Understanding the relationships between objectives in a multiobjective optimisation problem is important for developing tailored and efficient solving techniques. In particular, when tackling combinatorial optimisation problems with many objectives, that arise in real-world logistic scenarios, better support for the decision maker can be achieved through better understanding of the often complex fitness landscape. This paper makes a contribution in this direction by presenting a technique that allows a visualisation and analysis of the local and global relationships between objectives in optimisation problems with many objectives. The proposed technique uses four steps: First, the global pairwise relationships are analysed using the Kendall correlation method; then, the ranges of the values found on the given Pareto front are estimated and assessed; next, these ranges are used to plot a map using Gray code, similar to Karnaugh maps, that has the ability to highlight the trade-offs between multiple objectives; and finally, local relationships are identified using scatter plots. Experiments are presented for three combinatorial optimisation problems: multiobjective multidimensional knapsack problem, multiobjective nurse scheduling problem, and multiobjective vehicle routing problem with time windows . Results show that the proposed technique helps in the gaining of insights into the problem difficulty arising from the relationships between objectives.

We revisit the optimal transport problem over angular velocity dynamics given by the controlled Euler equation. The solution of this problem enables stochastic guidance of spin states of a rigid body (e.g., spacecraft) over hard deadline constraint by transferring a given initial state statistics to a desired terminal state statistics. This is an instance of generalized optimal transport over a nonlinear dynamical system. While prior work has reported existence-uniqueness and numerical solution of this dynamical optimal transport problem, here we present structural results about the equivalent Kantorovich a.k.a. optimal coupling formulation. Specifically, we focus on deriving the ground cost for the associated Kantorovich optimal coupling formulation. The ground cost equals to the cost of transporting unit amount of mass from a specific realization of the initial or source joint probability measure to a realization of the terminal or target joint probability measure, and determines the Kantorovich formulation. Finding the ground cost leads to solving a structured deterministic nonlinear optimal control problem, which is shown to be amenable to an analysis technique pioneered by Athans et. al. We show that such techniques have broader applicability in determining the ground cost (thus Kantorovich formulation) for a class of generalized optimal mass transport problems involving nonlinear dynamics with translated norm-invariant drift.

In the realm of data analysis and bioinformatics, representing time series data in a manner akin to biological sequences offers a novel approach to leverage sequence analysis techniques. Transforming time series signals into molecular sequence-type representations allows us to enhance pattern recognition by applying sophisticated sequence analysis techniques (e.g. $k$-mers based representation) developed in bioinformatics, uncovering hidden patterns and relationships in complex, non-linear time series data. This paper proposes a method to transform time series signals into biological/molecular sequence-type representations using a unique alphabetic mapping technique. By generating 26 ranges corresponding to the 26 letters of the English alphabet, each value within the time series is mapped to a specific character based on its range. This conversion facilitates the application of sequence analysis algorithms, typically used in bioinformatics, to analyze time series data. We demonstrate the effectiveness of this approach by converting real-world time series signals into character sequences and performing sequence classification. The resulting sequences can be utilized for various sequence-based analysis techniques, offering a new perspective on time series data representation and analysis.

Term rewriting plays a crucial role in software verification and compiler optimization. With dozens of highly parameterizable techniques developed to prove various system properties, automatic term rewriting tools work in an extensive parameter space. This complexity exceeds human capacity for parameter selection, motivating an investigation into automated strategy invention. In this paper, we focus on confluence, an important property of term rewrite systems, and apply machine learning to develop the first learning-guided automatic confluence prover. Moreover, we randomly generate a large dataset to analyze confluence for term rewrite systems. Our results focus on improving the state-of-the-art automatic confluence prover CSI: When equipped with our invented strategies, it surpasses its human-designed strategies both on the augmented dataset and on the original human-created benchmark dataset Cops, proving/disproving the confluence of several term rewrite systems for which no automated proofs were known before.

Business process management (BPM) has been widely used to discover, model, analyze, and optimize organizational processes. BPM looks at these processes with analysis techniques that assume a clearly defined start and end. However, not all processes adhere to this logic, with the consequence that their behavior cannot be appropriately captured by BPM analysis techniques. This paper addresses this research problem at a conceptual level. More specifically, we introduce the notion of vitalizing business processes that target the lifecycle process of one or more entities. We show the existence of lifecycle processes in many industries and that their appropriate conceptualizations pave the way for the definition of suitable modeling and analysis techniques. This paper provides a set of requirements for their analysis, and a conceptualization of lifecycle and vitalizing processes.

Stochastic Signal Analysis is a field of science concerned with the processing, modification and analysis of (stochastic) signals. Anyone with a background in Physics or Engineering knows to some degree about signal analysis techniques, what these technique are and how they can be used to analyze, model and classify signals. Data Scientists coming from a different fields, like Computer Science or Statistics, might not be aware of the analytical power these techniques bring with them. In this blog post, we will have a look at how we can use Stochastic Signal Analysis techniques, in combination with traditional Machine Learning Classifiers for accurate classification and modelling of time-series and signals. At the end of the blog-post you should be able understand the various signal-processing techniques which can be used to retrieve features from signals and be able to classify ECG signals (and even identify a person by their ECG signal), predict seizures from EEG signals, classify and identify targets in radar signals, identify patients with neuropathy or myopathyetc from EMG signals by using the FFT, etc etc. In this blog-post we'll discuss the following topics: You might often have come across the words time-series and signals describing datasets and it might not be clear what the exact difference between them is.

Each of the four weeks in the course will consist of two required components. First, an interactive textbook provides Python programming challenges that arise from real biological problems. If you haven't programmed in Python before, not to worry! We provide "Just-in-Time" exercises from the Codecademy Python track (https://www.codecademy.com/learn/python). And each page in our interactive textbook has its own discussion forum, where you can interact with other learners.