Helper and Equivalent Objectives:Efficient Approach for Constrained Optimization

Numerous multi-objective evolutionary algorithms have been designed for constrained optimisation over past two decades. The idea behind these algorithms is to transform constrained optimisation problems into multi-objective optimisation problems without any constraint, and then solve them. In this paper, we propose a new multi-objective method for constrained optimisation, which works by converting a constrained optimisation problem into a problem with helper and equivalent objectives. An equivalent objective means that its optimal solution set is the same as that to the constrained problem but a helper objective does not. Then this multi-objective optimisation problem is decomposed into a group of sub-problems using the weighted sum approach. Weights are dynamically adjusted so that each subproblem eventually tends to a problem with an equivalent objective. We theoretically analyse the computation time of the helper and equivalent objective method on a hard problem called ``wide gap''. In a ``wide gap'' problem, an algorithm needs exponential time to cross between two fitness levels (a wide gap). We prove that using helper and equivalent objectives can shorten the time of crossing the ``wide gap''. We conduct a case study for validating our method. An algorithm with helper and equivalent objectives is implemented. Experimental results show that its overall performance is ranked first when compared with other eight state-of-art evolutionary algorithms on IEEE CEC2017 benchmarks in constrained optimisation

BioSimulator.jl: Stochastic simulation in Julia

Biological systems with intertwined feedback loops pose a challenge to mathematical modeling efforts. Moreover, rare events, such as mutation and extinction, complicate system dynamics. Stochastic simulation algorithms are useful in generating time-evolution trajectories for these systems because they can adequately capture the influence of random fluctuations and quantify rare events. We present a simple and flexible package, BioSimulator.jl, for implementing the Gillespie algorithm, $\tau$-leaping, and related stochastic simulation algorithms. The objective of this work is to provide scientists across domains with fast, user-friendly simulation tools. We used the high-performance programming language Julia because of its emphasis on scientific computing. Our software package implements a suite of stochastic simulation algorithms based on Markov chain theory. We provide the ability to (a) diagram Petri Nets describing interactions, (b) plot average trajectories and attached standard deviations of each participating species over time, and (c) generate frequency distributions of each species at a specified time. BioSimulator.jl's interface allows users to build models programmatically within Julia. A model is then passed to the simulate routine to generate simulation data. The built-in tools allow one to visualize results and compute summary statistics. Our examples highlight the broad applicability of our software to systems of varying complexity from ecology, systems biology, chemistry, and genetics. The user-friendly nature of BioSimulator.jl encourages the use of stochastic simulation, minimizes tedious programming efforts, and reduces errors during model specification.Comment: 27 pages, 5 figures, 3 table

Synthesis of Model Transformations from Metamodels and Examples

Model transformations are central elements of model-driven engineering (MDE). However, model transformation development requires a high level of expertise in particular model transformation languages, and model transformation specifications are often difficult to manually construct, due to the lack of tool support, and the dependencies involved in transformation rules.In this thesis, we describe techniques for automatically or semi-automatically synthesising transformations from metamodels and examples, in order to reduce model transformation development costs and time, and improve model transformation quality.We proposed two approaches for synthesising transformations from metamodels. The first approach is the Data Structure Similarity Approach, an exhaustive metamodel matching approach, which extracts correspondences between metamodels by only focusing on the type of features. The other approach is the Search-based Optimisation Approach, which uses an optimisation algorithm to extract correspondences from metamodels by data structure similarity, name syntax similarity, and name semantic similarity. The correspondence patterns between the classes and features of two metamodels are extracted by either of these two methods. To enable the production of specifications in multiple model transformation languages from correspondences, we introduced an intermediate language which uses a simplified transformation notation to express transformation specifications in a language-independent manner, and defined the mapping rules from this intermediate language to different transformation languages.We also investigated Model Transformation by Examples Approach. We used machine learning techniques to learn model transformation rules from datasets of examples, so that the trained model could generate target model from source model directly.We evaluated our approaches on a range of cases of different kinds of transformation, and compared the model transformation accuracy and quality of our versions to the previously-developed manual versions of these cases.Key words: model transformation, model-driven engineering, transformation syn-thesis, metamodel matching, model transformation by example

Krotov: A Python implementation of Krotov's method for quantum optimal control

We present a new open-source Python package, krotov, implementing the quantum optimal control method of that name. It allows to determine time-dependent external fields for a wide range of quantum control problems, including state-to-state transfer, quantum gate implementation and optimization towards an arbitrary perfect entangler. Krotov's method compares to other gradient-based optimization methods such as gradient-ascent and guarantees monotonic convergence for approximately time-continuous control fields. The user-friendly interface allows for combination with other Python packages, and thus high-level customization