A. Gaspar-Cunha

Robustness in multi-objective optimization using evolutionary algorithms

Abstract This work discusses robustness assessment during multi-objective optimization with a Multi-Objective Evolutionary Algorithm (MOEA) using a combination of two types of robustness measures. Expectation quantifies simultaneously fitness and robustness, while variance assesses the deviation of the original fitness in the neighborhood of the solution. Possible equations for each type are assessed via application to several benchmark problems and the selection of the most adequate is carried out. Diverse combinations of expectation and variance measures are then linked to a specific MOEA proposed by the authors, their selection being done on the basis of the results produced for various multi-objective benchmark problems. Finally, the combination preferred plus the same MOEA are used successfully to obtain the fittest and most robust Pareto optimal frontiers for a few more complex multi-criteria optimization problems.

An integrated approach to automated innovization for discovering useful design principles: Case studies from engineering

Computational optimization methods are most often used to find a single or multiple optimal or near-optimal solutions to the underlying optimization problem describing the problem at hand. In this paper, we elevate the use of optimization to a higher level in arriving at useful problem knowledge associated with the optimal or near-optimal solutions to a problem. In the proposed innovization process, first a set of trade-off optimal or near-optimal solutions are found using an evolutionary algorithm. Thereafter, the trade-off solutions are analyzed to decipher useful relationships among problem entities automatically so as to provide a better understanding of the problem to a designer or a practitioner. We provide an integrated algorithm for the innovization process and demonstrate the usefulness of the procedure to three real-world engineering design problems. New and innovative design principles obtained in each case should clearly motivate engineers and practitioners for its further application to more complex problems and its further development as a more efficient data analysis procedure.

Methodology to select solutions from the pareto-optimal set: a comparative study

The resolution of a Multi-Objective Optimization Problem (MOOP) does not end when the Pareto-optimal set is found. In real problems, a single solution must be selected. Ideally, this solution must belong to the non-dominated solutions set and must take into account the preferences of a Decision Maker (DM). Therefore, the searching for a single solution (or solutions) in MOOP is done in two steps. First, a Pareto optimal set is found. Multi-Objective Evolutionary Algorithms (MOEA), based on the principle of Pareto optimality, are designed to produce the complete set of non-dominated solutions. Second, a methodology able to select a single solution from the set of non-dominated solutions (or a region of the Pareto frontier), and taking into account the preferences of a Decision Maker (DM), can be applied. In this work, a method, based on a weighted stress function, is proposed. It is able to integrate the users preferences in order to find the best region of the Pareto frontier accordingly with these preferences. This method was tested on some benchmark test problems, with two and three criteria. This methodology is able to select efficiently the best Pareto-frontier region for the specified relative importance of the criteria.

RPSGAe — Reduced Pareto Set Genetic Algorithm: Application to Polymer Extrusion

In this paper a Multiobjective Optimization Genetic Algorithm, denoted as Reduced Pareto Set Genetic Algorithm with Elitism (RPSGAe), is presented and its performance is assessed. The algorithm is compared with other Evolutionary Multiobjective Algorithms — EMOAs (SPEA2, PAES and NSGA-II) using problems from the literature and statistical comparison techniques. The results obtained showed that the RPSGAe algorithm has good overall performance. Finally, the RPSGAe algorithm was applied to the optimization of the polymer extrusion process. The aim is to implement an automatic optimization scheme capable of defining the values of important process parameters, such as operating conditions and screw geometry, yielding the best performance in terms of prescribed attributes. The results obtained for specific case studies have physical meaning and correspond to a successful process optimization.

Optimization of Processing Conditions for Polymer Twin-Screw Extrusion

Abstract The problem of setting the best operating conditions of a co-rotating twin-screw extruder is solved using an optimization approach based on Genetic Algorithms. Two possibilities are considered: i) the maximization of an objective function; ii) the simultaneous optimization of the individual criteria and the use of Pareto plots. The flow conditions inside the machine are simulated using the Ludovic© software. Various practical case studies are discussed, among them a reactive extrusion application. Generally, the methodology is sensitive to the influence of the main process criteria and provides solutions that are apparently sound.

Flow and Heat Transfer Along the Length of a Co-rotating Twin Screw Extruder

A global plasticating model for co-rotating twin screw extruders is presented, with the capability of predicting from hopper to die the evolution of pressure, temperature, shear rate, degree of fill, residence time and mechanical power consumption. The resultant software requires moderate computational resources, making it suitable for use with optimization algorithms. Predictions are compared with experimental measurements along the extruder axis for a number of runs involving changes in operating conditions and screw geometry. Globally, the results validate the software and also put in evidence the process steps where improvements in modeling are required.

The Design of Extrusion Screws: An Optimization Approach

Abstract The design of a screw for plasticating polymer extrusion based on scientific principles is still a challenging task, which has received surprisingly little attention in the literature. In the present work the design of a screw is considered as an optimization problem. The corresponding design methodology is discussed. Two alternative approaches are considered. In the first case, the aim is to maximize the value of an objective function that describes quantitatively the process performance in terms of pre-selected important process criteria. A multiobjective optimization scheme resorting to the use of optimal or non-dominated Pareto frontiers is also implemented, where the set of feasible individual solutions in terms of the various criteria is correlated, thus evidencing the compromise between them. The relevance of the solutions and the sensitivity of the method to changes in the criteria considered are demonstrated with a case study.

Feature selection using multi-objective evolutionary algorithms : application to cardiac SPECT diagnosis

An optimization methodology based on the use of Multi-Objective Evolutionary Algorithms (MOEA) in order to deal with problems of feature selection in data mining was proposed. For that purpose a Support Vector Machines (SVM) classifier was adopted. The aim being to select the best features and optimize the classifier parameters simultaneously while minimizing the number of features necessary and maximize the accuracy of the classifier and/or minimize the errors obtained. The validity of the methodology proposed was tested in a problem of cardiac Single Proton Emission Computed Tomography (SPECT). The results obtained allow one to conclude that MOEA is an efficient feature selection approach and the best results were obtained when the accuracy, the errors and the classifiers parameters are optimized simultaneously.

Financial distress model prediction using SVM

Financial distress prediction is of great importance to all stakeholders in order to enable better decision-making in evaluating firms. In recent years, the rate of bankruptcy has risen and it is becoming harder to estimate as companies become more complex and the asymmetric information between banks and firms increases. Although a great variety of techniques have been applied along the years, no comprehensive method incorporating an holistic perspective had hitherto been considered. Recently, SVM+ a technique proposed by Vapnik [17] provides a formal way to incorporate privileged information onto the learning models improving generalization. By exploiting additional information to improve traditional inductive learning we propose a prediction model where data is naturally separated into several groups according to the size of the firm. Experimental results in the setting of a heterogeneous data set of French companies demonstrated that the proposed model showed superior performance in terms of prediction accuracy in bankruptcy prediction and misclassification cost.

Multi-objective ant colony optimization for the twin-screw configuration problem

The twin-screw configuration problem (TSCP) consists of identifying the best location of a set of available screw elements along a screw shaft. Owing to its combinatorial nature, it can be seen as a sequencing problem. In addition, different conflicting objectives may have to be considered when defining a screw configuration and, thus, it is usually tackled as a multi-objective optimization problem. In this research, a multi-objective ant colony optimization (MOACO) algorithm was adapted to deal with the TSCP. The influence of different parameters of the MOACO algorithm was studied and its performance was compared with that of a previously proposed multi-objective evolutionary algorithm and a two-phase local search algorithm. The experimental results showed that MOACO algorithms have a significant potential for solving the TSCP.