characteristics of the Quadratic Assignment Problem (QAP) is a crucial step in gaining knowledge that can be used to design tailored meta-heuristic algorithms. One way to analyze the characteristics of the QAP is to decompose its objective function into a linear combination of orthogonal sub-functions that can be independently studied. In particular, this work focuses on a decomposition approach that has attracted considerable attention: The Elementary Landscape Decomposition (ELD).The main drawback of the ELD is that it does not allow an understandable characterization of what is being measured by each component of the decomposition. Thus, it turns out difficult to design new efficient meta-heuristic algorithms for the QAP based on the ELD. To address this issue, in this work, we delve deeper into the ELD by means of an additional decomposition of its elementary components. Conducted experiments show that the performed analysis may be used to explain the behaviour of ELD-based methods, providing critical information about their potential applications

On the Use of Second Order Neighbors to Escape from Local Optima

Designing efficient local search based algorithms requires to consider the specific properties of the problems. We introduce a simple and effi- cient strategy, the Extended Reach, that escapes from local optima ob- tained from a best improvement local search and apply it to the linear ordering problem (LOP), the traveling salesperson problem (TSP) and the quadratic assignment problem (QAP). This strategy is based on two landscape properties observed in the literature. First, it considers that a local optimum is usually located in the frontier of its own attraction basin, and thus, it is enough to inspect the second order neighbors to reach a (better) solution inside an attraction basin of a better local optimum. Second, taking into account that for the LOP and specific neighborhoods it is possible to discard solutions without the need of being evaluated, we extend this result to the TSP with the 2-opt neighborhood to avoid the unnecessary evaluation of solutions. Efficient ways of evaluating the second order neighbors are also presented, based on the cost differences, reducing significantly the computation cost. Experimental results on ran- dom and benchmark instances show that our strategy, indeed, escapes from local optima despite its simplicity.PID2019-104966GB-I00 AXA Research Fun

A simple method to estimate the significance level of the catch probability in the catch removal method in riverf ish populations

This work presents a method for estimating the signi®cance level of the capture probability when the capture removal method is used in riverine ®sh populations. The method is based on adjustment of the linear relationship between capture probability and an index of capture ef®cacy. With this method the population size, the statistic 2 and the signi®cance level of the capture probability can be estimated. This is a simple technique which can be applied in the ®eld at the time of sampling. It does not require the use of computers and can determine in situ whether the catch is valid to calculate the population density

A software tool for monitoring legal minimum lenght of landings: Case study of a fishery in sourthern Spain

Herramienta de interés para el control y la gestión de pesqueríasThe regulation of minimum legal size(MLS) of catches is a tool widely applied in the management of fisheries resources, although the MLS does not always coincide with the length at first maturit(LFM). The optimization of this management tool requires a series of quality control in fish markets and transportation. A software application has been developed to make the control of the landings of several target species easier and faster. In order to test and make this tool operational,six species of commercial interest were selected: four species of fish hand two species of bivalves. It is proposed to estimate the proportion of illegal specimens in the studied lot from the proportion of illegal individuals found in the samples taken from this lot.The input data for the application are the minimum legal size(MLS) of the species and the total length(TL)of each specimen sampled. The out put data is a statistical summary of the percentage of specimens of size less than the legal minimum(TL<=MLS)within different confidence intervals(90%,95% and 99%). The software developed will serve as a fast,efficient and easy to manage tool that allows inspectors to determine the degree of compliance on MLS control and to make a decision supported by statistical proof on fishing goods

Age, diet, growth and reproduction of a Population of Cobitis paludica (de Buen, 1930) in the Palancar Stream (southwest of Europe, Spain) (Pisces: Cobitidae)

A total sample of 99 specimens of the vulnerable fish species Cobitis paludica (de Buen, 1930), was collected on a monthly basis from a tributary of the River Guadalquivir between September 1990 and September 1991. Female longevity was 1 year longer than that of males, the former reaching age-class 5+. The diet of C. paludica consisted mainly of Ostracoda and chironomid larvae, benthic prey of small size and occasionally other resources, such as Macrobiotid eggs spawned during winter. Detritus in gastrointestinal content was scarce, which differs from other populations. Back-calculations of length were performed from scale annuli measurements. The relationship between standard length and scale radius was different for males and females. Females were larger than males of the same age. Both back-calculated length and theoretical length, calculated by applying von Bertalanffy’s model, were larger for females. The relationship between female standard length (SL) and fecundity (F) was log F = 7.465 + 5.5753 log SL

Some meristic characteristics of hybrids between Acipenser naccarii and Acipenser baerii

The aim of this study was to describe meristic characters of hybrid Acipenser naccarii x A. baeri, to be used as the basis for characterizing hybrid specimens in a complementary manner to as described for A. naccarii by Hernando et al. (1999). Thirty 2+ and 3+ year class individuals from the Region of Lombardy (Italy) were analysed for eight morphological variables (Soljan 1975; Holcick et al. 1989), and weight. Three indices, viz the relative position of barbels (CA), the ratio of snout width to length (FB) (Garrido-Ramos et al. 1997), and the Soljan index (Hernando et al. 1999), were used to characterize hybrids. A descriptive analyses of variables, simple and multiple regression analysis, and principal components relationships, were calculated. The relationships between TI and the indices was described using a stepwise multiple regression analysis: TI = 33.32 - 0.26 CA + 10.49 FB + 74.45 SOLJ (F = 1.96; Df = 3 )

Structural and catalytic properties of lanthanide (La, Eu, Gd) doped ceria

Este documento es la última versión enviada a la revista con los ajustes finales después de la revisión de los evaluadores.In this work, Ce0.9M0.1O2−δ mixed oxides (M=La, Eu and Gd) were synthesized by coprecipitation. Independent of the dopant cation, the obtained solids maintain the F-type crystalline structure, characteristic of CeO2 (fluorite structure) without phase segregation. The ceria lattice expands depending on the ionic radii of the dopant cation, as indicated by X-ray diffraction studies. This effect also agrees with the observed shift of the F2g Raman vibrational mode. The presence of the dopant cations in the ceria lattice increases the concentration of structural oxygen vacancies and the reducibility of the redox pair Ce4+/Ce3+. All synthesized materials show higher catalytic activity for the CO oxidation reaction than that of bare CeO2, being Eu-doped solid the one with the best catalytic performances despite of its lower surface area.Junta de Andalucía con su apoyo a la unidad TEP106Ministerio de Ciencia e Innovación mediante la subvención del proyecto: ENE2009-14522-C05-01 cofinanciado con fondos FEDER de la Unión EuropeaPrograma Alban a través de la beca predoctoral de W.Y. Hernández: (E06D101739CO

The performance of three ordination methods

The performance of robust principal component analysis (RPCA), detrended correspondence analysis (DCA) and non-metric multidimensional scaling (NMDS) with two demersal fish data sets were assessed in terms of their stability to bootstrap-generated sample variation and the method’s ability to reflect a well-known depth gradient. Stability was assessed for both species and site orderings and configurations, using scaled rank variance (SRV) and Spearman (q) and Procrustes correlations (t0). The NMDS site and species orderings showed the highest stability. DCA performed best in terms of site ordination stability, but NMDS performed best in terms of species ordination stability. In terms of matching the expected ecological variation, NMDS was the most sensitive method for the wider-depth gradient data and DCA was the most sensitive for the narrower-depth gradient data. According to the sensitivity and informative power criteria associated with the stability assessment, t0 was the best methodological approach for site ordinations, and SRV for species ordinations