Multi-objective optimization of environmentally conscious chemical supply chains under demand uncertainty

In this work, we analyze the effect of demand uncertainty on the multi-objective optimization of chemical supply chains (SC) considering simultaneously their economic and environmental performance. To this end, we present a stochastic multi-scenario mixed-integer linear program (MILP) with the unique feature of incorporating explicitly the demand uncertainty using scenarios with given probability of occurrence. The environmental performance is quantified following life cycle assessment (LCA) principles, which are represented in the model formulation through standard algebraic equations. The capabilities of our approach are illustrated through a case study. We show that the stochastic solution improves the economic performance of the SC in comparison with the deterministic one at any level of the environmental impact.

Feature selection by multi-objective optimisation: Application to network anomaly detection by hierarchical self-organising maps

Feature selection is an important and active issue in clustering and classification problems. By choosing an adequate feature subset, a dataset dimensionality reduction is allowed, thus contributing to decreasing the classification computational complexity, and to improving the classifier performance by avoiding redundant or irrelevant features. Although feature selection can be formally defined as an optimisation problem with only one objective, that is, the classification accuracy obtained by using the selected feature subset, in recent years, some multi-objective approaches to this problem have been proposed. These either select features that not only improve the classification accuracy, but also the generalisation capability in case of supervised classifiers, or counterbalance the bias toward lower or higher numbers of features that present some methods used to validate the clustering/classification in case of unsupervised classifiers. The main contribution of this paper is a multi-objective approach for feature selection and its application to an unsupervised clustering procedure based on Growing Hierarchical Self-Organising Maps (GHSOMs) that includes a new method for unit labelling and efficient determination of the winning unit. In the network anomaly detection problem here considered, this multi-objective approach makes it possible not only to differentiate between normal and anomalous traffic but also among different anomalies. The efficiency of our proposals has been evaluated by using the well-known DARPA/NSL-KDD datasets that contain extracted features and labelled attacks from around 2 million connections. The selected feature sets computed in our experiments provide detection rates up to 99.8% with normal traffic and up to 99.6% with anomalous traffic, as well as accuracy values up to 99.12%.

Robust solutions to multi-objective linear programs with uncertain data

In this paper we examine multi-objective linear programming problems in the face of data uncertainty both in the objective function and the constraints. First, we derive a formula for the radius of robust feasibility guaranteeing constraint feasibility for all possible scenarios within a specified uncertainty set under affine data parametrization. We then present numerically tractable optimality conditions for minmax robust weakly efficient solutions, i.e., the weakly efficient solutions of the robust counterpart. We also consider highly robust weakly efficient solutions, i.e., robust feasible solutions which are weakly efficient for any possible instance of the objective matrix within a specified uncertainty set, providing lower bounds for the radius of highly robust efficiency guaranteeing the existence of this type of solutions under affine and rank-1 objective data uncertainty. Finally, we provide numerically tractable optimality conditions for highly robust weakly efficient solutions.

Exposing market mechanism design trade-offs via multi-objective evolutionary search

Market mechanisms are a means by which resources in contention can be allocated between contending parties, both in human economies and those populated by software agents. Designing such mechanisms has traditionally been carried out by hand, and more recently by automation. Assessing these mechanisms typically involves them being evaluated with respect to multiple conflicting objectives, which can often be nonlinear, noisy, and expensive to compute. For typical performance objectives, it is known that designed mechanisms often fall short on being optimal across all objectives simultaneously. However, in all previous automated approaches, either only a single objective is considered, or else the multiple performance objectives are combined into a single objective. In this paper we do not aggregate objectives, instead considering a direct, novel application of multi-objective evolutionary algorithms (MOEAs) to the problem of automated mechanism design. This allows the automatic discovery of trade-offs that such objectives impose on mechanisms. We pose the problem of mechanism design, specifically for the class of linear redistribution mechanisms, as a naturally existing multi-objective optimisation problem. We apply a modified version of NSGA-II in order to design mechanisms within this class, given economically relevant objectives such as welfare and fairness. This application of NSGA-II exposes tradeoffs between objectives, revealing relationships between them that were otherwise unknown for this mechanism class. The understanding of the trade-off gained from the application of MOEAs can thus help practitioners with an insightful application of discovered mechanisms in their respective real/artificial markets.

Multi-objective optimization of the molecular structure of refrigerants

The aim of this work was to develop a new methodology, which can be used to design new refrigerants that are better than the currently used refrigerants. The methodology draws some parallels with the general approach of computer aided molecular design. However, the mathematical way of representing the molecular structure of an organic compound and the use of meta models during the optimization process make it different. In essence, this approach aimed to generate molecules that conform to various property requirements that are known and specified a priori. A modified way of mathematically representing the molecular structure of an organic compound having up to four carbon atoms, along with atoms of other elements such as hydrogen, oxygen, fluorine, chlorine and bromine, was developed. The normal boiling temperature, enthalpy of vaporization, vapor pressure, tropospheric lifetime and biodegradability of 295 different organic compounds, were collected from open literature and data bases or estimated. Surrogate models linking the previously mentioned quantities with the molecular structure were developed. Constraints ensuring the generation of structurally feasible molecules were formulated and used in commercially available optimization algorithms to generate molecular structures of promising new refrigerants. This study was intended to serve as a proof-of-concept of designing refrigerants using the newly developed methodology.

Structural damage estimation using dynamic data and multi-objective optimization

Peer reviewed

Defining efficient policies in a general equilibrium model: a multi-objective approach

Macroeconomic policy makers are typically concerned with several indicators of economic performance. We thus propose to tackle the design of macroeconomic policy using Multicriteria Decision Making (MCDM) techniques. More specifically, we employ Multiobjective Programming (MP) to seek so-called efficient policies. The MP approach is combined with a computable general equilibrium (CGE) model. We chose use of a CGE model since they have the dual advantage of being consistent with standard economic theory while allowing one to measure the effect(s) of a specific policy with real data. Applying the proposed methodology to Spain (via the 1995 Social Accounting Matrix) we first quantified the trade-offs between two specific policy objectives: growth and inflation, when designing fiscal policy. We then constructed a frontier of efficient policies involving real growth and inflation. In doing so, we found that policy in 1995 Spain displayed some degree of inefficiency with respect to these two policy objectives. We then offer two sets of policy recommendations that, ostensibly, could have helped Spain at the time. The first deals with efficiency independent of the importance given to both growth and inflation by policy makers (we label this set: general policy recommendations). A second set depends on which policy objective is seen as more important by policy makers: increasing growth or controlling inflation (we label this one: objective-specific recommendations).

Dynamic Multi-Objective Optimization With jMetal and Spark: a Case Study

Technologies for Big Data and Data Science are receiving increasing research interest nowadays. This paper introduces the prototyping architecture of a tool aimed to solve Big Data Optimization problems. Our tool combines the jMetal framework for multi-objective optimization with Apache Spark, a technology that is gaining momentum. In particular, we make use of the streaming facilities of Spark to feed an optimization problem with data from different sources. We demonstrate the use of our tool by solving a dynamic bi-objective instance of the Traveling Salesman Problem (TSP) based on near real-time traffic data from New York City, which is updated several times per minute. Our experiment shows that both jMetal and Spark can be integrated providing a software platform to deal with dynamic multi-optimization problems.

Algoritmo genético especializado na resolução de problemas com variáveis contínuas e altamente restritos

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Índices de confiabilidade devido a vegetação e planejamento de podas de árvores em redes de distribuição

Pós-graduação em Engenharia Elétrica - FEIS

Optimización de aperturas mediante técnicas de algoritmos evolutivos

Los sistemas de imagen por ultrasonidos son hoy una herramienta indispensable en aplicaciones de diagnóstico en medicina y son cada vez más utilizados en aplicaciones industriales en el área de ensayos no destructivos. El array es el elemento primario de estos sistemas y su diseño determina las características de los haces que se pueden construir (forma y tamaño del lóbulo principal, de los lóbulos secundarios y de rejilla, etc.), condicionando la calidad de las imágenes que pueden conseguirse. En arrays regulares la distancia máxima entre elementos se establece en media longitud de onda para evitar la formación de artefactos. Al mismo tiempo, la resolución en la imagen de los objetos presentes en la escena aumenta con el tamaño total de la apertura, por lo que una pequeña mejora en la calidad de la imagen se traduce en un aumento significativo del número de elementos del transductor. Esto tiene, entre otras, las siguientes consecuencias: Problemas de fabricación de los arrays por la gran densidad de conexiones (téngase en cuenta que en aplicaciones típicas de imagen médica, el valor de la longitud de onda es de décimas de milímetro) Baja relación señal/ruido y, en consecuencia, bajo rango dinámico de las señales por el reducido tamaño de los elementos. Complejidad de los equipos que deben manejar un elevado número de canales independientes. Por ejemplo, se necesitarían 10.000 elementos separados λ 2 para una apertura cuadrada de 50 λ. Una forma sencilla para resolver estos problemas existen alternativas que reducen el número de elementos activos de un array pleno, sacrificando hasta cierto punto la calidad de imagen, la energía emitida, el rango dinámico, el contraste, etc. Nosotros planteamos una estrategia diferente, y es desarrollar una metodología de optimización capaz de hallar de forma sistemática configuraciones de arrays de ultrasonido adaptados a aplicaciones específicas. Para realizar dicha labor proponemos el uso de los algoritmos evolutivos para buscar y seleccionar en el espacio de configuraciones de arrays aquellas que mejor se adaptan a los requisitos fijados por cada aplicación. En la memoria se trata el problema de la codificación de las configuraciones de arrays para que puedan ser utilizados como individuos de la población sobre la que van a actuar los algoritmos evolutivos. También se aborda la definición de funciones de idoneidad que permitan realizar comparaciones entre dichas configuraciones de acuerdo con los requisitos y restricciones de cada problema de diseño. Finalmente, se propone emplear el algoritmo multiobjetivo NSGA II como herramienta primaria de optimización y, a continuación, utilizar algoritmos mono-objetivo tipo Simulated Annealing para seleccionar y retinar las soluciones proporcionadas por el NSGA II. Muchas de las funciones de idoneidad que definen las características deseadas del array a diseñar se calculan partir de uno o más patrones de radiación generados por cada solución candidata. La obtención de estos patrones con los métodos habituales de simulación de campo acústico en banda ancha requiere tiempos de cálculo muy grandes que pueden hacer inviable el proceso de optimización con algoritmos evolutivos en la práctica. Como solución, se propone un método de cálculo en banda estrecha que reduce en, al menos, un orden de magnitud el tiempo de cálculo necesario Finalmente se presentan una serie de ejemplos, con arrays lineales y bidimensionales, para validar la metodología de diseño propuesta comparando experimentalmente las características reales de los diseños construidos con las predicciones del método de optimización. ABSTRACT Currently, the ultrasound imaging system is one of the powerful tools in medical diagnostic and non-destructive testing for industrial applications. Ultrasonic arrays design determines the beam characteristics (main and secondary lobes, beam pattern, etc...) which assist to enhance the image resolution. The maximum distance between the elements of the array should be the half of the wavelength to avoid the formation of grating lobes. At the same time, the image resolution of the target in the region of interest increases with the aperture size. Consequently, the larger number of elements in arrays assures the better image quality but this improvement contains the following drawbacks: Difficulties in the arrays manufacturing due to the large connection density. Low noise to signal ratio. Complexity of the ultrasonic system to handle large number of channels. The easiest way to resolve these issues is to reduce the number of active elements in full arrays, but on the other hand the image quality, dynamic range, contrast, etc, are compromised by this solutions In this thesis, an optimization methodology able to find ultrasound array configurations adapted for specific applications is presented. The evolutionary algorithms are used to obtain the ideal arrays among the existing configurations. This work addressed problems such as: the codification of ultrasound arrays to be interpreted as individuals in the evolutionary algorithm population and the fitness function and constraints, which will assess the behaviour of individuals. Therefore, it is proposed to use the multi-objective algorithm NSGA-II as a primary optimization tool, and then use the mono-objective Simulated Annealing algorithm to select and refine the solutions provided by the NSGA I I . The acoustic field is calculated many times for each individual and in every generation for every fitness functions. An acoustic narrow band field simulator, where the number of operations is reduced, this ensures a quick calculation of the acoustic field to reduce the expensive computing time required by these functions we have employed. Finally a set of examples are presented in order to validate our proposed design methodology, using linear and bidimensional arrays where the actual characteristics of the design are compared with the predictions of the optimization methodology.

Multi-criteria optimization manipulator trajectory planning

In the last twenty years genetic algorithms (GAs) were applied in a plethora of fields such as: control, system identification, robotics, planning and scheduling, image processing, and pattern and speech recognition (Bäck et al., 1997). In robotics the problems of trajectory planning, collision avoidance and manipulator structure design considering a single criteria has been solved using several techniques (Alander, 2003). Most engineering applications require the optimization of several criteria simultaneously. Often the problems are complex, include discrete and continuous variables and there is no prior knowledge about the search space. These kind of problems are very more complex, since they consider multiple design criteria simultaneously within the optimization procedure. This is known as a multi-criteria (or multiobjective) optimization, that has been addressed successfully through GAs (Deb, 2001). The overall aim of multi-criteria evolutionary algorithms is to achieve a set of non-dominated optimal solutions known as Pareto front. At the end of the optimization procedure, instead of a single optimal (or near optimal) solution, the decision maker can select a solution from the Pareto front. Some of the key issues in multi-criteria GAs are: i) the number of objectives, ii) to obtain a Pareto front as wide as possible and iii) to achieve a Pareto front uniformly spread. Indeed, multi-objective techniques using GAs have been increasing in relevance as a research area. In 1989, Goldberg suggested the use of a GA to solve multi-objective problems and since then other researchers have been developing new methods, such as the multi-objective genetic algorithm (MOGA) (Fonseca & Fleming, 1995), the non-dominated sorted genetic algorithm (NSGA) (Deb, 2001), and the niched Pareto genetic algorithm (NPGA) (Horn et al., 1994), among several other variants (Coello, 1998). In this work the trajectory planning problem considers: i) robots with 2 and 3 degrees of freedom (dof ), ii) the inclusion of obstacles in the workspace and iii) up to five criteria that are used to qualify the evolving trajectory, namely the: joint traveling distance, joint velocity, end effector / Cartesian distance, end effector / Cartesian velocity and energy involved. These criteria are used to minimize the joint and end effector traveled distance, trajectory ripple and energy required by the manipulator to reach at destination point. Bearing this ideas in mind, the paper addresses the planning of robot trajectories, meaning the development of an algorithm to find a continuous motion that takes the manipulator from a given starting configuration up to a desired end position without colliding with any obstacle in the workspace. The chapter is organized as follows. Section 2 describes the trajectory planning and several approaches proposed in the literature. Section 3 formulates the problem, namely the representation adopted to solve the trajectory planning and the objectives considered in the optimization. Section 4 studies the algorithm convergence. Section 5 studies a 2R manipulator (i.e., a robot with two rotational joints/links) when the optimization trajectory considers two and five objectives. Sections 6 and 7 show the results for the 3R redundant manipulator with five goals and for other complementary experiments are described, respectively. Finally, section 8 draws the main conclusions.

Multiarea optimal power flow using multiobjective evolutionary algorithm

In this work the multiarea optimal power flow (OPF) problem is decoupled into areas creating a set of regional OPF subproblems. The objective is to solve the optimal dispatch of active and reactive power for a determined area, without interfering in the neighboring areas. The regional OPF subproblems are modeled as a large-scale nonlinear constrained optimization problem, with both continuous and discrete variables. Constraints violated are handled as objective functions of the problem. In this way the original problem is converted to a multiobjective optimization problem, and a specifically-designed multiobjective evolutionary algorithm is proposed for solving the regional OPF subproblems. The proposed approach has been examined and tested on the RTS-96 and IEEE 354-bus test systems. Good quality suboptimal solutions were obtained, proving the effectiveness and robustness of the proposed approach. ©2009 IEEE.

Double-objective economic statistical design of the VP T-2 control chart: Wald's identity approach

Research has shown that applying the T-2 control chart by using a variable parameters (VP) scheme yields rapid detection of out-of-control states. In this paper, the problem of economic statistical design of the VP T-2 control chart is considered as a double-objective minimization problem with the statistical objective being the adjusted average time to signal and the economic objective being expected cost per hour. We then find the Pareto-optimal designs in which the two objectives are met simultaneously by using a multi-objective genetic algorithm. Through an illustrative example, we show that relatively large benefits can be achieved by applying the VP scheme when compared with usual schemes, and in addition, the multi-objective approach provides the user with designs that are flexible and adaptive.