arXiv subjects

Frank Neumann

Publications and source records attributed to Frank Neumann.

At least 109 records · Page 6Linked to original sources

arXiv2021

Time Complexity Analysis of Randomized Search Heuristics for the Dynamic Graph Coloring Problem

We contribute to the theoretical understanding of randomized search heuristics for dynamic problems. We consider the classical vertex coloring problem on graphs and investigate the dynamic setting where edges are added to the current graph. We then analyze the expected time for randomized search heuristics to recompute high quality solutions. The (1+1)~Evolutionary Algorithm and RLS operate in a setting where the number of colors is bounded and we are minimizing the number of conflicts. Iterated local search algorithms use an unbounded color palette and aim to use the smallest colors and, consequently, the smallest number of colors. We identify classes of bipartite graphs where reoptimization is as hard as or even harder than optimization from scratch, i.e., starting with a random initialization. Even adding a single edge can lead to hard symmetry problems. However, graph classes that are hard for one algorithm turn out to be easy for others. In most cases our bounds show that reoptimization is faster than optimizing from scratch. We further show that tailoring mutation operators to parts of the graph where changes have occurred can significantly reduce the expected reoptimization time. In most settings the expected reoptimization time for such tailored algorithms is linear in the number of added edges. However, tailored algorithms cannot prevent exponential times in settings where the original algorithm is inefficient.

cs.NE↗

arXiv2021

Entropy-Based Evolutionary Diversity Optimisation for the Traveling Salesperson Problem

Computing diverse sets of high-quality solutions has gained increasing attention among the evolutionary computation community in recent years. It allows practitioners to choose from a set of high-quality alternatives. In this paper, we employ a population diversity measure, called the high-order entropy measure, in an evolutionary algorithm to compute a diverse set of high-quality solutions for the Traveling Salesperson Problem. In contrast to previous studies, our approach allows diversifying segments of tours containing several edges based on the entropy measure. We examine the resulting evolutionary diversity optimisation approach precisely in terms of the final set of solutions and theoretical properties. Experimental results show significant improvements compared to a recently proposed edge-based diversity optimisation approach when working with a large population of solutions or long segments.

cs.NE↗

arXiv2021

Evolutionary Diversity Optimization and the Minimum Spanning Tree Problem

In the area of evolutionary computation the calculation of diverse sets of high-quality solutions to a given optimization problem has gained momentum in recent years under the term evolutionary diversity optimization. Theoretical insights into the working principles of baseline evolutionary algorithms for diversity optimization are still rare. In this paper we study the well-known Minimum Spanning Tree problem (MST) in the context of diversity optimization where population diversity is measured by the sum of pairwise edge overlaps. Theoretical results provide insights into the fitness landscape of the MST diversity optimization problem pointing out that even for a population of $μ=2$ fitness plateaus (of constant length) can be reached, but nevertheless diverse sets can be calculated in polynomial time. We supplement our theoretical results with a series of experiments for the unconstrained and constraint case where all solutions need to fulfill a minimal quality threshold. Our results show that a simple $(μ+1)$-EA can effectively compute a diversified population of spanning trees of high quality.

cs.NE↗

arXiv2021

Breeding Diverse Packings for the Knapsack Problem by Means of Diversity-Tailored Evolutionary Algorithms

In practise, it is often desirable to provide the decision-maker with a rich set of diverse solutions of decent quality instead of just a single solution. In this paper we study evolutionary diversity optimization for the knapsack problem (KP). Our goal is to evolve a population of solutions that all have a profit of at least $(1-\varepsilon)\cdot OPT$, where OPT is the value of an optimal solution. Furthermore, they should differ in structure with respect to an entropy-based diversity measure. To this end we propose a simple $(μ+1)$-EA with initial approximate solutions calculated by a well-known FPTAS for the KP. We investigate the effect of different standard mutation operators and introduce biased mutation and crossover which puts strong probability on flipping bits of low and/or high frequency within the population. An experimental study on different instances and settings shows that the proposed mutation operators in most cases perform slightly inferior in the long term, but show strong benefits if the number of function evaluations is severely limited.

cs.NE↗

arXiv2021

Heuristic Strategies for Solving Complex Interacting Large-Scale Stockpile Blending Problems

The Stockpile blending problem is an important component of mine production scheduling, where stockpiles are used to store and blend raw material. The goal of blending material from stockpiles is to create parcels of concentrate which contain optimal metal grades based on the material available. The volume of material that each stockpile provides to a given parcel is dependent on a set of mine schedule conditions and customer demands. Therefore, the problem can be formulated as a continuous optimization problem. In the real-world application, there are several constraints required to guarantee parcels that meet the demand of downstream customers. It is a challenge in solving the stockpile blending problems since its scale can be very large. We introduce two repaired operators for the problems to convert the infeasible solutions into the solutions without violating the two tight constraints. Besides, we introduce a multi-component fitness function for solving the large-scale stockpile blending problem which can maximize the volume of metal over the plan and maintain the balance between stockpiles according to the usage of metal. Furthermore, we investigate the well-known approach in this paper, which is used to solve optimization problems over continuous space, namely the differential evolution (DE) algorithm. The experimental results show that the DE algorithm combined with two proposed duration repair methods is significantly better in terms of the values of results than the results on real-world instances for both one-month problems and large-scale problems.

cs.NE↗

arXiv2021

A General Method to Find Highly Coordinating Communities in Social Media through Inferred Interaction Links

Political misinformation, astroturfing and organised trolling are online malicious behaviours with significant real-world effects. Many previous approaches examining these phenomena have focused on broad campaigns rather than the small groups responsible for instigating or sustaining them. To reveal latent (i.e., hidden) networks of cooperating accounts, we propose a novel temporal window approach that relies on account interactions and metadata alone. It detects groups of accounts engaging in various behaviours that, in concert, come to execute different goal-based strategies, a number of which we describe. The approach relies upon a pipeline that extracts relevant elements from social media posts, infers connections between accounts based on criteria matching the coordination strategies to build an undirected weighted network of accounts, which is then mined for communities exhibiting high levels of evidence of coordination using a novel community extraction method. We address the temporal aspect of the data by using a windowing mechanism, which may be suitable for near real-time application. We further highlight consistent coordination with a sliding frame across multiple windows and application of a decay factor. Our approach is compared with other recent similar processing approaches and community detection methods and is validated against two relevant datasets with ground truth data, using content, temporal, and network analyses, as well as with the design, training and application of three one-class classifiers built using the ground truth; its utility is furthermore demonstrated in two case studies of contentious online discussions.

cs.SI↗

arXiv2021

Advanced Ore Mine Optimisation under Uncertainty Using Evolution

In this paper, we investigate the impact of uncertainty in advanced ore mine optimisation. We consider Maptek's software system Evolution which optimizes extraction sequences based on evolutionary computation techniques and quantify the uncertainty of the obtained solutions with respect to the ore deposit based on predictions obtained by ensembles of neural networks. Furthermore, we investigate the impact of staging on the obtained optimized solutions and discuss a wide range of components for this large scale stochastic optimisation problem which allow to mitigate the uncertainty in the ore deposit while maintaining high profitability.

cs.LG↗

arXiv2021

Heuristic Strategies for Solving Complex Interacting Stockpile Blending Problem with Chance Constraints

Heuristic algorithms have shown a good ability to solve a variety of optimization problems. Stockpile blending problem as an important component of the mine scheduling problem is an optimization problem with continuous search space containing uncertainty in the geologic input data. The objective of the optimization process is to maximize the total volume of materials of the operation and subject to resource capacities, chemical processes, and customer requirements. In this paper, we consider the uncertainty in material grades and introduce chance constraints that are used to ensure the constraints with high confidence. To address the stockpile blending problem with chance constraints, we propose a differential evolution algorithm combining two repair operators that are used to tackle the two complex constraints. In the experiment section, we compare the performance of the approach with the deterministic model and stochastic models by considering different chance constraints and evaluate the effectiveness of different chance constraints.

cs.NE↗

arXiv2021

Runtime Analysis of RLS and the (1+1) EA for the Chance-constrained Knapsack Problem with Correlated Uniform Weights

Addressing a complex real-world optimization problem is a challenging task. The chance-constrained knapsack problem with correlated uniform weights plays an important role in the case where dependent stochastic components are considered. We perform runtime analysis of a randomized search algorithm (RSA) and a basic evolutionary algorithm (EA) for the chance-constrained knapsack problem with correlated uniform weights. We prove bounds for both algorithms for producing a feasible solution. Furthermore, we investigate the behavior of the algorithms and carry out analyses on two settings: uniform profit value and the setting in which every group shares an arbitrary profit profile. We provide insight into the structure of these problems and show how the weight correlations and the different types of profit profiles influence the runtime behavior of both algorithms in the chance-constrained setting.

cs.DS↗

arXiv2020

Pareto Optimization for Subset Selection with Dynamic Partition Matroid Constraints

In this study, we consider the subset selection problems with submodular or monotone discrete objective functions under partition matroid constraints where the thresholds are dynamic. We focus on POMC, a simple Pareto optimization approach that has been shown to be effective on such problems. Our analysis departs from singular constraint problems and extends to problems of multiple constraints. We show that previous results of POMC's performance also hold for multiple constraints. Our experimental investigations on random undirected maxcut problems demonstrate POMC's competitiveness against the classical GREEDY algorithm with restart strategy.

cs.NE↗

arXiv2020

Gabriel-Zisman Cohomology and spectral sequences

Extending constructions by Gabriel and Zisman, we develop a functorial framework for the cohomology and homology of simplicial sets with very general coefficient systems given by functors on simplex categories into abelian categories. Furthermore we construct Leray type spectral sequences for any map of simplicial sets. We also show that these constructions generalise and unify the various existing versions of cohomology and homology of small categories and as a bonus provide new insight into their functoriality.

math.KT↗

arXiv2020

Equivariant cohomology for differentiable stacks

We construct and analyse models of equivariant cohomology for differentiable stacks with Lie group actions extending classical results for smooth manifolds due to Borel, Cartan and Getzler. We also derive various spectral sequences for the equivariant cohomology of a differentiable stack generalising among others Bott's spectral sequence which converges to the cohomology of the classifying space of a Lie group.

math.AT↗

arXiv2020

Computing Diverse Sets of Solutions for Monotone Submodular Optimisation Problems

Submodular functions allow to model many real-world optimisation problems. This paper introduces approaches for computing diverse sets of high quality solutions for submodular optimisation problems. We first present diversifying greedy sampling approaches and analyse them with respect to the diversity measured by entropy and the approximation quality of the obtained solutions. Afterwards, we introduce an evolutionary diversity optimisation approach to further improve diversity of the set of solutions. We carry out experimental investigations on popular submodular benchmark functions that show that the combined approaches achieve high quality solutions of large diversity.

cs.AI↗

arXiv2020

Improved Runtime Results for Simple Randomised Search Heuristics on Linear Functions with a Uniform Constraint

In the last decade remarkable progress has been made in development of suitable proof techniques for analysing randomised search heuristics. The theoretical investigation of these algorithms on classes of functions is essential to the understanding of the underlying stochastic process. Linear functions have been traditionally studied in this area resulting in tight bounds on the expected optimisation time of simple randomised search algorithms for this class of problems. Recently, the constrained version of this problem has gained attention and some theoretical results have also been obtained on this class of problems. In this paper we study the class of linear functions under uniform constraint and investigate the expected optimisation time of Randomised Local Search (RLS) and a simple evolutionary algorithm called (1+1) EA. We prove a tight bound of $Θ(n^2)$ for RLS and improve the previously best known upper bound of (1+1) EA from $O(n^2 \log (Bw_{\max}))$ to $O(n^2\log B)$ in expectation and to $O(n^2 \log n)$ with high probability, where $w_{\max}$ and $B$ are the maximum weight of the linear objective function and the bound of the uniform constraint, respectively. Also, we obtain a tight bound of $O(n^2)$ for the (1+1) EA on a special class of instances. We complement our theoretical studies by experimental investigations that consider different values of $B$ and also higher mutation rates that reflect the fact that $2$-bit flips are crucial for dealing with the uniform constraint.

cs.NE↗

arXiv2020

Who's in the Gang? Revealing Coordinating Communities in Social Media

Political astroturfing and organised trolling are online malicious behaviours with significant real-world effects. Common approaches examining these phenomena focus on broad campaigns rather than the small groups responsible. To reveal latent networks of cooperating accounts, we propose a novel temporal window approach that relies on account interactions and metadata alone. It detects groups of accounts engaging in behaviours that, in concert, execute different goal-based strategies, which we describe. Our approach is validated against two relevant datasets with ground truth data.

cs.SI↗

arXiv2020

The Dynamic Travelling Thief Problem: Benchmarks and Performance of Evolutionary Algorithms

Many real-world optimisation problems involve dynamic and stochastic components. While problems with multiple interacting components are omnipresent in inherently dynamic domains like supply-chain optimisation and logistics, most research on dynamic problems focuses on single-component problems. With this article, we define a number of scenarios based on the Travelling Thief Problem to enable research on the effect of dynamic changes to sub-components. Our investigations of 72 scenarios and seven algorithms show that -- depending on the instance, the magnitude of the change, and the algorithms in the portfolio -- it is preferable to either restart the optimisation from scratch or to continue with the previously valid solutions.

cs.NE↗

arXiv2020

Maximizing Submodular or Monotone Functions under Partition Matroid Constraints by Multi-objective Evolutionary Algorithms

Many important problems can be regarded as maximizing submodular functions under some constraints. A simple multi-objective evolutionary algorithm called GSEMO has been shown to achieve good approximation for submodular functions efficiently. While there have been many studies on the subject, most of existing run-time analyses for GSEMO assume a single cardinality constraint. In this work, we extend the theoretical results to partition matroid constraints which generalize cardinality constraints, and show that GSEMO can generally guarantee good approximation performance within polynomial expected run time. Furthermore, we conducted experimental comparison against a baseline GREEDY algorithm in maximizing undirected graph cuts on random graphs, under various partition matroid constraints. The results show GSEMO tends to outperform GREEDY in quadratic run time.

cs.NE↗

arXiv2020

Using Neural Networks and Diversifying Differential Evolution for Dynamic Optimisation

Dynamic optimisation occurs in a variety of real-world problems. To tackle these problems, evolutionary algorithms have been extensively used due to their effectiveness and minimum design effort. However, for dynamic problems, extra mechanisms are required on top of standard evolutionary algorithms. Among them, diversity mechanisms have proven to be competitive in handling dynamism, and recently, the use of neural networks have become popular for this purpose. Considering the complexity of using neural networks in the process compared to simple diversity mechanisms, we investigate whether they are competitive and the possibility of integrating them to improve the results. However, for a fair comparison, we need to consider the same time budget for each algorithm. Thus, instead of the usual number of fitness evaluations as the measure for the available time between changes, we use wall clock timing. The results show the significance of the improvement when integrating the neural network and diversity mechanisms depends on the type and the frequency of changes. Moreover, we observe that for differential evolution, having a proper diversity in population when using neural networks plays a key role in the neural network's ability to improve the results.

cs.NE↗