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Local Optimal Sets and Bounded Archiving on Multi-objective NK-Landscapes with Correlated Objectives

The properties of local optimal solutions in multi-objective combinatorial optimization problems are crucial for the effectiveness of local search algorithms, particularly when these algorithms are based on Pareto dominance. Such local search algorithms typically return a set of mutually nondominated Pareto local optimal (PLO) solutions, that is, a PLO-set. This paper investigates two aspects of PLO-sets by means of experiments with Pareto local search (PLS). First, we examine the impact of several problem characteristics on the properties of PLO-sets for multi-objective NK-landscapes with correlated objectives. In particular, we report that either increasing the number of objectives or decreasing the correlation between objectives leads to an exponential increment on the size of PLO-sets, whereas the variable correlation has only a minor effect. Second, we study the running time and the quality reached when using bounding archiving methods to limit the size of the archive handled by PLS, and thus, the maximum size of the PLO-set found. We argue that there is a clear relationship between the running time of PLS and the difficulty of a problem instance.Comment: appears in Parallel Problem Solving from Nature - PPSN XIII, Ljubljana : Slovenia (2014

Local Optimal Sets and Bounded Archiving on Multi-objective NK-Landscapes with Correlated Objectives

The properties of local optimal solutions in multi-objective combinatorial optimization problems are crucial for the effectiveness of local search algorithms, particularly when these algorithms are based on Pareto dominance. Such local search algorithms typically return a set of mutually nondominated Pareto local optimal (PLO) solutions, that is, a PLO-set. This paper investigates two aspects of PLO-sets by means of experiments with Pareto local search (PLS). First, we examine the impact of several problem characteristics on the properties of PLO-sets for multi-objective NK-landscapes with correlated objectives. In particular, we report that either increasing the number of objectives or decreasing the correlation between objectives leads to an exponential increment on the size of PLO-sets, whereas the variable correlation has only a minor effect. Second, we study the running time and the quality reached when using bounding archiving methods to limit the size of the archive handled by PLS, and thus, the maximum size of the PLO-set found. We argue that there is a clear relationship between the running time of PLS and the difficulty of a problem instance.Comment: appears in Parallel Problem Solving from Nature - PPSN XIII, Ljubljana : Slovenia (2014

The molecular size continuum of soil organic phosphorus and its chemical associations

The chemical nature of most organic P (Porg) in soil remains ‘unresolved’ but is accounted for by a broad signal in the phosphomonoester region of solution 31P nuclear magnetic resonance (NMR) spectra. The molecular size range of this broad NMR signal and its molecular structure remain unclear. The aim of this study was to elucidate the chemical nature of Porg with increasing molecular size in soil extracts combining size exclusion chromatography (SEC) with solution 31P NMR spectroscopy. Gel-filtration SEC was carried out on NaOH-EDTA extracts of four soils (range 238-1135 mg Porg/kgsoil) to collect fractions with molecular sizes of 70 kDa. These were then analysed by NMR spectroscopy. Organic P was detected across the entire molecular size continuum from 70 kDa. Concentrations of Porg in the >10kDa fraction ranged from 107 to 427 mg P/kgsoil and exhibited on average three to four broad signals in the phosphomonoester region of NMR spectra. These broad signals were most prominent in the 10-20 and 20-50 kDa fractions, accounting for on average 77 % and 74 % of total phosphomonoesters, respectively. Our study demonstrates that the broad signal is present in all investigated molecular size fractions and comprises on average three to four components of varying NMR peak line width (20 to 250 Hz). The stereoisomers myo- and scyllo-inositol hexakisphosphates (IP6) were also present across multiple molecular size ranges but were predominant in the 5-10 kDa fraction. The proportion of IP associated with large molecular size fractions >10 kDa was on average 23 % (SD=39 %) of total IP across all soils. These findings suggest that stabilisation of IP in soil includes processes associated with the organic phase

Analysis of objectives relationships in multiobjective problems using trade-off region maps

Understanding the relationships between objectives in many-objective optimisation problems is desirable in order to develop more effective algorithms. We propose a techniquefor the analysis and visualisation of complex relationships between many (three or more) objectives. This technique looks at conflicting, harmonious and independent objectives relationships from different perspectives. To do that, it uses correlation, trade-off regions maps and scatter-plots in a four step approach. We apply the proposed technique to a set of instances of the well-known multiobjective multidimensional knapsack problem. The experimental results show that with the proposed technique we can identify local and complex relationships between objectives, trade-offs not derived from pairwise relationships, gaps in the fitness landscape, and regions of interest. Such information can be used to tailor the development of algorithms

Phosphorus species in sequentially extracted soil organic matter fractions

The majority of organic P (Porg) in soil is considered to be part of soil organic matter (SOM) associations, but its chemical nature is largely ‘unresolved’. In this study, we investigated the Porg composition in different SOM fractions of a Gleysol soil using the Humeomics sequential chemical fractionation (SCF) procedure combined with nuclear magnetic resonance (NMR) spectroscopy. In summary, SCF procedure with subsequent NaOH-EDTA extraction of the soil residue extracted a total of 1769 mg P/kgsoil compared to 1682 mg P/kgsoil of a single-step NaOH-EDTA extraction. Approximately 38 % of the extracted Porg was present in the form of the unresolved Porg pool, which was represented by one or two underlying broad signals in the phosphomonoester region of solution 31P NMR spectra. The SCF revealed that phosphomonoesters were recovered in each fraction: 47 % of the unresolved phosphomonoesters were associated with the SOM fraction released by breaking ester bonds (40 %) and ether bonds (7 %), whereas about 30 % of this unresolved Porg pool appeared in the SOM fraction closely associated with the soil mineral phase. Furthermore, the extractability of inositol phosphates (IP) was increased from 312 mg P/kgsoil to 534 mg P/kgsoil (factor 1.7) using the SCF procedure compared to a single-step NaOH-EDTA extraction. Previous studies have reported the presence of IP in molecular size fractions greater than 10 kDa. Our findings on the removal of IP with the fractionation of the SOM could explain the presence of IP in these large associations. We demonstrate that major pools of Porg are closely associated with SOM structures, comprising a diverse array of chemical species and bonding types. These results forward our understanding of Porg stabilisation, P transformation, and P cycling in terrestrial ecosystems towards an association point of view

Pareto Local Optima of Multiobjective NK-Landscapes with Correlated Objectives

International audienceIn this paper, we conduct a fitness landscape analysis for multiobjective combinatorial optimization, based on the local optima of multiobjective NK-landscapes with objective correlation. In single-objective optimization, it has become clear that local optima have a strong impact on the performance of metaheuristics. Here, we propose an extension to the multiobjective case, based on the Pareto dominance. We study the co-influence of the problem dimension, the degree of non-linearity, the number of objectives and the correlation degree between objective functions on the number of Pareto local optima

The mechanism of the colour shift of astaxanthin in alpha-crustacyanin as investigated by C-13 MAS NMR and specific isotope enrichment

By selective isotope enrichment of astaxanthin, MAS NMR and semi-empirical modelling, ligand-protein interactions associated with the red shift in alpha-crustacyanin, the major blue astaxanthin binding carotenoprotein complex from the carapace of the lobster Homarus gammarus, have been analysed. C-13 Magic Angle Spinning (MAS) NMR spectra were obtained after reconstitution with astaxanthins labelled in the centre of the molecule or at the two keto groups. The MAS data reveal electrostatic polarizations of the conjugated chain. In addition, solid state NMR results for pure unlabelled astaxanthin can be compared with natural abundance C-13 MAS data for canthaxanthin and beta-carotene, to address the effect of the ring functionalities on the electronic properties of the polyene chain. Quantum chemical calculations were performed to reconcile the MAS data with one of several simple and straightforward mechanisms for the colour shift. The results point towards a colour shift mechanism in which the astaxanthin may be doubly charged, possibly by a double protonation of the two ring keto groups.Bio-organic SynthesisSolid state NMR/Biophysical Organic Chemistr

Deconstructing the Big Valley Search Space Hypothesis

The big valley hypothesis suggests that, in combinatorial optimisation, local optima of good quality are clustered and surround the global optimum. We show here that the idea of a single valley does not always hold. Instead the big valley seems to de-construct into several valleys, also called ‘funnels’ in theoretical chemistry. We use the local optima networks model and propose an effective procedure for extracting the network data. We conduct a detailed study on four selected TSP instances of moderate size and observe that the big valley decomposes into a number of sub-valleys of different sizes and fitness distributions. Sometimes the global optimum is located in the largest valley, which suggests an easy to search landscape, but this is not generally the case. The global optimum might be located in a small valley, which offers a clear and visual explanation of the increased search difficulty in these cases. Our study opens up new possibilities for analysing and visualising combinatorial landscapes as complex networks