On the Neutrality of Flowshop Scheduling Fitness Landscapes

Solving efficiently complex problems using metaheuristics, and in particular local searches, requires incorporating knowledge about the problem to solve. In this paper, the permutation flowshop problem is studied. It is well known that in such problems, several solutions may have the same fitness value. As this neutrality property is an important one, it should be taken into account during the design of optimization methods. Then in the context of the permutation flowshop, a deep landscape analysis focused on the neutrality property is driven and propositions on the way to use this neutrality to guide efficiently the search are given.Comment: Learning and Intelligent OptimizatioN Conference (LION 5), Rome : Italy (2011

On the Impact of Multiobjective Scalarizing Functions

Recently, there has been a renewed interest in decomposition-based approaches for evolutionary multiobjective optimization. However, the impact of the choice of the underlying scalarizing function(s) is still far from being well understood. In this paper, we investigate the behavior of different scalarizing functions and their parameters. We thereby abstract firstly from any specific algorithm and only consider the difficulty of the single scalarized problems in terms of the search ability of a (1+lambda)-EA on biobjective NK-landscapes. Secondly, combining the outcomes of independent single-objective runs allows for more general statements on set-based performance measures. Finally, we investigate the correlation between the opening angle of the scalarizing function's underlying contour lines and the position of the final solution in the objective space. Our analysis is of fundamental nature and sheds more light on the key characteristics of multiobjective scalarizing functions.Comment: appears in Parallel Problem Solving from Nature - PPSN XIII, Ljubljana : Slovenia (2014

Fitness landscape of the cellular automata majority problem: View from the Olympus

In this paper we study cellular automata (CAs) that perform the computational Majority task. This task is a good example of what the phenomenon of emergence in complex systems is. We take an interest in the reasons that make this particular fitness landscape a difficult one. The first goal is to study the landscape as such, and thus it is ideally independent from the actual heuristics used to search the space. However, a second goal is to understand the features a good search technique for this particular problem space should possess. We statistically quantify in various ways the degree of difficulty of searching this landscape. Due to neutrality, investigations based on sampling techniques on the whole landscape are difficult to conduct. So, we go exploring the landscape from the top. Although it has been proved that no CA can perform the task perfectly, several efficient CAs for this task have been found. Exploiting similarities between these CAs and symmetries in the landscape, we define the Olympus landscape which is regarded as the ''heavenly home'' of the best local optima known (blok). Then we measure several properties of this subspace. Although it is easier to find relevant CAs in this subspace than in the overall landscape, there are structural reasons that prevent a searcher from finding overfitted CAs in the Olympus. Finally, we study dynamics and performance of genetic algorithms on the Olympus in order to confirm our analysis and to find efficient CAs for the Majority problem with low computational cost

Clarifying the Difference in Local Optima Network Sampling Algorithms

We conduct the first ever statistical comparison between two Local Optima Network (LON) sampling algorithms. These methodologies attempt to capture the connectivity in the local optima space of a fitness landscape. One sampling algorithm is based on a random-walk snowballing procedure, while the other is centred around multiple traced runs of an Iterated Local Search. Both of these are proposed for the Quadratic Assignment Problem (QAP), making this the focus of our study. It is important to note the sampling algorithm frameworks could easily be modified for other domains. In our study descriptive statistics for the obtained search space samples are contrasted and commented on. The LON features are also used in linear mixed models and random forest regression for predicting heuristic optimisation performance of two prominent heuristics for the QAP on the underlying combinatorial problems. The model results are then used to make deductions about the sampling algorithms’ utility. We also propose a specific set of LON metrics for use in future predictive models alongside previously-proposed network metrics, demonstrating the payoff in doing so

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

Tunnelling Crossover Networks for the Asymmetric TSP

Local optima networks are a compact representation of fitness landscapes that can be used for analysis and visualisation. This paper provides the first analysis of the Asymmetric Travelling Salesman Problem using local optima networks. These are generated by sampling the search space by recording the progress of an existing evolutionary algorithm based on the Generalised Asymmetric Partition Crossover. They are compared to networks sampled through the Chained Lin-Kernighan heuristic across 25 instances. Structural differences and similarities are identified, as well as examples where crossover smooths the landscape

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

Force-based Cooperative Search Directions in Evolutionary Multi-objective Optimization

International audienceIn order to approximate the set of Pareto optimal solutions, several evolutionary multi-objective optimization (EMO) algorithms transfer the multi-objective problem into several independent single-objective ones by means of scalarizing functions. The choice of the scalarizing functions' underlying search directions, however, is typically problem-dependent and therefore difficult if no information about the problem characteristics are known before the search process. The goal of this paper is to present new ideas of how these search directions can be computed \emph{adaptively} during the search process in a \emph{cooperative} manner. Based on the idea of Newton's law of universal gravitation, solutions attract and repel each other \emph{in the objective space}. Several force-based EMO algorithms are proposed and compared experimentally on general bi-objective $\rho$MNK landscapes with different objective correlations. It turns out that the new approach is easy to implement, fast, and competitive with respect to a $(\mu+\lambda)$-SMS-EMOA variant, in particular if the objectives show strong positive or negative correlations

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