Coding by Design: GPT-4 empowers Agile Model Driven Development

Generating code from a natural language using Large Language Models (LLMs) such as ChatGPT, seems groundbreaking. Yet, with more extensive use, it's evident that this approach has its own limitations. The inherent ambiguity of natural language presents challenges for complex software designs. Accordingly, our research offers an Agile Model-Driven Development (MDD) approach that enhances code auto-generation using OpenAI's GPT-4. Our work emphasizes "Agility" as a significant contribution to the current MDD method, particularly when the model undergoes changes or needs deployment in a different programming language. Thus, we present a case-study showcasing a multi-agent simulation system of an Unmanned Vehicle Fleet. In the first and second layer of our approach, we constructed a textual representation of the case-study using Unified Model Language (UML) diagrams. In the next layer, we introduced two sets of constraints that minimize model ambiguity. Object Constraints Language (OCL) is applied to fine-tune the code constructions details, while FIPA ontology is used to shape communication semantics and protocols. Ultimately, leveraging GPT-4, our last layer auto-generates code in both Java and Python. The Java code is deployed within the JADE framework, while the Python code is deployed in PADE framework. Concluding our research, we engaged in a comprehensive evaluation of the generated code. From a behavioural standpoint, the auto-generated code aligned perfectly with the expected UML sequence diagram. Structurally, we compared the complexity of code derived from UML diagrams constrained solely by OCL to that influenced by both OCL and FIPA-ontology. Results indicate that ontology-constrained model produce inherently more intricate code, but it remains manageable and low-risk for further testing and maintenance

Hybrid Evolutionary Approach to Multi-objective Path Planning for UAVs

The goal of Multi-Objective Path Planning (MOPP) is to find Pareto-optimal paths for autonomous agents with respect to several optimization goals like minimizing risk, path length, travel time, or energy consumption. In this work, we formulate a MOPP for Unmanned Aerial Vehicles (UAVs). We utilize a path representation based on Non-Uniform Rational B-Splines (NURBS) and propose a hybrid evolutionary approach combining an Evolution Strategy (ES) with the exact Dijkstra algorithm. Moreover, we compare our approach in a statistical analysis to state-of-the-art exact (Dijkstra's algorithm), gradient-based (L-BFGS-B), and evolutionary (NSGA-II) algorithms with respect to calculation time and quality features of the obtained Pareto fronts indicating convergence and diversity of the solutions. We evaluate the methods on a realistic 2D urban path planning scenario based on real-world data exported from OpenStreetMap. The examination's results indicate that our approach is able to find significantly better solutions for the formulated problem than standard Evolutionary Algorithms (EAs). Moreover, the proposed method is able to obtain more diverse sets of trade-off solutions for different objectives than the standard exact approaches. Thus, the method combines the strengths of both approaches

Deformation Clustering Methods for Topologically Optimized Structures under Crash Load based on Displacement Time Series

Multi-objective Topology Optimization has been receiving more and more attention in structural design recently. It attempts to maximize several performance objectives by redistributing the material in a design space for a given set of boundary conditions and constraints, yielding many Paretooptimal solutions. However, the high number of solutions makes it difficult to identify preferred designs. Therefore, an automatic way of summarizing solutions is needed for selecting interesting designs according to certain criteria, such as crashworthiness, deformation, and stress state. One approach for summarization is to cluster similar designs and obtain design representatives based on a suitable metric. For example, with Euclidean distance of the objective functions as the metric, design groups with similar performance can be identified and only the representative designs from different clusters may be analyzed. However, previous research has not dealt with the deformation-related time-series data of structures with different topologies. Since the non-linear dynamic behavior of designs is important in various fields such as vehicular crashworthiness, a clustering method based on time-dependent behavior of structures is proposed here. To compare the time-series displacement data of selected nodes in the structure and to create similarity matrices of those datasets, euclidean metrics and Dynamic Time Warping (DTW) are introduced. This is combined with clustering techniques such as k-medoids and Ordering Points To Identify the Clustering Structure (OPTICS), and we investigate the use of unsupervised learning methods to identify and group similar designs using the time series of nodal displacement data. In the first part, we create simple time-series datasets using a mass-spring system to validate the proposed methods. Each dataset has predefined clusters of data with distinct behavior such as different periods or modes. Then, we demonstrate that the combination of metrics for comparison of time series (Euclidean and DTW) and the clustering method (k-medoids and OPTICS) can identify the clusters of similar behavior accurately. In the second part, we apply these methods to a more realistic, engineering dataset of nodal displacement time series describing the crash behavior of topologically-optimized designs. We identify similar structures and obtain representative designs from each cluster. This reveals that the suggested method is useful in analyzing dynamic crash behavior and supports the designers in selecting representative structures based on deformation data at the early stages of the design process

Reference vector based a posteriori preference articulation for evolutionary multiobjective optimization

Cheng R, Olhofer M, Jin Y. Reference vector based a posteriori preference articulation for evolutionary multiobjective optimization. In: 2015 IEEE Congress on Evolutionary Computation (CEC). IEEE; 2015: 939-946.Multiobjective evolutionary algorithms (MOEAs) usually achieve a set of nondominated solutions as the approximation of the Pareto front. In order to utilize the solutions, a final decision making process is indispensable in most cases in which a small number of solutions have to be selected. In this process a decision maker selects the solutions according to his or her preferences or based on the knowledge acquired by observing the approximated Pareto front. Due to the limited number of solutions an algorithm can obtain, in particular when the number of objectives is large, a decision maker may be interested in sampling additional solutions in some preferred regions. This paper proposes to use a reference vector based preference articulation (RVPA) method to obtain such additional solutions in preferred regions. After describing the proposed method in detail, experiments are conducted on six benchmark MOPs to assess the performance of the proposed RVPA method. Our empirical results show that, by setting reference vectors in the objective space, the proposed RVPA is able to obtain corresponding solutions in the preferred regions at a much lower cost compared to e.g. a re-start strategy. In addition, by setting the reference vectors in a uniform way, the proposed RVPA method is also able to improve the general quality (convergence and distribution) of the solutions obtained by an MOEA

Benchmark Problems and Performance Indicators for Search of Knee Points in Multi-objective Optimization

In multi-objective optimization, it is non-trivial for decision makers to articulate preferences without a priori knowledge, which is particular true when the number of objectives becomes large. Depending on the shape of the Pareto front, optimal solutions such as knee points may be of interest. Although several multi- and many-objective optimization test suites have been proposed, little work has been reported focusing on designing multi-objective problems whose Pareto front contains complex knee regions. Likewise, few performance indicators dedicated to evaluating an algorithm’s ability of accurately locating all knee points in high-dimensional objective space have been suggested. This paper proposes a set of multi-objective optimization test problems whose Pareto front consists of complex knee regions, aiming to assess the capability of evolutionary algorithms to accurately identify all knee points. Various features related to knee points have been taken into account in designing the test problems, including symmetry, differentiability, degeneration. These features are also combined with other challenges in solving optimization problems, such as multimodality, linkage between decision variables, non-uniformity and scalability of the Pareto front. The proposed test problems are scalable to both decision and objective spaces. Accordingly, new performance indicators are suggested for evaluating the capability of optimization algorithms in locating the knee points. The proposed test problems together with the performance indicators offer a new means to develop and assess preference-based evolutionary algorithms for solving multi- and many-objective optimization problems.</p

A Multiobjective Evolutionary Algorithm for Finding Knee Regions Using Two Localized Dominance Relationships

Yu G, Jin Y, Olhofer M. A Multiobjective Evolutionary Algorithm for Finding Knee Regions Using Two Localized Dominance Relationships. IEEE Transactions on Evolutionary Computation. 2021;25(1):145-158.In preference-based optimization, knee points are considered the naturally preferred tradeoff solutions, especially when the decision maker has little a priori knowledge about the problem to be solved. However, identifying all convex knee regions of a Pareto front remains extremely challenging, in particular in a high-dimensional objective space. This article presents a new evolutionary multiobjective algorithm for locating knee regions using two localized dominance relationships. In the environmental selection, the α-dominance is applied to each subpopulation partitioned by a set of predefined reference vectors, thereby guiding the search toward different potential knee regions while removing possible dominance resistant solutions. A knee-oriented-dominance measure making use of the extreme points is then proposed to detect knee solutions in convex knee regions and discard solutions in concave knee regions. Our experimental results demonstrate that the proposed algorithm outperforms the state-of-the-art knee identification algorithms on a majority of multiobjective optimization test problems having up to eight objectives and a hybrid electric vehicle controller design problem with seven objectives

Benchmark Problems and Performance Indicators for Search of Knee Points in Multiobjective Optimization

Yu G, Jin Y, Olhofer M. Benchmark Problems and Performance Indicators for Search of Knee Points in Multiobjective Optimization. IEEE Transactions on Cybernetics. 2020;50(8):3531-3544.In multiobjective optimization, it is nontrivial for decision makers to articulate preferences without a priori knowledge, which is particularly true when the number of objectives becomes large. Depending on the shape of the Pareto front, optimal solutions such as knee points may be of interest. Although several multi- and many-objective optimization test suites have been proposed, little work has been reported focusing on designing multiobjective problems whose Pareto front contains complex knee regions. Likewise, few performance indicators dedicated to evaluate an algorithm's ability of accurately locating all knee points in high-dimensional objective space have been suggested. This paper proposes a set of multiobjective optimization test problems whose Pareto front consists of complex knee regions, aiming to assess the capability of evolutionary algorithms to accurately identify all knee points. Various features related to knee points have been taken into account in designing the test problems, including symmetry, differentiability, and degeneration. These features are also combined with other challenges in solving the optimization problems, such as multimodality, linkage between decision variables, nonuniformity, and scalability of the Pareto front. The proposed test problems are scalable to both decision and objective spaces. Accordingly, new performance indicators are suggested for evaluating the capability of optimization algorithms in locating the knee points. The proposed test problems, together with the performance indicators, offer a new means to develop and assess preference-based evolutionary algorithms for solving multi- and many-objective optimization problems

A Method for a Posteriori Identification of Knee Points Based on Solution Density

Many evolutionary algorithms have been proposed and demonstrated to have excellent performance in striking a balance between convergence and diversity in dealing with multiobjective optimization problems. However, little attention has been paid to the decision making stage where a small number of solutions are selected to be presented to the user. It is believed that knee points are considered to be the naturally preferred solutions when no specific preferences are available, because knee solutions incur a large loss in at least one objective to gain a small amount in other objectives. One common issue in the identification of knee points is that some knee points are easily ignored and knees in concave regions are hard to be identified. To resolve these issues, this paper proposes a novel method for knee identification, which first maps the non-dominated solutions to a constructed hyperplane and then divides them into groups, each representing a candidate knee region, based on the density of the solutions projected on the hyperplane. Finally, the convexity and curvature of the candidate knee groups are determined and only those having a strong curvature are kept. The proposed method is empirically demonstrated to be effective in identifying knee points located in both convex and concave regions on three existing test problems and one newly proposed test problem

A Framework for Evolutionary Optimization with Approximate Fitness Functions

It is a common engineering practice to use approximate models instead of the original computationally expensive model in optimization. When an approximate model is used for evolutionary optimization, the convergence properties of the evolutionary algorithm are unclear due to the approximation error. In this paper, extensive empirical studies on convergence of an evolution strategy are carried out on two bench-mark problems. It is found that incorrect convergence will occur if the approximate model has false optima. To address this problem, individual and generation based evolution control is introduced and the resulting effects on the convergence properties are presented. A framework for managing approximate models in generation-based evolution control is proposed. This framework is well suited for parallel evolutionary optimization that is able to guarantee the correct convergence of the evolutionary algorithm and to reduce the computation costs as much as possible. Control o..