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  • 1.
    Bandaru, Sunith
    et al.
    University of Skövde, School of Engineering Science. University of Skövde, The Virtual Systems Research Centre.
    Aslam, Tehseen
    University of Skövde, School of Engineering Science. University of Skövde, The Virtual Systems Research Centre.
    Ng, Amos
    University of Skövde, School of Engineering Science. University of Skövde, The Virtual Systems Research Centre.
    Deb, Kalyanmoy
    Department of Electrical and Computer Engineering, Michigan State University, East Lansing, USA.
    Generalized higher-level automated innovization with application to inventory management2015In: European Journal of Operational Research, ISSN 0377-2217, E-ISSN 1872-6860, Vol. 243, no 2, p. 480-496Article in journal (Refereed)
    Abstract [en]

    This paper generalizes the automated innovization framework using genetic programming in the context of higher-level innovization. Automated innovization is an unsupervised machine learning technique that can automatically extract significant mathematical relationships from Pareto-optimal solution sets. These resulting relationships describe the conditions for Pareto-optimality for the multi-objective problem under consideration and can be used by scientists and practitioners as thumb rules to understand the problem better and to innovate new problem solving techniques; hence the name innovization (innovation through optimization). Higher-level innovization involves performing automated innovization on multiple Pareto-optimal solution sets obtained by varying one or more problem parameters. The automated innovization framework was recently updated using genetic programming. We extend this generalization to perform higher-level automated innovization and demonstrate the methodology on a standard two-bar bi-objective truss design problem. The procedure is then applied to a classic case of inventory management with multi-objective optimization performed at both system and process levels. The applicability of automated innovization to this area should motivate its use in other avenues of operational research.

  • 2.
    Bandaru, Sunith
    et al.
    University of Skövde, School of Engineering Science. University of Skövde, The Virtual Systems Research Centre.
    Deb, Kalyanmoy
    BEACON Center for the Study of Evolution in Action, Department of Electrical and Computer Engineering, Michigan State University, USA.
    Metaheuristic Techniques2017In: Decision Sciences: Theory and Practice / [ed] Raghu Nandan Sengupta, Aparna Gupta, Joydeep Dutta, Boca Raton: CRC Press, 2017, p. 693-750Chapter in book (Refereed)
  • 3.
    Bandaru, Sunith
    et al.
    University of Skövde, School of Engineering Science. University of Skövde, The Virtual Systems Research Centre.
    Deb, Kalyanmoy
    Michigan State University, USA.
    Temporal Innovization: Evolution of Design Principles Using Multi-objective Optimization2015In: Proceedings of the 8th International Conference on Evolutionary Multi-Criterion Optimization (EMO 2015), Springer, 2015, Vol. 9018, p. 79-93Conference paper (Refereed)
    Abstract [en]

    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.

  • 4.
    Bandaru, Sunith
    et al.
    University of Skövde, School of Engineering Science. University of Skövde, The Virtual Systems Research Centre.
    Gaur, Abhinav
    Department of Electrical and Computer Engineering, Michigan State University, USA.
    Deb, Kalyanmoy
    Department of Electrical and Computer Engineering, Michigan State University, USA.
    Khare, Vineet
    Amazon Development Centre (India) Pvt. Ltd., Bengaluru, India.
    Chougule, Rahul
    Department of Mechanical Engineering, Walchand College of Engineering, Sangli, India.
    Bandyopadhyay, Pulak
    General Motors R&D Center, Warren, USA.
    Development, analysis and applications of a quantitative methodology for assessing customer satisfaction using evolutionary optimization2015In: Applied Soft Computing, ISSN 1568-4946, E-ISSN 1872-9681, Vol. 30, p. 265-278Article in journal (Refereed)
    Abstract [en]

    Consumer-oriented companies are getting increasingly more sensitive about customer's perception of their products, not only to get a feedback on their popularity, but also to improve the quality and service through a better understanding of design issues for further development. However, a consumer's perception is often qualitative and is achieved through third party surveys or the company's recording of after-sale feedback through explicit surveys or warranty based commitments. In this paper, we consider an automobile company's warranty records for different vehicle models and suggest a data mining procedure to assign a customer satisfaction index (CSI) to each vehicle model based on the perceived notion of the level of satisfaction of customers. Based on the developed CSI function, customers are then divided into satisfied and dissatisfied customer groups. The warranty data are then clustered separately for each group and analyzed to find possible causes (field failures) and their relative effects on customer's satisfaction (or dissatisfaction) for a vehicle model. Finally, speculative introspection has been made to identify the amount of improvement in CSI that can be achieved by the reduction of some critical field failures through better design practices. Thus, this paper shows how warranty data from customers can be utilized to have a better perception of ranking of a product compared to its competitors in the market and also to identify possible causes for making some customers dissatisfied and eventually to help percolate these issues at the design level. This closes the design cycle loop in which after a design is converted into a product, its perceived level of satisfaction by customers can also provide valuable information to help make the design better in an iterative manner. The proposed methodology is generic and novel, and can be applied to other consumer products as well.

  • 5.
    Bandaru, Sunith
    et al.
    University of Skövde, School of Engineering Science. University of Skövde, The Virtual Systems Research Centre.
    Ng, Amos H. C.
    University of Skövde, School of Engineering Science. University of Skövde, The Virtual Systems Research Centre.
    Deb, Kalyanmoy
    Department of Electrical and Computer Engineering, Michigan State University, USA.
    Data mining methods for knowledge discovery in multi-objective optimization: Part A - Survey2017In: Expert systems with applications, ISSN 0957-4174, E-ISSN 1873-6793, Vol. 70, p. 139-159Article, review/survey (Refereed)
    Abstract [en]

    Real-world optimization problems typically involve multiple objectives to be optimized simultaneously under multiple constraints and with respect to several variables. While multi-objective optimization itself can be a challenging task, equally difficult is the ability to make sense of the obtained solutions. In this two-part paper, we deal with data mining methods that can be applied to extract knowledge about multi-objective optimization problems from the solutions generated during optimization. This knowledge is expected to provide deeper insights about the problem to the decision maker, in addition to assisting the optimization process in future design iterations through an expert system. The current paper surveys several existing data mining methods and classifies them by methodology and type of knowledge discovered. Most of these methods come from the domain of exploratory data analysis and can be applied to any multivariate data. We specifically look at methods that can generate explicit knowledge in a machine-usable form. A framework for knowledge-driven optimization is proposed, which involves both online and offline elements of knowledge discovery. One of the conclusions of this survey is that while there are a number of data mining methods that can deal with data involving continuous variables, only a few ad hoc methods exist that can provide explicit knowledge when the variables involved are of a discrete nature. Part B of this paper proposes new techniques that can be used with such datasets and applies them to discrete variable multi-objective problems related to production systems. 

    The full text will be freely available from 2019-01-01 01:00
  • 6.
    Bandaru, Sunith
    et al.
    University of Skövde, School of Engineering Science. University of Skövde, The Virtual Systems Research Centre.
    Ng, Amos H. C.
    University of Skövde, School of Engineering Science. University of Skövde, The Virtual Systems Research Centre.
    Deb, Kalyanmoy
    Department of Electrical and Computer Engineering, Michigan State University, USA.
    Data mining methods for knowledge discovery in multi-objective optimization: Part B - New developments and applications2017In: Expert systems with applications, ISSN 0957-4174, E-ISSN 1873-6793, Vol. 70, p. 119-138Article in journal (Refereed)
    Abstract [en]

    The first part of this paper served as a comprehensive survey of data mining methods that have been used to extract knowledge from solutions generated during multi-objective optimization. The current paper addresses three major shortcomings of existing methods, namely, lack of interactiveness in the objective space, inability to handle discrete variables and inability to generate explicit knowledge. Four data mining methods are developed that can discover knowledge in the decision space and visualize it in the objective space. These methods are (i) sequential pattern mining, (ii) clustering-based classification trees, (iii) hybrid learning, and (iv) flexible pattern mining. Each method uses a unique learning strategy to generate explicit knowledge in the form of patterns, decision rules and unsupervised rules. The methods are also capable of taking the decision maker's preferences into account to generate knowledge unique to preferred regions of the objective space. Three realistic production systems involving different types of discrete variables are chosen as application studies. A multi-objective optimization problem is formulated for each system and solved using NSGA-II to generate the optimization datasets. Next, all four methods are applied to each dataset. In each application, the methods discover similar knowledge for specified regions of the objective space. Overall, the unsupervised rules generated by flexible pattern mining are found to be the most consistent, whereas the supervised rules from classification trees are the most sensitive to user-preferences. 

    The full text will be freely available from 2019-01-01 01:00
  • 7.
    Deb, Kalyanmoy
    et al.
    University of Skövde, School of Technology and Society. University of Skövde, The Virtual Systems Research Centre. Indian Institute of Technology, Kanpur, Uttar Pradesh, India / Aalto University School of Economics , Finland.
    Datta, Rituparna
    ndian Institute of Technology, Kanpur, Uttar Pradesh, India.
    A bi-objective constrained optimization algorithm using a hybrid evolutionary and penalty function approach2013In: Engineering optimization (Print), ISSN 0305-215X, E-ISSN 1029-0273, Vol. 45, no 5, p. 503-527Article in journal (Refereed)
    Abstract [en]

    Constrained optimization is a computationally difficult task, particularly if the constraint functions are nonlinear and non-convex. As a generic classical approach, the penalty function approach is a popular methodology which degrades the objective function value by adding a penalty proportional to the constraint violation. However, the penalty function approach has been criticized for its sensitivity to the associated penalty parameters. Since its inception, evolutionary algorithms have been modified in various ways to solve constrained optimization problems. Of them, the recent use of a bi-objective evolutionary algorithm in which the minimization of the constraint violation is included as an additional objective has received significant attention. In this article, a combination of a bi-objective evolutionary approach with the classical penalty function methodology is proposed, in a manner complementary to each other. The evolutionary approach provides an appropriate estimate of the penalty parameter, while the solution of an unconstrained penalized function by a classical method induces a convergence property to the overall hybrid algorithm. The working of the procedure on a number of standard numerical test problems and an engineering design problem is demonstrated. In most cases, the proposed hybrid methodology is observed to take one or more orders of magnitude fewer function evaluations to find the constrained minimum solution accurately than some of the best reported existing methodologies.

  • 8.
    Deb, Kalyanmoy
    et al.
    Department of Electrical and Computer Engineering, Michigan State University, USA.
    Siegmund, Florian
    University of Skövde, School of Engineering Science. University of Skövde, The Virtual Systems Research Centre.
    Ng, Amos H. C.
    University of Skövde, School of Engineering Science. University of Skövde, The Virtual Systems Research Centre.
    R-HV: A Metric for Computing Hyper-volume for Reference Point-based EMOs2015In: Swarm, Evolutionary, and Memetic Computing: 5th International Conference, SEMCCO 2014, Bhubaneswar, India, December 18-20, 2014, Revised Selected Papers / [ed] Bijaya Ketan Panigrahi, Ponnuthurai Nagaratnam Suganthan & Swagatam Das, Springer, 2015, p. 98-110Chapter in book (Refereed)
    Abstract [en]

    For evaluating performance of a multi-objective optimizationfor finding the entire efficient front, a number of metrics, such as hypervolume, inverse generational distance, etc. exists. However, for evaluatingan EMO algorithm for finding a subset of the efficient frontier, the existing metrics are inadequate. There does not exist many performancemetrics for evaluating a partial preferred efficient set. In this paper, wesuggest a metric which can be used for such purposes for both attainableand unattainable reference points. Results on a number of two-objectiveproblems reveal its working principle and its importance in assessingdifferent algorithms. The results are promising and encouraging for itsfurther use.

  • 9.
    Ng, Amos
    et al.
    University of Skövde, The Virtual Systems Research Centre. University of Skövde, School of Technology and Society.
    Deb, Kalyanmoy
    University of Skövde, The Virtual Systems Research Centre. University of Skövde, School of Technology and Society.
    Dudas, Catarina
    University of Skövde, The Virtual Systems Research Centre. University of Skövde, School of Technology and Society.
    Simulation-based Innovization for production systems improvement: An industrial case study2009In: The International 3rd Swedish Production Symposium / [ed] B.-G. Rosén, The Swedish Production Academy , 2009, p. 278-286Conference paper (Refereed)
    Abstract [en]

    This paper introduces a new methodology for the design, analysis, and optimization of production systems. The methodology is based on the Innovization procedure originally introduced for unveiling new and innovative design principles in engineering design problems. Although the Innovization method is based on multi-objective optimization and post-optimality analyses of optimized solutions, it extends the scope beyond an optimization task and attempts to discover new design/operational rules/principles related to decision variables and objectives, in order to enable a deeper understanding of the problem. By integrating the concept of Innovization with discrete-event simulation, a new set of powerful tools can be developed for general systems analysis, which is particularly suitable for production systems. After describing the Simulation-based Innovization procedure and its difference from conventional simulation analysis methods, the results of an industrial case study, carried out for the improvement of an assembly line at an automotive manufacturer in Sweden, are presented.

  • 10.
    Ng, Amos H. C.
    et al.
    University of Skövde, School of Engineering Science. University of Skövde, The Virtual Systems Research Centre.
    Dudas, Catarina
    University of Skövde, School of Engineering Science. University of Skövde, The Virtual Systems Research Centre.
    Boström, Henrik
    Stockholm University, Sweden.
    Kalyanmoy, Deb
    Michigan State University, USA.
    Interleaving Innovization with Evolutionary Multi-Objective Optimization in Production System Simulation for Faster ConvergenceOptimization2013In: Learning and Intelligent Optimization: 7th International Conference, LION 7, Catania, Italy, January 7-11, 2013, Revised Selected Papers / [ed] Giuseppe Nicosia, Panos Pardalos, Berlin, Heidelberg: Springer Berlin/Heidelberg, 2013, p. 1-18Chapter in book (Refereed)
    Abstract [en]

    This paper introduces a novel methodology for the optimization, analysis and decision support in production systems engineering. The methodology is based on the innovization procedure, originally introduced to unveil new and innovative design principles in engineering design problems. The innovization procedure stretches beyond an optimization task and attempts to discover new design/operational rules/principles relating to decision variables and objectives, so that a deeper understanding of the underlying problem can be obtained. By integrating the concept of innovization with simulation and data mining techniques, a new set of powerful tools can be developed for general systems analysis. The uniqueness of the approach introduced in this paper lies in that decision rules extracted from the multi-objective optimization using data mining are used to modify the original optimization. Hence, faster convergence to the desired solution of the decision-maker can be achieved. In other words, faster convergence and deeper knowledge of the relationships between the key decision variables and objectives can be obtained by interleaving the multi-objective optimization and data mining process. In this paper, such an interleaved approach is illustrated through a set of experiments carried out on a simulation model developed for a real-world production system analysis problem.

  • 11.
    Ng, Amos H. C.
    et al.
    University of Skövde, School of Technology and Society. University of Skövde, The Virtual Systems Research Centre.
    Dudas, Catarina
    University of Skövde, School of Technology and Society. University of Skövde, The Virtual Systems Research Centre.
    Nießen, Johannes
    University of Skövde, School of Technology and Society. University of Skövde, The Virtual Systems Research Centre.
    Deb, Kalyanmoy
    University of Skövde, School of Technology and Society. University of Skövde, The Virtual Systems Research Centre.
    Simulation-Based Innovization Using Data Mining for Production Systems Analysis2011In: Multi-objective Evolutionary Optimisation for Product Design and Manufacturing / [ed] Lihui Wang, Amos H. C. Ng, Kalyanmoy Deb, Springer London, 2011, p. 401-429Chapter in book (Refereed)
    Abstract [en]

    This chapter introduces a novel methodology for the analysis and optimization of production systems. The methodology is based on the innovization procedure, originally introduced for unveiling new and innovative design principles in engineering design problems. Although the innovization method is based on multi-objective optimization and post-optimality analyses of optimised solutions, it stretches the scope beyond an optimization task and attempts to discover new design/operational rules/principles relating to decision variables and objectives, so that a deeper understanding of the problem can be obtained. By integrating the concept of innovization with discrete-event simulation and data mining techniques, a new set of powerful tools can be developed for general systems analysis, particularly suitable for production systems. The uniqueness of the integrated approach proposed in this chapter lies on applying data mining to the data sets generated from simulation-based multi-objective optimization, in order to automatically or semi-automatically discover and interpret the hidden relationships and patterns for optimal production systems design/reconfiguration.

  • 12.
    Ng, Amos H. C.
    et al.
    University of Skövde, School of Technology and Society. University of Skövde, The Virtual Systems Research Centre.
    Dudas, Catarina
    University of Skövde, The Virtual Systems Research Centre. University of Skövde, School of Technology and Society.
    Pehrsson, Leif
    University of Skövde, School of Technology and Society. University of Skövde, The Virtual Systems Research Centre.
    Deb, Kalyanmoy
    University of Skövde, The Virtual Systems Research Centre.
    Knowledge Discovery in Production simulation By Interleaving Multi-Objective Optimization and Data Mining2012In: Proceedings of the SPS12 conference 2012, The Swedish Production Academy , 2012, p. 461-471Conference paper (Refereed)
  • 13.
    Ng, Amos
    et al.
    University of Skövde, School of Technology and Society. University of Skövde, The Virtual Systems Research Centre.
    Jägstam, Mats
    University of Skövde, School of Technology and Society. University of Skövde, The Virtual Systems Research Centre.
    Pehrsson, Leif
    Volvo Car Corporation.
    Deb, Kalyanmoy
    Indian Institute of Technology Kanpur, India.
    Improving Factory Productivity and Energy Efficiency Through Holistic Simulation Optimisation2011In: The 21st International Conference on Multiple Criteria Decision Making, University of Jyväskylä , 2011, p. 235-Conference paper (Refereed)
    Abstract [en]

    There is an urgent need for the automotive inductry to explore strategies and methods to accelerate the industrial efficiency progress and support decision making in order to regain profitability. At the same time, decision making should not be made strictly from a view of productivity and investment cost. Manufactures worldwide are taking steps towards more sustainable manufacturing. Sustainability, in terms of "Energy Efficiency", "Lean", "Lead Time Efficiency" and other forms of reuse/conservation of resources has become a paramount factor that needs to be considered not only during the operational stage but from the very first day a production system is designed or configured. Therefore, to optimise a manufacturing system today is not only about maximising capacity and minimising costs, it is also about minimising energy use, minimising loss, minimising manufacturing lead time and other sustainability measures. The aim of the presentation is to introduce an innovative simulation-based optimisation and knowledge elicitation methodology for decision-making support within the production systems lifecycle to increase the profitability (increasing cost effectiveness) and simultaneously sustainability (increasing energy efficiency, reducing losses/wastes and shorten Order to Delivery Time) of the Swedish manufacturing industry. The methodology is so called Holistic Simulation Optimisation (HSO) because unlike today's industrial practice that productivity, cost and sustainability are optimised separately, the framework proposed takes into account productivity, cost, and sustainability in a multi-level and multi-objective context. The HSO methodology is realised through the development of a software toolset that synergistically integrates Discrete Event Simulation with the sustainability and cost models that have been developed or extended by industrial companies with state-of-the-art multi-objective optimisation and data mining technologies. The potential benefits of using the HSO methodology on the efficiency of the production systems that are measurable and can be verified quantitatively are: 5-15% increase in productivity; 10-20% reduction in manufacturing lead time; reduction in environmental wastes, in terms of energy use and other forms of losses (10-20%). The paper will present how these estimations are based on the case studies conducted in Swedish automotive industry.

  • 14.
    Siegmund, Florian
    et al.
    University of Skövde, The Virtual Systems Research Centre. University of Skövde, School of Technology and Society.
    Bernedixen, Jacob
    University of Skövde, The Virtual Systems Research Centre. University of Skövde, School of Technology and Society.
    Pehrsson, Leif
    University of Skövde, The Virtual Systems Research Centre. University of Skövde, School of Technology and Society.
    Ng, Amos H. C.
    University of Skövde, The Virtual Systems Research Centre. University of Skövde, School of Technology and Society.
    Deb, Kalyanmoy
    Department of Mechanical Engineering, Indian Institute of Technology Kanpur, India.
    Reference point-based evolutionary multi-objective optimization for industrial systems simulation2012In: Proceedings of the 2012 Winter Simulation Conference (WSC) / [ed] C. Laroque, J. Himmelspach, R. Pasupathy, O. Rose, and A. M. Uhrmacher, IEEE conference proceedings, 2012Conference paper (Refereed)
    Abstract [en]

    In Multi-objective Optimization the goal is to present a set of Pareto-optimal solutions to the decision maker (DM). One out of these solutions is then chosen according to the DM preferences. Given that the DM has some general idea of what type of solution is preferred, a more efficient optimization could be run. This can be accomplished by letting the optimization algorithm make use of this preference information and guide the search towards better solutions that correspond to the preferences. One example for such kind of algorithms is the reference point-based NSGA-II algorithm (R-NSGA-II), by which user-specified reference points can be used to guide the search in the objective space and the diversity of the focused Pareto-set can be controlled. In this paper, the applicability of the R-NSGA-II algorithm in solving industrial-scale simulation-based optimization problems is illustrated through a case study of the improvement of a production line.

  • 15.
    Siegmund, Florian
    et al.
    University of Skövde, School of Technology and Society. University of Skövde, The Virtual Systems Research Centre.
    Deb, Kalyanmoy
    Department of Electrical and Computer Engineering, Michigan State University, USA.
    Karlsson, Alexander
    University of Skövde, School of Technology and Society. University of Skövde, The Virtual Systems Research Centre.
    Ng, Amos H. C.
    University of Skövde, School of Technology and Society. University of Skövde, The Virtual Systems Research Centre.
    Dynamic Resampling for Guided Evolutionary Multi-Objective Optimization of Stochastic Systems2013Conference paper (Refereed)
    Abstract [en]

    In Multi-objective Optimization many solutions have to be evaluated in order to provide the decision maker with a diverse Pareto-front. In Simulation-based Optimization the number of optimization function evaluations is very limited. If preference information is available however, the available function evaluations can be used more effectively by guiding the optimization towards interesting, preferred regions. One such algorithm for guided search is the R-NSGA-II algorithm. It takes reference points provided by the decision maker and guides the optimization towards areas of the Pareto-front close to the reference points.In Simulation-based Optimization the modeled systems are often stochastic and a reliable quality assessment of system configurations by resampling requires many simulation runs. Therefore optimization practitioners make use of dynamic resampling algorithms that distribute the available function evaluations intelligently on the solutions to be evaluated. Criteria for sampling allocation can be a.o. objective value variability, closeness to the Pareto-front indicated by elapsed time, or the dominance relations between different solutions based on distances between objective vectors and their variability.In our work we combine R-NSGA-II with several resampling algorithms based on the above mentioned criteria. Due to the preference information R-NSGA-II has fitness information based on distance to reference points at its disposal. We propose a resampling strategy that allocates more samples to solutions close to a reference point.Previously, we proposed extensions of R-NSGA-II that adapt algorithm parameters like population size, population diversity, or the strength of the Pareto-dominance relation continuously to optimization problem characteristics. We show how resampling algorithms can be integrated with those extensions.The applicability of the proposed algorithms is shown in a case study of an industrial production line for car manufacturing.

  • 16.
    Siegmund, Florian
    et al.
    University of Skövde, School of Technology and Society. University of Skövde, The Virtual Systems Research Centre.
    Deb, Kalyanmoy
    Department of Electrical and Computer Engineering, Michigan State University, USA.
    Ng, Amos H. C.
    University of Skövde, School of Technology and Society. University of Skövde, The Virtual Systems Research Centre.
    Adaptive Guided Evolutionary Multi-Objective Optimization2013Conference paper (Refereed)
    Abstract [en]

    In Multi-objective Optimization many solutions have to be evaluated in order to provide the decision maker with a diverse Pareto-front. In Simulation-based Optimization the number of optimization function evaluations is very limited. If preference information is available however, the available function evaluations can be used more effectively by guiding the optimization towards interesting, preferred regions. One such algorithm for guided search is the Reference-point guided NSGA-II. It takes reference points provided by the decision maker and guides the optimization towards areas of the Pareto-front close to the reference points.We propose several extensions of R-NSGA-II. In the beginning of the optimization runtime the population is spread-out in the objective space while towards the end of the runtime most solutions are close to reference points. The purpose of a large population is to avoid local optima and to explore the search space which is less important when the algorithm has converged to the reference points. Therefore, we reduce the population size towards the end of the runtime. R-NSGA-II controls the objective space diversity through the epsilon parameter. We reduce the diversity in the population as it approaches the reference points. In a previous study we showed that R-NSGA-II keeps a high diversity until late in the optimization run which is caused by the Pareto-fitness. This slows down the progress towards the reference points. We constrain the Pareto-fitness to force a faster convergence. For the same reason an approach is presented that delays the use of the Pareto-fitness: Initially, the fitness is based only on reference point distance and diversity. Later, when the population has converged towards the Pareto-front, Pareto-fitness is considered as primary-, and distance as secondary fitness.

  • 17.
    Siegmund, Florian
    et al.
    University of Skövde, School of Technology and Society. University of Skövde, The Virtual Systems Research Centre.
    Ng, Amos H. C.
    University of Skövde, School of Technology and Society. University of Skövde, The Virtual Systems Research Centre.
    Deb, Kalyanmoy
    Department of Mechanical Engineering, Indian Institute of Technology, Kanpur, India.
    A Comparative Study of Dynamic Resampling Strategies for Guided Evolutionary Multi-Objective Optimization2013In: 2013 IEEE Congress on Evolutionary Computation, CEC 2013, IEEE conference proceedings, 2013, p. 1826-1835Conference paper (Refereed)
    Abstract [en]

    In Evolutionary Multi-objective Optimization many solutions have to be evaluated to provide the decision maker with a diverse choice of solutions along the Pareto-front, in particular for high-dimensional optimization problems. In Simulation-based Optimization the modeled systems are complex and require long simulation times. In addition the evaluated systems are often stochastic and reliable quality assessment of system configurations by resampling requires many simulation runs. As a countermeasure for the required high number of simulation runs caused by multiple optimization objectives the optimization can be focused on interesting parts of the Pareto-front, as it is done by the Reference point-guided NSGA-II algorithm (R-NSGA-II) [9]. The number of evaluations needed for the resampling of solutions can be reduced by intelligent resampling algorithms that allocate just as much sampling budget needed in different situations during the optimization run. In this paper we propose and compare resampling algorithms that support the R-NSGA-II algorithm on optimization problems with stochastic evaluation functions. © 2013 IEEE.

  • 18.
    Siegmund, Florian
    et al.
    University of Skövde, School of Engineering Science. University of Skövde, The Virtual Systems Research Centre.
    Ng, Amos H. C.
    University of Skövde, School of Engineering Science. University of Skövde, The Virtual Systems Research Centre.
    Deb, Kalyanmoy
    Department of Electrical and Computer Engineering, Michigan State University, USA.
    A Comparative Study of Fast Adaptive Preference-Guided Evolutionary Multi-objective Optimization2017In: Evolutionary Multi-Criterion Optimization: 9th International Conference, EMO 2017, Münster, Germany, March 19-22, 2017, Proceedings / [ed] Heike Trautmann, Rudolph Günter, Kathrin Klamroth, Oliver Schütze, Margaret Wiecek, Yaochu Jin, and Christian Grimme, Springer, 2017, Vol. 10173, p. 560-574Conference paper (Refereed)
    Abstract [en]

    In Simulation-based Evolutionary Multi-objective Optimization, the number of simulation runs is very limited, since the complex simulation models require long execution times. With the help of preference information, the optimization result can be improved by guiding the optimization towards relevant areas in the objective space with, for example, the Reference Point-based NSGA-II algorithm (R-NSGA-II). Since the Pareto-relation is the primary fitness function in R-NSGA-II, the algorithm focuses on exploring the objective space with high diversity. Only after the population has converged closeto the Pareto-front does the influence of the reference point distance as secondary fitness criterion increase and the algorithm converges towards the preferred area on the Pareto-front.In this paper, we propose a set of extensions of R-NSGA-II which adaptively control the algorithm behavior, in order to converge faster towards the reference point. The adaption can be based on criteria such as elapsed optimization time or the reference point distance, or a combination thereof. In order to evaluate the performance of the adaptive extensions of R-NSGA-II, a performance metric for reference point-based EMO algorithms is used, which is based on the Hypervolume measure called the Focused Hypervolume metric. It measures convergence and diversity of the population in the preferred area around the reference point. The results are evaluated on two benchmark problems ofdifferent complexity and a simplistic production line model.

  • 19.
    Siegmund, Florian
    et al.
    University of Skövde, School of Engineering Science. University of Skövde, The Virtual Systems Research Centre.
    Ng, Amos H. C.
    University of Skövde, School of Engineering Science. University of Skövde, The Virtual Systems Research Centre.
    Deb, Kalyanmoy
    Department of Electrical and Computer Engineering, Michigan State University, USA.
    A Ranking and Selection Strategy for Preference-based Evolutionary Multi-objective Optimization of Variable-Noise Problems2016In: 2016 IEEE Congress on Evolutionary Computation (CEC), IEEE conference proceedings, 2016, p. 3035-3044Conference paper (Refereed)
    Abstract [en]

    In simulation-based Evolutionary Multi-objective Optimization the number of simulation runs is very limited, since the complex simulation models require long execution times. With the help of preference information, the optimization result can be improved by guiding the optimization towards relevant areas in the objective space, for example with the R-NSGA-II algorithm [9], which uses a reference point specified by the decision maker. When stochastic systems are simulated, the uncertainty of the objective values might degrade the optimization performance. By sampling the solutions multiple times this uncertainty can be reduced. However, resampling methods reduce the overall number of evaluated solutions which potentially worsens the optimization result. In this article, a Dynamic Resampling strategy is proposed which identifies the solutions closest to the reference point which guides the population of the Evolutionary Algorithm. We apply a single-objective Ranking and Selection resampling algorithm in the selection step of R-NSGA-II, which considers the stochastic reference point distance and its variance to identify the best solutions. We propose and evaluate different ways to integrate the sampling allocation method into the Evolutionary Algorithm. On the one hand, the Dynamic Resampling algorithm is made adaptive to support the EA selection step, and it is customized to be used in the time-constrained optimization scenario. Furthermore, it is controlled by other resampling criteria, in the same way as other hybrid DR algorithms. On the other hand, R-NSGA-II is modified to rely more on the scalar reference point distance as fitness function. The results are evaluated on a benchmark problem with variable noise landscape.

  • 20.
    Siegmund, Florian
    et al.
    University of Skövde, School of Engineering Science. University of Skövde, The Virtual Systems Research Centre.
    Ng, Amos H. C.
    University of Skövde, School of Engineering Science. University of Skövde, The Virtual Systems Research Centre.
    Deb, Kalyanmoy
    Department of Electrical and Computer Engineering, Michigan State University, USA.
    Dynamic Resampling for Preference-based Evolutionary Multi-Objective Optimization of Stochastic Systems2015Conference paper (Refereed)
    Abstract [en]

    In Multi-objective Optimization many solutions have to be evaluated in order to provide the decision maker with a diverse choice of solutions along the Pareto-front. In Simulation-based Optimization the number of optimization function evaluations is usually very limited due to the long execution times of the simulation models. If preference information is available however, the available number of function evaluations can be used more effectively. The optimization can be performed as a guided, focused search which returns solutions close to interesting, preferred regions of the Pareto-front. One such algorithm for guided search is the Reference-point guided Non-dominated Sorting Genetic Algorithm II, R-NSGA-II. It is a population-based Evolutionary Algorithm that finds a set of non-dominated solutions in a single optimization run. R-NSGA-II takes reference points in the objective space provided by the decision maker and guides the optimization towards areas of the Pareto-front close the reference points.

    In Simulation-based Optimization the modeled and simulated systems are often stochastic and a common method to handle objective noise is Resampling. Reliable quality assessment of system configurations by resampling requires many simulation runs. Therefore, the optimization process can benefit from Dynamic Resampling algorithms that distribute the available function evaluations among the solutions in the best possible way. Solutions can vary in their sampling need. For example, solutions with highly variable objective values have to be sampled more times to reduce their objective value standard error. Dynamic resampling algorithms assign as much samples to them as is needed to reduce the uncertainty about their objective values below a certain threshold. Another criterion the number of samples can be based on is a solution's closeness to the Pareto-front. For solutions that are close to the Pareto-front it is likely that they are member of the final result set. It is therefore important to have accurate knowledge of their objective values available, in order to be able to to tell which solutions are better than others. Usually, the distance to the Pareto-front is not known, but another criterion can be used as an indication for it instead: The elapsed optimization time. A third example of a resampling criterion can be the dominance relations between different solutions. The optimization algorithm has to determine for pairs of solutions which is the better one. Here both distances between objective vectors and the variance of the objective values have to be considered which requires a more advanced resampling technique. This is a Ranking and Selection problem.

    If R-NSGA-II is applied in a scenario with a stochastic fitness function resampling algorithms have to be used to support it in the best way and avoid a performance degradation due to uncertain knowledge about the objective values of solutions. In our work we combine R-NSGA-II with several resampling algorithms that are based on the above mentioned resampling criteria or combinations thereof and evaluate which are the best criteria the sampling allocation can be based on, in which situations.

    Due to the preference information R-NSGA-II has an important fitness information about the solutions at its disposal: The distance to reference points. We propose a resampling strategy that allocates more samples to solutions close to a reference point. This idea is then extended with a resampling technique that compares solutions based on their distance to the reference point. We base this algorithm on a classical Ranking and Selection algorithm, Optimal Computing Budget Allocation, and show how OCBA can be applied to support R-NSGA-II. We show the applicability of the proposed algorithms in a case study of an industrial production line for car manufacturing.

  • 21.
    Siegmund, Florian
    et al.
    University of Skövde, The Virtual Systems Research Centre. University of Skövde, School of Technology and Society.
    Ng, Amos H. C.
    University of Skövde, The Virtual Systems Research Centre. University of Skövde, School of Technology and Society.
    Deb, Kalyanmoy
    Department of Mechanical Engineering, Indian Institute of Technology Kanpur, India.
    Finding a preferred diverse set of Pareto-optimal solutions for a limited number of function calls2012In: 2012 IEEE Congress on Evolutionary Computation, IEEE conference proceedings, 2012, p. 2417-2424Conference paper (Refereed)
    Abstract [en]

    Evolutionary Multi-objective Optimization aims at finding a diverse set of Pareto-optimal solutions whereof the decision maker can choose the solution that fits best to her or his preferences. In case of limited time (of function evaluations) for optimization this preference information may be used to speed up the search by making the algorithm focus directly on interesting areas of the objective space. The R-NSGA-II algorothm (1) uses reference points to which the search is guided specified according to the preferences of the user. In this paper, we propose an extension to R-NSGA-II that limits the Pareto-fitness to speed up the search for a limited number of function calls. It avoids to automatically select all solutions of the first front of the candidate set into the next population. In this way non-preferred Pareto-optimal solutions are not considered thereby accelerating the search process. With focusing comes the necessity to maintain diversity. In R-NSGA-II this is achieved with the help of a clustering algorithm which keeps the found solutions above a minimum distance ε. In this paper, we propose a self-adaptive ε approach that autonomously provides the decision maker with a more diverse solution set if the found Pareto-set is situated further away from a reference point. Similarly, the approach also varies the diversity inside of the Pareto-set. This helps the decision maker to get a better overview of the available solutions and supports decisions about how to adapt the reference points.

  • 22.
    Siegmund, Florian
    et al.
    University of Skövde, School of Engineering Science. University of Skövde, The Virtual Systems Research Centre.
    Ng, Amos H. C.
    University of Skövde, School of Engineering Science. University of Skövde, The Virtual Systems Research Centre.
    Deb, Kalyanmoy
    Department of Electrical and Computer Engineering, Michigan State University, East Lansing, USA.
    Hybrid Dynamic Resampling Algorithms for Evolutionary Multi-objective Optimization of Invariant-Noise Problems2016In: Applications of Evolutionary Computation: 19th European Conference, EvoApplications 2016, Porto, Portugal, March 30 – April 1, 2016, Proceedings, Part II / [ed] Giovanni Squillero, Paolo Burelli, 2016, Vol. 9598, p. 311-326Conference paper (Refereed)
    Abstract [en]

    In Simulation-based Evolutionary Multi-objective Optimization (EMO) the available time for optimization usually is limited. Since many real-world optimization problems are stochastic models, the optimization algorithm has to employ a noise compensation technique for the objective values. This article analyzes Dynamic Resampling algorithms for handling the objective noise. Dynamic Resampling improves the objective value accuracy by spending more time to evaluate the solutions multiple times, which tightens the optimization time limit even more. This circumstance can be used to design Dynamic Resampling algorithms with a better sampling allocation strategy that uses the time limit. In our previous work, we investigated Time-based Hybrid Resampling algorithms for Preference-based EMO. In this article, we extend our studies to general EMO which aims to find a converged and diverse set of alternative solutions along the whole Pareto-front of the problem. We focus on problems with an invariant noise level, i.e. a flat noise landscape.

  • 23.
    Siegmund, Florian
    et al.
    University of Skövde, School of Engineering Science. University of Skövde, The Virtual Systems Research Centre.
    Ng, Amos H. C.
    University of Skövde, School of Engineering Science. University of Skövde, The Virtual Systems Research Centre.
    Deb, Kalyanmoy
    Department of Electrical and Computer Engineering, Michigan State University, USA.
    Hybrid Dynamic Resampling for Guided Evolutionary Multi-Objective Optimization2015In: Evolutionary Multi-Criterion Optimization: 8th International Conference, EMO 2015, Guimarães, Portugal, March 29 --April 1, 2015. Proceedings, Part I / [ed] António Gaspar-Cunha, Carlos Henggeler Antunes, Carlos Coello Coello, Springer, 2015, p. 366-380Conference paper (Refereed)
    Abstract [en]

    In Guided Evolutionary Multi-objective Optimization the goal is to find a diverse, but locally focused non-dominated front in a decision maker’s area of interest, as close as possible to the true Pareto-front. The optimization can focus its efforts towards the preferred area and achieve a better result [9, 17, 7, 13]. The modeled and simulated systems are often stochastic and a common method to handle the objective noise is Resampling. The given preference information allows to define better resampling strategies which further improve the optimization result. In this paper, resampling strategies are proposed that base the sampling allocation on multiple factors, and thereby combine multiple resampling strategies proposed by the authors in [15]. These factors are, for example, the Pareto-rank of a solution and its distance to the decision maker’s area of interest. The proposed hybrid Dynamic Resampling Strategy DR2 is evaluated on the Reference point-guided NSGA-II optimization algorithm (R-NSGA-II) [9].

  • 24.
    Wang, Lihui
    et al.
    University of Skövde, School of Technology and Society. University of Skövde, The Virtual Systems Research Centre.
    Ng, Amos H. C.University of Skövde, School of Technology and Society. University of Skövde, The Virtual Systems Research Centre.Deb, KalyanmoyUniversity of Skövde, School of Technology and Society. University of Skövde, The Virtual Systems Research Centre.
    Multi-objective Evolutionary Optimisation for Product Design and Manufacturing2011Collection (editor) (Refereed)
1 - 24 of 24
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