David Greiner

Improving computational mechanics optimum design using helper objectives: an application in frame bar structures

Considering evolutionary multiobjective algorithms for improving single objective optimization problems is focused in this work on introducing the concept of helper objectives in a computational mechanics problem: the constrained mass minimization in real discrete frame bar structures optimum design. The number of different cross-section types of the structure is proposed as a helper objective. It provides a discrete functional landscape where the nondominated frontier is constituted of a low number of discrete isolated points. Therefore, the population diversity treatment becomes a key point in the multiobjective approach performance. Two different-sized test cases, four mutation rates and two codifications (binary and gray) are considered in the performance analysis of four algorithms: single-objective elitist evolutionary algorithm, NSGAII, SPEA2 and DENSEA. Results show how an appropriate multiobjective approach that makes use of the proposed helper objective outperforms the single objective optimization in terms of average final solutions and enhanced robustness related to mutation rate variations.

Single- and multi-objective shape design of Y-noise barriers using evolutionary computation and boundary elements

The optimum shape design of Y-noise barriers is carried out using single and multi-objective evolutionary algorithms and the Boundary Element Method (BEM). Reduction of noise impact efficiency (using the insertion loss-IL-magnitude) and cost of the barrier (using its total length magnitude) are considered. A two-dimensional problem of sound propagation in the frequency domain is handled, defined by a fixed position emitting source, which pulses in a frequency range, and receptor. A noise barrier (limiting its maximum effective height) is situated between both. Its shape is modified to minimize the receptor measured sound level, which is calculated using BEM. Results of an inverse problem using the IL barrier curve as reference are successfully performed to validate the methodology. The proposed methodology is then used to obtain Y-barriers with 15% and 30% improved IL spectrum. Finally, six non-dominated solutions of the multi-objective optimum design problem are presented in detail.

Gray coding in evolutionary multicriteria optimization: application in frame structural optimum design

A comparative study of the use of Gray coding in multicriteria evolutionary optimisation is performed using the SPEA2 and NSGAII algorithms and applied to a frame structural optimisation problem. A double minimization is handled: constrained mass and number of different cross-section types. Influence of various mutation rates is considered. The comparative statistical results of the test case cover a convergence study during evolution by means of certain metrics that measure front amplitude and distance to the optimal front. Results in a 55 bar-sized frame test case show that the use of the Standard Binary Reflected Gray code compared versus Binary code allows to obtain fast and more accurate solutions, more coverage of non-dominated fronts; both with improved robustness in frame structural multiobjective optimum design.

Advances in Evolutionary and Deterministic Methods for Design, Optimization and Control in Engineering and Sciences

This book contains state-of-the-art contributions in the field of evolutionary and deterministic methods for design, optimization and control in engineering and sciences. Specialists have written each of the 34 chapters as extended versions of selected papers presented at the International Conference on Evolutionary and Deterministic Methods for Design, Optimization and Control with Applications to Industrial and Societal Problems (EUROGEN 2013). The conference was one of the Thematic Conferences of the European Community on Computational Methods in Applied Sciences (ECCOMAS). Topics treated in the various chapters are classified in the following sections: theoretical and numerical methods and tools for optimization (theoretical methods and tools; numerical methods and tools) and engineering design and societal applications (turbo machinery; structures, materials and civil engineering; aeronautics and astronautics; societal applications; electrical and electronics applications), focused particularly on intelligent systems for multidisciplinary design optimization (mdo) problems based on multi-hybridized software, adjoint-based and one-shot methods, uncertainty quantification and optimization, multidisciplinary design optimization, applications of game theory to industrial optimization problems, applications in structural and civil engineering optimum design and surrogate models based optimization methods in aerodynamic design.

Robust Design of Noise Attenuation Barriers with Evolutionary Multiobjective Algorithms and the Boundary Element Method

Multiobjective shape design of acoustic attenuation barriers is handled using a boundary element method modeling and evolutionary algorithms. Noise barriers are widely used for environmental protection near population nucleus in order to reduce the noise impact. The minimization of the acoustic pressure and the minimization of the cost of the barrier -considering its total length- are taken into account. First, a single receiver point is considered; then the case of multiple receiver locations is introduced, searching for a single robust shape design where the acoustic attenuation is minimized simultaneously in different locations using probabilistic dominance relation. The case of Y-shaped barriers with upper absorbing surface is presented here. Results include a comparative between the strategy of introducing a single objective optimum in the initial multiobjective population (seeded approach) and the standard approach. The methodology is capable to provide improved robust noise barrier designs successfully.

A Flexible Evolutionary Agent: cooperation and competition among real-coded evolutionary operators

Since it has currently became essential to design more efficient and robust alternative techniques to solve hard optimisation problems in industry or science, and of easy use for practitioners, here a new way of developing simple Artificial Intelligence based Evolutionary Algorithms will be introduced. Our evolutionary computational implementation is a new idea in optimisation. Any evolutionary operators and their associated parameters from well-established evolutionary methods can be considered in such a way that the entire algorithm or intelligent agent-based software performs with very high efficiency without a prior need to investigate which method will be the best for a given optimisation problem.The implementation presented, named Flexible Evolution (FE), has capacity to adapt the operators, the parameters and the algorithm to the circumstances faced at each step of every optimisation run and is able to take into account lessons learned by different research works in the adaptation of operators and parameters. The FE uses Artificial Intelligence concepts to manage internal procedures to adopt decisions and correct the wrong ones. Our aim in this paper will be to give the keys to design these types of procedures, and more specifically, to find the way of achieving an optimum performance of the operators involved in the search, in our case by means of a function included in our algorithm called Sampling Engine. An early implementation has been already developed and tested in our previous works [66–68], so in this paper, new results of a second software implementation are presented comparing the results with those obtained by other methods, using well-known hard test functions.

Safety systems optimum design by multicriteria evolutionary algorithms

In this work new safety systems multiobjective optimum design methodologies are introduced and compared. Various multicriteria evolutionary algorithms are analysed (SPEA2, NSGAII and controlled elitist-NSGAII) and applied to a Containment Spray Injection System of a nuclear power plant. Influence of various mutation rates is considered. A double minimization is handled: unavailability and cost of the system. The comparative statistical results of the test case show a convergence study during evolution by means of certain metrics that measure front coverage and distance to the optimal front. Results succeed in solving the problem.

Multiple-Objective Genetic Algorithm Using the Multiple Criteria Decision Making Method TOPSIS

The so called second generation of Multi-Objective Evolutionary Algorithms (MOEAs) like NSGA-II, are highly efficient and obtain Pareto optimal fronts characterized mainly by a wider spread and visually distributed fronts. The subjacent idea is to provide the decision-makers (DM) with the most representative set of alternatives in terms of objective values, reserving the articulation of preferences to an a posteriori stage. Nevertheless, in many real discrete problems the number of solutions that belong the Pareto front is unknown and if the specified size of the non-dominated population in the MOEA is less than the number of solutions of the problem, the found front will be incomplete for a posteriori Making Decision. A possible strategy to overcome this difficulty is to promote those solutions placed in the region of interest while neglecting the others during the search, according to some DMs preferences. We propose TOPSISGA, that merges the second generation of MOEAs (we use NSGA-II) with the well known multiple criteria decision making technique TOPSIS whose main principle is to identify as preferred solutions those ones with the shortest distance to the positive ideal solution and the longest distance from the negative ideal solution. The method induces an ordered list of alternatives in accordance to the DMs preferences based on Similarity to the ideal point.

Introducing reference point using g-dominance in optimum design considering uncertainties: an application in structural engineering

Considering uncertainties in engineering optimum design is often a requirement. Here, the use of the deterministic optimum design as the reference point in g-dominance is proposed. The multiobjective optimum robust design in a structural engineering test case where uncertainties in the external loads are taken into account is proposed as application, where the simultaneous minimization of the constrained weight average and the standard deviation of the constraints violation are the objective functions. Results include a comparison between both non-dominated sorting genetic algorithm II (NSGA-II) and strength Pareto evolutionary algorithm (SPEA2), including S-metric (hypervolume) statistical comparisons with and without the g-dominance approach. The methodology is capable to provide robust optimum structural frame designs successfully.

New Evolutionary Methodologies for Integrated Safety System Design and Maintenance Optimization

In this work we present new methodologies for Integrated Safety System Design and Maintenance Optimization (ISSDMO) based on evolutionary processes. The main characteristics of the proposed approaches are: Optimization guided by Single or Double loop Multiple objective Evolutionary Algorithms, Safety Systems modeled using Fault Trees with enhanced logic to consider design alternatives for complex systems and Fault Tree direct quantitative evaluation performed with an advanced self-adaptable two-stage method. The multiple objective integrated optimal design of Safety Systems is solved, considering not only the combination of models assigned to each subsystem, but also different configurations of the system where the maintenance strategy is taken into account as well. For optimization we introduce a new double loop Evolutionary Algorithm for integer-coded variables based on the Flexible Evolution concepts. The inner loop is devoted to search the optimum maintenance strategy for a given design, while the outer loop takes care for obtaining the optimum design of the system. For comparative purposes two advanced single loop Genetic Algorithm with binary coding and integer coding of all variables (design and maintenance) has been developed too. Multiple objective optimization procedures are used in all the abovementioned algorithms. To evaluate fault trees, we use an efficient direct algorithm based on a Monte Carlo Variance Reduction Technique called Restricted Sampling (RS), which provides accuracy estimates for the system unavailability as well as exact intervals and, in many cases, the exact solution. The combination of the aforementioned processes constitutes a new methodology for ISSDMO, which overcomes difficulties faced by traditional approaches based on single loop Genetic Algorithms and Binary Decision Diagrams. As a practical example, the integrated design optimization of a typical safety system is developed: The Containment Spray System of a Nuclear Power Plant. The results obtained with all developed algorithms are compared in order to obtain significant conclusions. Among others the results reveal that, from an optimization point of view, the single and double loop approaches may be seen complementary methods, since none of them overcomes the others but contributes to identify solutions with different characteristics.