A Parameterless-Niching-Assisted Bi-objective Approach to Multimodal Optimization

Abstract-Evolutionary algorithms are becoming increasingly popular for multimodal and multi-objective optimization. Their population based nature allows them to be modified in a way so as to locate and preserve multiple optimal solutions (referred to as Pareto-optimal solutions in multi-objective optimization). These modifications are called niching methods, particularly in the context of multimodal optimization. In evolutionary multiobjective optimization, the concept of dominance and diversity preservation inherently causes niching. This paper proposes an approach to multimodal optimization which combines this power of dominance with traditional variable-space niching. The approach is implemented within the NSGA-II framework and its performance is studied on 20 benchmark problems. The simplicity of the approach and the absence of any special niching parameters are the hallmarks of this study

Applicability of genetic algorithms to reconstruction of projected data from ultrasonic tomography

In this paper simulation studies of the ultrasound computerized tomography (CT) technique employing time of flight data is presented. An enhanced genetic algorithm based reconstruction technique is proposed that is capable of detecting multiple types of inclusions in the test specimen to be reconstructed. It is assumed that the physical properties of the inclusions are known a priori. The preliminary results of our algorithm for a simple configuration are found to be better than those reported with MART1. In addition to being able to identify inclusions of different materials, both the shape and location of the inclusions could be reconstructed using the proposed algorithm. The results are found to be consistent and satisfactory for a wide range of grid sizes and geometries of inclusion(s). Based on the regression analysis an empirical relation between the number of unknowns and the reconstruction time is found which enables one to predict the reconstruction time for higher resolutions

Interactive knowledge discovery and knowledge visualization for decision support in multi-objective optimization

In many practical applications, the end-goal of multi-objective optimization is to select an implementable solution that is close to the Pareto-optimal front while satisfying the decision maker’s preferences. The decision making process is challenging since it involves the manual consideration of all solutions. The field of multi-criteria decision making offers many methods that help the decision maker in this process. However, most methods only focus on analyzing the solutions’ objective values. A more informed decision generally requires the additional knowledge of how different preferences affect the variable values. One difficulty in realizing this is that while the preferences are often expressed in the objective space, the knowledge required to implement a preferred solution exists in the decision space. In this paper, we propose a decision support system that allows interactive knowledge discovery and knowledge visualization to support practitioners by simultaneously considering preferences in the objective space and their impact in the decision space. The knowledge discovery step can use either of two recently proposed data mining techniques for extracting decision rules that conform to given preferences, while the extracted knowledge is visualized via a novel graph-based approach that allows the discovery of important variables, their values and their interactions with other variables. The result is an intuitive and interactive decision support system that aids the entire decision making process — from solution visualization to knowledge visualization. We demonstrate the usefulness of this system on benchmark optimization problems up to 10 objectives and real-world problems with up to six objectives.CC BY 4.0Corresponding author: Henrik Smedberg. E-mail addresses: [email protected] (H. Smedberg), [email protected] (S. Bandaru).The authors acknowledge the financial support received from KK-stiftelsen (The Knowledge Foundation, Stockholm, Sweden) under the Research Profile 2018 project Virtual Factories with Knowledge-Driven Optimization. For more information, please visit www.virtualfactories.se/</p

Temporal Innovization : Evolution of Design Principles Using Multi-objective Optimization

Multi-objective optimization yields multiple solutions each of which is no better or worse than the others when the objectives are conflicting. These solutions lie on the Pareto-optimal front which is a lower-dimensional slice of the objective space. Together, the solutions may possess special properties that make them optimal over other feasible solutions. Innovization is the process of extracting such special properties (or design principles) from a trade-off dataset in the form of mathematical relationships between the variables and objective functions. In this paper, we deal with a closely related concept called temporal innovization. While innovization concerns the design principles obtained from the trade-off front, temporal innovization refers to the evolution of these design principles during the optimization process. Our study indicates that not only do different design principles evolve at different rates, but that they start evolving at different times. We illustrate temporal innovization using several examples.KDISC

On the Performance of Classification Algorithms for Learning Pareto-Dominance Relations

Multi-objective evolutionary algorithms (MOEAs)are often criticized for their high-computational costs. Thisbecomes especially relevant in simulation-based optimizationwhere the objectives lack a closed form and are expensive toevaluate. Over the years, meta-modeling or surrogate modelingtechniques have been used to build inexpensive approximationsof the objective functions which reduce the overall number offunction evaluations (simulations). Some recent studies however,have pointed out that accurate models of the objective functionsmay not be required at all since evolutionary algorithms onlyrely on the relative ranking of candidate solutions. Extendingthis notion to MOEAs, algorithms which can ‘learn’ Paretodominancerelations can be used to compare candidate solutionsunder multiple objectives. With this goal in mind, in thispaper, we study the performance of ten different off-the-shelfclassification algorithms for learning Pareto-dominance relationsin the ZDT test suite of benchmark problems. We considerprediction accuracy and training time as performance measureswith respect to dimensionality and skewness of the training data.Being a preliminary study, this paper does not include results ofintegrating the classifiers into the search process of MOEAs.KDISC

Virtual Factories with Knowledge-Driven Optimization as a New Research Profile

This paper conceptually introduces VF-KDO (Virtual Factories with Knowledge-Driven Optimization, a research profile of the University of Skovde, Sweden, which is underway from 2018-2026. The goal of this research profile is to deliver radical innovations in manufacturing research essential to the design and operation of next-generation manufacturing systems. A unique concept proposed in VF-KDO is: knowledge extracted for decision support is achieved through systematically exploring, e.g., using advanced, interactive data analytics techniques on optimal solutions generated via many-objective optimizations on virtual factory models. As the word 'driven' means 'motivated' or 'manipulated', so does KDO have some two-fold meanings: (1) optimizations that aim at generating knowledge, not only mathematically optimal solutions; (2) knowledge-controlled optimizations, instead of some blind/black-box processes. It is this concept of KDO, combining with modular, virtual factory models at different levels, which distinguishes VF-KDO from other related research efforts found internationally and in Sweden. The cutting-edge research topics involved in the research profile and their synergy with the digitalization efforts of the 7 partner companies, in form of the development of an intelligent decision support system, can be used to improve the competiveness of the Swedish manufacturing industry by supporting their holistic, optimal and sustainable decision making. CC BY-NC 4.0</p

On the scalability of meta-models in simulation-based optimization of production systems

Optimization of production systems often involves numerous simulations of computationally expensive discrete-event models. When derivative-free optimization is sought, one usually resorts to evolutionary and other population-based meta-heuristics. These algorithms typically demand a large number of objective function evaluations, which in turn, drastically increases the computational cost of simulations. To counteract this, meta-models are used to replace expensive simulations with inexpensive approximations. Despite their widespread use, a thorough evaluation of meta-modeling methods has not been carried out yet to the authors' knowledge. In this paper, we analyze 10 different meta-models with respect to their accuracy and training time as a function of the number of training samples and the problem dimension. For our experiments, we choose a standard discrete-event model of an unpaced flow line with scalable number of machines and buffers. The best performing meta-model is then used with an evolutionary algorithm to perform multi-objective optimization of the production model

Innovative Design and Analysis of Production Systems by Multi-objective Optimization and Data Mining

This paper presents an innovative approach for the design and analysis of production systems using multi-objective optimization and data mining. The innovation lies on how these two methods using different computational intelligence algorithms can be synergistically integrated and used interactively by production systems designers to support their design decisions. Unlike ordinary optimization approaches for production systems design which several design objectives are linearly combined into a single mathematical function, multi-objective optimization that can generate multiple design alternatives and sort their performances into an efficient frontier can enable the designer to have a more complete picture about how the design decision variables, like number of machines and buffers, can affect the overall performances of the system. Such kind of knowledge that can be gained by plotting the efficient frontier cannot be sought by single-objective based optimizations. Additionally, because of the multiple optimal design alternatives generated, they constitute a dataset that can be fed into some data mining algorithms for extracting the knowledge about the relationships among the design variables and the objectives. This paper addresses the specific challenges posed by the design of discrete production systems for this integrated optimization and data mining approach and then outline a new interactive data mining algorithm developed to meet these challenges, illustrated with a real-world production line design example

KKT proximity measure for testing convergence in smooth multi-objective optimization

An earlier study defined a KKT-proximity measure to test the convergence property of an evolutionary algorithm for solving single-objective optimization problems. In this paper, we extend this measure for testing convergence of a set of non-dominated solutions to the Pareto-optimal front in the case of smooth multi-objective optimization problems. Simulation results of NSGA-II on different two and three objective test problems indicate the suitability of using the proximity measure as a convergence metric for terminating a simulation of an evolutionary multi-criterion optimization algorithm

Online Knowledge Extraction and Preference Guided Multi-Objective Optimization in Manufacturing

The integration of simulation-based optimization and data mining is an emerging approach to support decision-making in the design and improvement of manufacturing systems. In such an approach, knowledge extracted from the optimal solutions generated by the simulation-based optimization process can provide important information to decision makers, such as the importance of the decision variables and their influence on the design objectives, which cannot easily be obtained by other means. However, can the extracted knowledge be directly used during the optimization process to further enhance the quality of the solutions? This paper proposes such an online knowledge extraction approach that is used together with a preference-guided multi-objective optimization algorithm on simulation models of manufacturing systems. Specifically, it introduces a combination of the multi-objective evolutionary optimization algorithm, NSGA-II, and a customized data mining algorithm, called Flexible Pattern Mining (FPM), which can extract knowledge in the form of rules in an online and automatic manner, in order to guide the optimization to converge towards a decision maker's preferred region in the objective space. Through a set of application problems, this paper demonstrates how the proposed FPM-NSGA-II can be used to support higher quality decision-making in manufacturing