Blas Galván

Optimization of constrained multiple-objective reliability problems using evolutionary algorithms

This paper illustrates the use of multi-objective optimization to solve three types of reliability optimization problems: to find the optimal number of redundant components, find the reliability of components, and determine both their redundancy and reliability. In general, these problems have been formulated as single objective mixed-integer non-linear programming problems with one or several constraints and solved by using mathematical programming techniques or special heuristics. In this work, these problems are reformulated as multiple-objective problems (MOP) and then solved by using a second-generation Multiple-Objective Evolutionary Algorithm (MOEA) that allows handling constraints. The MOEA used in this paper (NSGA-II) demonstrates the ability to identify a set of optimal solutions (Pareto front), which provides the Decision Maker with a complete picture of the optimal solution space. Finally, the advantages of both MOP and MOEA approaches are illustrated by solving four redundancy problems taken from the literature.

Use of multiple objective evolutionary algorithms in optimizing surveillance requirements

This paper presents the development and application of a double-loop Multiple Objective Evolutionary Algorithm that uses a Multiple Objective Genetic Algorithm to perform the simultaneous optimization of periodic Test Intervals (TI) and Test Planning (TP). It takes into account the time-dependent effect of TP performed on stand-by safety-related equipment. TI and TP are part of the Surveillance Requirements within Technical Specifications at Nuclear Power Plants. It addresses the problem of multi-objective optimization in the space of dependable variables, i.e. TI and TP, using a novel flexible structure of the optimization algorithm. Lessons learnt from the cases of application of the methodology to optimize TI and TP for the High-Pressure Injection System are given. The results show that the double-loop Multiple Objective Evolutionary Algorithm is able to find the Pareto set of solutions that represents a surface of non-dominated solutions that satisfy all the constraints imposed on the objective functions and decision variables. Decision makers can adopt then the best solution found depending on their particular preference, e.g. minimum cost, minimum unavailability.

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.

Application of Dempster–Shafer theory for the quantification and propagation of the uncertainty caused by the use of AIS data

Abstract This paper proposes a novel method to quantify the uncertainty inherent to the paths that ships will navigate in the future, from the information provided by the AIS system on the paths followed by the ships in the past. In the framework of the Dempster–Shafer theory, the proposed method analyzes the information contained in a known distribution of vessel traffic on a waterway to construct the corresponding Dempster–Shafer structure. From this structure, using the confidence limits of Kolmogorov–Smirnov, it is possible to estimate the evidential measures (belief and plausibility) of all possible distributions of traffic on that waterway. The interesting facts of this proposal are that these evidential measures are, according to the probabilistic interpretation proposed by Dempster [1] , the lower and upper bounds of an interval that contains future distributions of maritime traffic on the waterway under consideration. Therefore, it can be concluded that knowledge of the traffic on a waterway in a given period allows delimit, with a certain confidence level, the uncertainty associated with the randomness of the trajectories that follow the ships during periods of equal duration. The results obtained by the proposed method for the studied case of the Canary Islands are presented, showing reasonable agreement with the results obtained by the software IWRAP Mk2.

An intrinsic order criterion to evaluate large, complex fault trees

A new efficient algorithm is introduced to evaluate (non) coherent fault trees, obtaining exact lower & upper bounds on system unavailability, with a prespecified maximum error. The algorithm is based on the canonical normal form of the Boolean function, but overcomes the large number of terms needed, by using an intrinsic order criterion (IOC) to select the elementary states to evaluate. This intrinsic order implies lexicographic (truth table) order. The criterion guarantees a priori that the probability of a given elementary system state is always greater than or equal to the probability of another state, for any set of basic probabilities. IOC is exclusively based on the positions of 0 & 1 in the binary n-tuples defining the elementary states. The algorithm does not require any qualitative analysis of the fault tree. The computational cost mainly depends on the basic event probabilities, and is related to system complexity, only because the Boolean function must be evaluated.

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.

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.