Multiple Criteria Optimization

The demand for high-speed craft (mainly catamarans) used as passenger vessel has increased significantly in the recent years. Looking towards the future and trying to respond to the increasing requirement, high-speed crafts international market is passing through deep changes. Different types of high-speed crafts are being used for passenger transport. However, catamarans and monohulls have been the main choice not only for passenger vessel but also as ferryboat. Generally speaking, the efficient hydrodynamic hull shapes, engine improvements, and lighter hull structures using aluminum and composite materials make possible the increase in cruising speed. The high demand for catamarans are due to its proven performance in calm waters, large deck area compared to monohull crafts and higher speed efficiency using less power. Although the advantages aforementioned, the performance of catamaran vessels in wave conditions still needs to be improved. The high-speed crafts (HSC) market is demanding different HSC designs and a wide range of dimensions focusing on lower resistance and power for higher speed. Therefore, the hull resistance optimization is a key element for a high-speed hull success. In addition to that, trade-off high-speed catamaran (HSCat) design has been improved to achieve main characteristics and hull geometry. This paper presents a contribution to HSCat preliminary design phase. The HSCat preliminary design problem is raised and one solution is attained by multiple criteria optimization technique. The mathematical model was developed considering: hull arrangement (area and volume), lightweight material application (aluminum hull), hull resistance evaluation (using a slender body theory), as well as wave interference effect between hulls, calculated with 3D theory application. Goal programming optimization system was applied to solve the HSCat preliminary design. Finally this paper includes an illustrative example showing the mathematical model and the optimization solution. An HSCat passenger inland transport in Amazon area preliminary design was used as case study. The problem is presented, the main constrains analyzed and the optimum solution shown. Trade off graphs was also included to highlight the mathematical model convergence process.

The practical problem we are trying to model is: we have to cover a room with a material (carpet or linolleum). This material is in a roll of fixed width. We want to cover the room with a minimum number of pieces and to waste a minimum amount of material. We ...

The practical problem we are trying to model is: we have to cover a room with a material (carpet or linolleum). This material is in a roll of fixed width. We want to cover the room with a minimum number of pieces and to waste a minimum amount of material. We ...

Research in combinatorial optimization initially focused on finding optimal solutions to various problems. Researchers realized the importance of alternative approaches when faced with large practical problems that took too long to solve optimally and this led to approaches like simulated annealing and genetic algorithms which could not guarantee optimality, but yielded good solutions within a reasonable amount of computing time. In this paper we report on our experiments with stochastic greedy algorithms (SGA)perturbed versions of standard greedy algorithms. SGA incorporates the novel idea of learning from optimal solutions, inspired by data-mining and other learning approaches. SGA learns some characteristics of optimal solutions and then applies them while generating its solutions. We report results based on applying this approach to three different problemsknapsack, combinatorial auctions and single-machine job sequencing. Overall, the method consistently produces solutions significantly closer to optimal than standard greedy approaches. SGA can be seen in the space of approximate algorithms as falling between the very quick greedy approaches and the relatively slower soft computing approaches like genetic algorithms and simulated annealing. SGA is easy to understand and implement --once a greedy solution approach is known for a problem, it becomes possible to very quickly rig up a SGA for the problem. SGA has explored only one aspect of learning from optimal solutions. We believe that there is a lot of scope for variations on the theme, and the broad idea of learning from optimal solutions opens up possibilities for new streams of research.

Research in combinatorial optimization initially focused on finding optimal solutions to various problems. Researchers realized the importance of alternative approaches when faced with large practical problems that took too long to solve optimally and this led to approaches like simulated annealing and genetic algorithms which could not guarantee optimality, but yielded good solutions within a reasonable amount of computing time. In this paper we report on our experiments with stochastic greedy algorithms (SGA)perturbed versions of standard greedy algorithms. SGA incorporates the novel idea of learning from optimal solutions, inspired by data-mining and other learning approaches. SGA learns some characteristics of optimal solutions and then applies them while generating its solutions. We report results based on applying this approach to three different problemsknapsack, combinatorial auctions and single-machine job sequencing. Overall, the method consistently produces solutions significantly closer to optimal than standard greedy approaches. SGA can be seen in the space of approximate algorithms as falling between the very quick greedy approaches and the relatively slower soft computing approaches like genetic algorithms and simulated annealing. SGA is easy to understand and implement --once a greedy solution approach is known for a problem, it becomes possible to very quickly rig up a SGA for the problem. SGA has explored only one aspect of learning from optimal solutions. We believe that there is a lot of scope for variations on the theme, and the broad idea of learning from optimal solutions opens up possibilities for new streams of research.

Interim Reports on work of the International Institute for Applied Systems Analysis receive only limited review. Views or opinions expressed herein do not necessarily represent those of the Institute, its National Member Organizations, or other organizations supporting the work.- ii-Foreword Practically all important decisions involve analysis of several (or even many), typically conflicting, criteria. Analysis of trade-offs between criteria is difficult because such trade-offs for most problems are practically impossible to be defined a-priori even by analysts experienced in Multi-Criteria Analysis (MCA). Therefore the trade-offs emerge during an interactive MCA which actually supports a learning process about the trade-offs. How-ever, in some situations an objective MCA is desired, i.e., the trade-offs are elicited rather from the data than from preferences of actual decision-makers. Therefore effective MCA methods are important for actual support of decision-making processes, esp...

One approach to Human Centered Processing is to take into account preferences of users within the context of multiple criteria optimization. The preference model of a problem encloses all the information needed to evaluate the quality of solutions. In this article, we propose a new soft constraint called preference constraint, based on the decision theory concept of binary preference relations. Preference-based constraint systems are defined and a generic algorithm, searching for best quality solutions, is then described. Finally, global constraints, based on a customizable level consistency [39], are proposed for solving the preference constraint associated to the Pareto aggregation rule. This new model offers greater flexibility to represent and make complex decisions on computers. ©

Public organizations lack adequate models and methods to efficiently support and manage processes related to information security and IT investments. The objective is to optimize the management of strategic projects planned to improve the information security of a public organization and make efficient use of its available resources. The deductive method and exploratory research were used to review and analyze the available information. A mathematical model resulted that optimizes two objectives: (1) minimizing the costs of the strategic projects to be executed, and (2) maximizing the percentage of improvement in the organization’s information security. According to the result of the simulation, a subset of planned strategic projects was obtained that allows improving the information security of a public organization from 84.64% to 92.20%, considering the budgetary limitations of the organization. It was concluded that the proposed model is efficient, practical and can be a support ...

Placement of Software Defined Networking (SDN) controllers and forwarders in large networks contexts is still a research open issue, given the different network contexts, providers’ policies and possible optimization criteria. Multicriteria decision algorithms can provide valuable solutions. This paper is an extension of a previous preliminary work, considering here large network environments and the additional problem of forwarding nodes assignment to SDN

This paper introduces a strategy to enrich swarm intelligence algorithms with the preferences of the Decision Maker (DM) represented in an ordinal classifier based on interval outranking. Ordinal classification is used to bias the search toward the Region of Interest (RoI), the privileged zone of the Pareto frontier containing the most satisfactory solutions according to the DM’s preferences. We applied this hybridising strategy to two swarm intelligence algorithms, i.e., Multi-objective Grey Wolf Optimisation and Indicator-based Multi-objective Ant Colony Optimisation for continuous domains. The resulting hybrid algorithms were called GWO-InClass and ACO-InClass. To validate our strategy, we conducted experiments on the DTLZ problems, the most widely studied test suit in the framework of multi-objective optimisation. According to the results, our approach is suitable when many objective functions are treated. GWO-InClass and ACO-InClass demonstrated the capacity of reaching the RoI...

Posttensioned (PT) elements in steel buildings can substantially mitigate permanent seismic damages and the associated post-earthquake repair costs during earthquakes. In this paper, a response surface methodology (RSM) is used to predict and optimize the lateral response characteristics of PT steel beam-column connections with top-and-seat angles. The monotonic lateral response characteristics considered in the study include: initial stiffness, load capacity, and ultimate drift of PT connections, as well as load and drift levels corresponding to the gap-opening (decompression) in PT connections. Based on the results of finite element simulations and extensive sensitivity studies, six influential parameters are considered as input variables in this study. These parameters are posttensioning strand force, beam depth, beam flange thickness and width, span length, and column height. By using a desirability approach, the lateral response of PT steel beam-column connections is optimized. The optimization studies aim at maximizing the initial stiffness, load capacity, and ultimate drift of PT connections and/or minimizing the amount of steel in the beam section, which contributes to the final cost of frame structures. The multi-criteria optimization studies reveal the regions of factor space where optimal conditions are achieved. The optimized solutions are then confirmed by performing simulation runs with the optimal factor combinations. Among the results, it is shown that damage occurs earlier in PT connections with deeper beams and greater posttensioning strand forces. The dominant limit state for the PT connections was beam local buckling starting at early drifts of 1.2%, whereas the first occurrence of angle fracture was at about 4% drifts, and two limit states of strand yielding and bolt extensive yielding were not observed in the analyzed PT connections.

In this study, we investigate a single-item, periodic-review inventory problem where the production capacity is limited and unmet demand is backordered. We assume that customer demand in each period is a stationary, discrete random variable. Linear holding and backorder cost are charged per unit at the end of a period. In addition to the variable cost charged per unit ordered, a positive fixed ordering cost is incurred with each order given. The optimization criterion is the minimization of the expected cost per period over a planning horizon. We investigate the infinite horizon problem by modeling the problem as a discrete-time Markov chain. We propose a heuristic for the problem based on a particular solution of this stationary model, and conduct a computational study on a set of instances, providing insight on the performance of the heuristic.

Optimal path planning in dynamic environments for an unmanned vehicle is a complex task of mobile robotics that requires an integrated approach. This paper describes a path planning algorithm, which allows to build a preliminary motion trajectory using global information about environment, and then dynamically adjust the path in real-time by varying objective function weights. We introduce a set of key parameters for path optimization and the algorithm implementation in MATLAB. The developed algorithm is suitable for fast and robust trajectory tuning to a dynamically changing environment and is capable to provide efficient planning for mobile robots.

Optimal path planning in dynamic environments for an unmanned vehicle is a complex task of mobile robotics that requires an integrated approach. This paper describes a path planning algorithm, which allows to build a preliminary motion trajectory using global information about environment, and then dynamically adjust the path in real-time by varying objective function weights. We introduce a set of key parameters for path optimization and the algorithm implementation in MATLAB. The developed algorithm is suitable for fast and robust trajectory tuning to a dynamically changing environment and is capable to provide efficient planning for mobile robots.

The leximin ranking of vectors of values taken from a totally ordered set is sometimes encountered in ®elds like operational research, social choice or numerical analysis, but has seldom been studied in connexion with fuzzy optimization. In this paper we prove that a leximin-optimal solution to a vector ranking problem on the unit hypercube can be obtained as the limit of optimal solutions to a problem of fuzzy multiple criteria optimization where fuzzy sets are aggregated either using a triangular norm or a generalized mean or an ordered weighted average (OWA) operation.

The finance industry relies heavily on the risk modelling and analysis toolbox to assess the risk profiles of entities such as individual and corporate borrowers and investment vehicles. Such toolbox includes a variety of parametric and non-parametric methods for predicting risk class belonging. In this paper, we expand such toolbox by proposing an integrated framework for implementing a full classification analysis based on a reference point method; namely, in-sample classification and out-of-sample classification. The empirical performance of the proposed reference point method-based classifier is tested on a UK dataset of bankrupt and non-bankrupt firms. Our findings conclude that the proposed classifier can deliver a very high predictive performance, which makes it a real contender in industry applications in banking and investment. Three main features of the proposed classifier drive its outstanding performance; namely, its nonparametric nature, the design of our RPM score-based cutoff point procedure for in-sample classification, and the choice of a k-Nearest Neighbour as an out-of-sample classifier which is trained on the in-sample classification provided by the reference point method based classifier.

Two of the main approaches in multiple criteria optimization are optimization over the efficient set and utility function program. These are nonconvex optimization problems in which local optima can be different from global optima. Existing global optimization methods for solving such problems can only work well for problems of moderate dimensions. In this article, we propose some ways to reduce the number of criteria and the dimension of a linear multiple criteria optimization problem. By the concept of so-called representative and extreme criteria, which is motivated by the concept of redundant (or nonessential) objective functions of Gal and Leberling, we can reduce the number of criteria without altering the set of efficient solutions. Furthermore, by using linear independent criteria, the linear multiple criteria optimization problem under consideration can be transformed into an equivalent linear multiple criteria optimization problem in the space of linear independent criteria. This equivalence is understood in a sense that efficient solutions of each problem can be derived from efficient solutions of the other by some affine transformation. As a result, such criteria and dimension reduction techniques could help to increase the efficiency of existing algorithms and to develop new methods for handling global optimization problems arisen from multiple objective optimization.

One of the most important and interesting approaches in multiple criteria optimization is the problem of optimizing some function over the set of ecient solutions. This is a very dicult multiextremal global optimization problem, even for the case that the underlying multiple criteria program is linear and the function to be optimized over the ecient set is linear as well. In this article, we consider the problem of maximizing a special function over the ecient set of a multiple criteria concave maximization problem under the assumption that the objective function is a nondecreasing composite quasiconvex function of the concave criteria. We show that this problem can be formulated as a special global optimization problem in the outcome space. An algorithm of the outer approximation type is proposed for solving the resulting problem. Preliminary computational experiments show that this algorithm can work well for problems with a small number of criteria (less than 8), while the dimension of the decision space can be fairly large.

En el presente artículo se realiza un estudio de diferentes esquemas de solución reflejados en la literatura, que tratan el problema de la distribución de piezas irregulares en superficies planas con anidamiento bidimensional (Nesting). Fueron analizados diferentes esquemas de solución, siendo los que consideran la geometría real de la pieza, durante la evaluación y posicionamiento de las mismas sobre la superficie a cortar, los que garantizan el mayor aprovechamiento del material. El esquema propuesto se caracteriza por un tratamiento gráfico de las piezas que permite acelerar el proceso de reconocimiento y evaluación de opciones de acoplamiento entre ellas, así como la creación de poblaciones de conglomerados crecientes para su ubicación definitiva en la superficie a cortar. En la generación de poblaciones de opciones de solución, se utiliza un algoritmo derivado del método de Integración de Variables, además se realiza la comparación de los resultados obtenidos por el método propuesto, con otros resultados generados por procedimientos desarrollados por diferentes autores, alcanzando mejorar los valores de aprovechamiento de material y la reducción del tiempo de generación de soluciones. Palabras claves: Distribución de piezas irregulares en superficies; optimización; Métodos Evolutivos; Anidamiento bidimensional; tratamiento gráfico de contornos de superficies. Irregular parts nesting problem optimization.

En el presente artículo se realiza un estudio de diferentes esquemas de solución reflejados en la literatura, que tratan el problema de la distribución de piezas irregulares en superficies planas con anidamiento bidimensional (Nesting). Fueron analizados diferentes esquemas de solución, siendo los que consideran la geometría real de la pieza, durante la evaluación y posicionamiento de las mismas sobre la superficie a cortar, los que garantizan el mayor aprovechamiento del material. El esquema propuesto se caracteriza por un tratamiento gráfico de las piezas que permite acelerar el proceso de reconocimiento y evaluación de opciones de acoplamiento entre ellas, así como la creación de poblaciones de conglomerados crecientes para su ubicación definitiva en la superficie a cortar. En la generación de poblaciones de opciones de solución, se utiliza un algoritmo derivado del método de Integración de Variables, además se realiza la comparación de los resultados obtenidos por el método propuesto, con otros resultados generados por procedimientos desarrollados por diferentes autores, alcanzando mejorar los valores de aprovechamiento de material y la reducción del tiempo de generación de soluciones. Palabras claves: Distribución de piezas irregulares en superficies; optimización; Métodos Evolutivos; Anidamiento bidimensional; tratamiento gráfico de contornos de superficies. Irregular parts nesting problem optimization.

In this paper, we develop a framework for determining optimal respiratory airflow patterns for a multicompartment lung mechanics system with nonlinear resistance and compliance parameters. First, a nonlinear multicompartment lung mechanics model that accounts for nonlinearities in both the airway resistances and the lung compliances is developed. In particular, we assume that the resistive losses are characterized by a Rohrer-type model with resistive losses defined as the sum of linear and quadratic terms of the airflow. The proposed model is more realistic than those presented in the literature, since it takes into account the heterogeneity of lung anatomy and function as well as the nonlinearity of lung resistance and compliance parameters. This model can be used to provide a better understanding of pulmonary function as well as the process of mechanical ventilation. Next, using the proposed nonlinear multicompartment lung model, we develop a framework for determining optimal respiratory airflow patterns. Specifically, an optimization criterion that involves the minimization of the oxygen consumption of the lung muscles and lung volume acceleration for the inspiratory phase, and the minimization of the elastic potential energy and rapid airflow rate changes for the expiratory phase is formulated and solved. The solution to the formulated optimization problem is derived using classical calculus of variation techniques. Finally, several illustrative numerical examples are presented to illustrate the efficacy of the proposed nonlinear multicompartment lung model and the corresponding optimal airflow patterns. Comparison with experimental data shows that our nonlinear resistance model predicts the airflow patterns more accurately than linear resistance models. Moreover, the optimization criterion used in this paper also provides a more accurate prediction of the optimal airflow patterns.

The skyline is a popular operator to extract records from a database when a record scoring function is not available. However, the result of a skyline query can be very large. The problem addressed in this paper is the automatic selection of a small number (k) of representative skyline records. Existing approaches have only focused on partial aspects of this problem. Some try to identify sets of diverse records giving an overall approximation of the skyline. These techniques, however, are sensitive to the scaling of attributes or to the insertion of non-skyline records into the database. Others exploit some knowledge of the record scoring function to identify the most significant record, but not sets of records representative of the whole skyline. In this paper, we introduce a novel approach taking both the significance of all the records and their diversity into account, adapting to available knowledge of the scoring function, but also working under complete ignorance. We show the intractability of the problem and present approximate algorithms. We experimentally show that our approach is efficient, scalable and that it improves existing works in terms of the significance and diversity of the results.

Present work intends the mathematical modeling and solution algorithm for the optimal materials and it thickness selection of the refractory linning of steel casting ladles task. In it solution the Exploration of Variable Codes Algorithm of the Integration of Variables Method is used. The proposed model constitutes an improvement of the previously published one. The obtained numeric results and their comparison with the published previous algorithm, applied to the proposed model are offered. The numeric comparison of both algorithms sample that the one proposed in this article offers better results that the one used for the comparison.

Hasta el presente, el problema de la selección de materiales refractarios y aislantes no se ha tratado, en toda su complejidad, como una tarea de optimización bajo criterios múltiples, sino básicamente como un problema de carácter metalúrgico. En este artículo, se expone el modelado matemático de la tarea de selección óptima bajo criterios múltiples y se analiza su complejidad matemática, considerando las dimensiones de los materiales por capas y por zonas, y la interacción entre zonas. La complejidad de la tarea formulada requiere su descomposición en tareas más sencillas, por zonas de la cazuela. Se realiza la validación experimental de los resultados numéricos obtenidos, con lo cual se evidencia la eficiencia y la calidad que se obtienen con los procedimientos utilizados. Estos procedimientos se derivan de la aplicación del método de integración de variables. En particular, se utiliza el operador de búsqueda aleatoria del extremo de una función de un código variable aplicado al p...

Deterministic global optimization algorithms like Piyavskii-Shubert, direct, ego and many more, have a recognized standing, for problems with many local optima. Although many single objective optimization algorithms have been extended to multiple objectives, completely deterministic algorithms for nonlinear problems with guarantees of convergence to global Pareto optimality are still missing. For instance, deterministic algorithms usually make use of some form of scalarization, which may lead to incomplete representations of the Pareto optimal set. Thus, all global Pareto optima may not be obtained, especially in nonconvex cases. On the other hand, algorithms attempting to produce representations of the globally Pareto optimal set are usually based on heuristics. We analyze the concept of global convergence for multiobjective optimization algorithms and propose a convergence criterion based on the Hausdorff distance in the decision space. Under this light, we consider the well-known global optimization algorithm direct, analyze the available algorithms in the literature that extend direct to multiple objectives and discuss possible alternatives. In particular, we propose a novel definition for the notion of potential Pareto optimality extending the notion of potential optimality defined in direct. We also discuss its advantages and disadvantages when compared with algorithms existing in the literature.

A new interactive multiple objective programming procedure is developed that combines the strengths of the Interactive Weighted Tchebycheff Procedure (Steuer and Choo 1983) and the Interactive FFANN Procedure (Sun, Stam and Steuer 1993). In this new procedure, nondominated trial solutions are generated by solving Augmented Weighted Tchebycheff Programs (Steuer 1986), based on which the decision maker articulates his/her preference information by assigning "values" to these solutions or by making pairwise comparisons. The elicited preference information is used to train a feed-forward artificial neural network, which in turn is used to screen new trial solutions for presentation to decision maker in the next iteration. Computational results are reported, comparing the current procedure with the Interactive Weighted Tchebycheff Procedure and the Interactive FFANN Procedure. The results show that this new procedure yields good quality solutions.

Although Cape Town city in South Africa is generally regarded as the most stable and prosperous city in the region, there are still approximately 7.5 million people living in informal settlements and about 2.5 million housing units are needed. This motivates the so-called Empower Shack project, aiming to develop upgrading strategies for these informal settlements. To facilitate the fulfillment of this project, urban design prototyping tools are researched and developed with the capabilities for fast urban design synthesis. In this paper we present a computational method for fast interactive synthesis of urban planning prototypes. For the generation of mock-up urban layouts, one hierarchical slicing structure, namely, the slicing tree is introduced to abstractly represent the parcels, as an extension of the existing generative method for street network. It has been proved that our methods can interactively assist the urban planning process in practice. However, the slicing tree data structure has several limitations that hinder the further improvement of the generated urban layouts. In the future, the development of a new data structure is required to fulfill urban synthesis for urban layout generation with Evolutionary Multi-objective Optimization methods and evaluation strategies should be developed to verify the generated results.

In this work a multicriteria simulation optimization method previously developed in our research group was applied to the experimental optimization of a 3D printed prototype. Both, simulation and prototyping, share the objective of providing as much information as possible about a product before its actual manufacturing. The prototype is an interlocking device that can be assembled without fastening devices or substances and reassembled into different planar assemblies. The design of the prototype considers two conflicting criteria simultaneously: maximal flexural strength and minimal mass. Multicriteria simulation optimization allows to manipulate a set of design variables to identify configurations with the best possible balances among both criteria. This method consists of an iterative framework based on experimental design and Pareto efficiency conditions. The aim of this work is to show the potential of the method beyond its initial intended use in simulation to approach truly experimental work.

Proportional fairness has been shown to maximize the aggregate utility of rate control for elastic traffic in a resource sharing communication network, and has been applied to a broad range of resource allocation problems. For a refined analysis, however, the representation of proportional fairness as a relation between vectors with positive components will often not provide the level of detail that is needed. Therefore, we study the representation as a fuzzy relation, and propose several ways to specify a measure function to allocate a degree of (proportional) relatedness. The approaches are based on combinatorial aspects, especially size and number of related subvectors, and geometric aspects, especially the minimum effort to change a vector to become related. A case study demonstrates that the introduced fuzzy fairness relations can be used to numerically evaluate the suitability of the maxmin fair state to represent the proportional fair state in a resource sharing network problem with maximum link capacities.

This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. Highlights • Investigate a winner determination problem of a flexible iterative combinatorial auction.

One of the major shortcomings of widely used<br> scientometric indicators is that different disciplines cannot be<br> compared with each other. The issue of cross-disciplinary<br> normalization has been long discussed, but even the classification<br> of publications into scientific domains poses problems. Structural<br> properties of citation networks offer new possibilities, however, the<br> large size and constant growth of these networks asks for precaution.<br> Here we present a new tool that in order to perform cross-field<br> normalization of scientometric indicators of individual publications<br> relays on the structural properties of citation networks. Due to the<br> large size of the networks, a systematic procedure for identifying<br> scientific domains based on a local community detection algorithm<br> is proposed. The algorithm is tested with different benchmark<br> and real-world networks. The...

We study how visual interaction techniques considered in visual analytics can be utilized when implementing interactive multiobjective optimization methods, where a decision maker iteratively participates in the solution process. We want to benefit from previous research and avoid re-inventing ideas. Our aim is to widen awareness and increase the applicability of interactive methods for solving real-world problems. As a concrete approach, we introduce seven high-level tasks that are relevant for interactive methods. These high-level tasks are based on low-level tasks proposed in the visual analytics literature. In addition, we give an example on how the high-level tasks can be implemented and demonstrate this in the context of a real-world multiobjective optimization problem related to wastewater treatment plant operation. Finally, we make recommendations for implementations of interactive methods. We conclude that task-based visual analytics can help in implementing interaction between human decision makers and interactive multiobjective optimization methods.

In this work, we propose a new technique for efficiently exploring a multiobjective design space to find non-dominated solutions in the presence of uncertainty. Our approach uses a two-stage optimization technique. In the first-stage, the design problem is represented by a multi-objective optimization problem considering the performances associated with design parameters. In the second stage, the design problem is expressed as a single objective optimization problem taking into account the operating performances of the process under uncertainty. We propose a new hybrid algorithm to efficiently explore a multi-objective design space. Our algorithm combines the advantage of both gradient-based and non-gradient-based optimization algorithm. A genetic algorithm (GA) is used to handle the multi-objective optimization problem in the first stage. In comparison, the sequential quadratic programming (SQP) method with problem decomposition is applied to solve the sub-problems in the second stage. Our proposed technique can improve the speed of computation and reduce computational time. The proposed methodology is implemented by integrating in-house software with commercial software. We illustrate the applicability of the proposed methodology in a case study.

Public and private organizations continuously invest on projects. With a number of candidate projects bigger than those ones that can be funded, the organization faces the problem of selecting a portfolio of projects that maximizes the expected benefits. The selection is made on the evaluation of project groups and not on the evaluation of single projects. However, there is a factor that must be taken account, since it can significantly change the evaluation of groups: synergy. This is that two or more projects are complemented in a way that generates an additional benefit to they already own individually. Redundancy, a special case of synergy, occurs when two or more projects cannot be financed simultaneously. Both features add complexity to the evaluation of project groups. This article presents an evaluation of the two most used alternatives for handling synergy, in order to incorporate it into an ant-colony metaheuristic for solving project portfolio selection.

Background: The study of the prehistoric origins and dispersal routes of domesticated plants is often based on the analysis of either archaeobotanical or genetic data. As more data become available, spatially explicit models of crop dispersal can be used to combine different types of evidence. Methodology/Principal Findings: We present a model in which a crop disperses through a landscape that is represented by a conductance matrix. From this matrix, we derive least-cost distances from the geographical origin of the crop and use these to predict the age of archaeological crop remains and the heterozygosity of crop populations. We use measures of the overlap and divergence of dispersal trajectories to predict genetic similarity between crop populations. The conductance matrix is constructed from environmental variables using a number of parameters. Model parameters are determined with multiple-criteria optimization, simultaneously fitting the archaeobotanical and genetic data. The consilience reached by the model is the extent to which it converges around solutions optimal for both archaeobotanical and genetic data. We apply the modelling approach to the dispersal of maize in the Americas. Conclusions/Significance: The approach makes possible the integrative inference of crop dispersal processes, while controlling model complexity and computational requirements.

In outbound systems, a computer automatically calls designated parties from a given list. The computer recognizes and processes busy signals, no-answers, and telephone company messages. Answered calls are routed to call center agents. Typically, the computer predicts when agents will become free and dials in anticipation of agent availability, thereby reducing the time agents wait between connections. A key analytical challenge is to determine the pacing, that is, when to dial the next call. If the pacing is too slow, agent time is wasted. If the pacing is too fast, a called party answers when no agent is available, creating a nuisance for the called party (who usually hangs up), a wasted expense for the system. Research in this area is mostly proprietary; there is scant research literature. The solution resulted in the first U.S. patent based on queueing theory (Samuelson 1989). This method estimates service durations, times from dialing to answer, and proportions of dial attempts that result in answers, and uses these statistics, updated frequently, to synchronize dialing attempts to finish shortly after predicted agent service completions (Samuelson 1999). Other patents, such as David (1997), expand and extend this method.

One approach to Human Centered Processing is to take into account preferences of users within the context of multiple criteria optimization. The preference model of a problem encloses all the information needed to evaluate the quality of solutions. In this article, we propose a new soft constraint called preference constraint, based on the decision theory concept of binary preference relations. Preference-based constraint systems are defined and a generic algorithm, searching for best quality solutions, is then described. Finally, global constraints, based on a customizable level consistency [39], are proposed for solving the preference constraint associated to the Pareto aggregation rule. This new model offers greater flexibility to represent and make complex decisions on computers. ©

The paper presents a multi-criteria optimization approach to modeling negotiation process. The negotiation process is modeled as a special multi-criteria problem. The method for finding solutions is the interactive selection process of some proposals. The parties shall submit their proposals on the subjects of the negotiations. These proposals are parameters of the multi-criteria optimization problem. Selection of solutions is accomplished by solving the optimization problem with parameters that define the aspirations of each party involved in the negotiations. Finally, evaluation of the solutions obtained by the parties is made.

Ecosystem service research has gained attraction, and the topic is also high on the policy agenda. Projects such as TEEB have generalized results of individual case studies to provide guidelines for policy makers and stakeholders. Seppelt et al. (2011) raised critical questions about four facets that characterize the holistic ideal of ecosystem services research: (i) biophysical realism of ecosystem data and models; (ii) consideration of trade-offs between ecosystem services; (iii) recognition of off-site effects; and (iv) comprehensive but shrewd involvement of stakeholders within assessment studies. An extended and updated analysis of ecosystem service case studies showed that the majority of these facets were still not addressed by the majority of case studies. Whilst most indicators did not improve within the span analyzed (1996-2013), we found a tendency for an increasing geographical spread of the case studies. Moreover, we incorporated an additional facet, namely the relevanc...

The finance industry relies heavily on the risk modelling and analysis toolbox to assess the risk profiles of entities such as individual and corporate borrowers and investment vehicles. Such toolbox includes a variety of parametric and non-parametric methods for predicting risk class belonging. In this paper, we expand such toolbox by proposing an integrated framework for implementing a full classification analysis based on a reference point method; namely, in-sample classification and out-of-sample classification. The empirical performance of the proposed reference point method-based classifier is tested on a UK dataset of bankrupt and non-bankrupt firms. Our findings conclude that the proposed classifier can deliver a very high predictive performance, which makes it a real contender in industry applications in banking and investment. Three main features of the proposed classifier drive its outstanding performance; namely, its nonparametric nature, the design of our RPM score-based cutoff point procedure for in-sample classification, and the choice of a k-Nearest Neighbour as an out-of-sample classifier which is trained on the in-sample classification provided by the reference point method based classifier.

Interactive multiobjective optimization methods cannot necessarily be easily used when (industrial) multiobjective optimization problems are involved. There are at least two important factors to be considered with any interactive method: computationally expensive functions and aspects of human behavior. In this paper, we propose a method based on the existing NAUTILUS method and call it the Enhanced NAUTILUS (E-NAUTILUS) method. This method borrows the motivation of NAUTILUS along with the human aspects related to avoiding trading-off and anchoring bias and extends its applicability for computationally expensive multiobjective optimization problems. In the E-NAUTILUS method, a set of Pareto optimal solutions is calculated in a pre-processing stage before the decision maker is involved. When the decision maker interacts with the solution process in the interactive decision making stage, no new optimization problem is solved, thus, avoiding the waiting time for the decision maker to obtain new solutions according to her/his preferences. In this stage, starting from the worst possible objective function values, the decision maker is shown a set of points in the objective space, from which (s)he chooses one as the preferable point. At successive iterations, (s)he always sees points which improve all the objective values achieved by the previously chosen point. In this way, the decision maker remains focused on the solution process, as there is no loss in any objective function value between successive iterations. The last post-processing stage ensures the Pareto optimality of the final solution. A real-life engineering problem is used to demonstrate how E-NAUTILUS works in practice.

Many recent applications involve processing and analyzing uncertain data. In this paper, we combine the feature of top-k objects with that of skyline to model the problem of top-k skyline objects against uncertain data. The problem of efficiently computing top-k skyline objects on large uncertain datasets is challenging in both discrete and continuous cases. In this paper, firstly an efficient exact algorithm for computing the top-k skyline objects is developed for discrete cases. To address applications where each object may have a massive set of instances or a continuous probability density function, we also develop an efficient randomized algorithm with an E-approximation guarantee. Moreover, our algorithms can be immediately extended to efficiently compute p-skyline; that is, retrieving the uncertain objects with skyline probabilities above a given threshold. Our extensive experiments on synthetic and real data demonstrate the efficiency of both algorithms and the randomized algorithm is highly accurate. They also show that our techniques significantly outperform the existing techniques for computing p-skyline.

The problem of aggregating multiple criteria to form an overall measure is of considerable importance in many disciplines. The ordered weighted averaging (OWA) aggregation, introduced by Yager, uses weights assigned to the ordered values rather than to the specific criteria. This allows one to model various aggregated preferences, preserving simultaneously the impartiality (neutrality) with respect to the individual criteria. However, importance weighted averaging is a central task in multicriteria decision problems of many kinds. It can be achieved with the Weighted OWA (WOWA) aggregation, introduced by Torra, covering both the weighted means and the OWA averages as special cases. In this paper we analyze the monotonicity properties of the WOWA aggregation with respect to changes of importance weights. In particular, we demonstrate that a rank reversal phenomenon may occur in the sense that increasing the importance weight for a given criterion may enforce the opposite WOWA ranking than that imposed by the criterion values.

A Markov decision process (MDP) is a general model for solving planning problems under uncertainty. It has been extended to multiobjective MDP to address multicriteria or multiagent problems in which the value of a decision must be evaluated according to several viewpoints, sometimes conflicting. Although most of the studies concentrate on the determination of the set of Pareto-optimal policies, we focus here on a more specialized problem that concerns the direct determination of policies achieving well-balanced tradeoffs. To this end, we introduce a reference point method based on the optimization of a weighted ordered weighted average (WOWA) of individual disachievements. We show that the resulting notion of optimal policy does not satisfy the Bellman principle and depends on the initial state. To overcome these difficulties, we propose a solution method based on a linear programming (LP) reformulation of the problem. Finally, we illustrate the feasibility of the proposed method o...

We discuss design issues pertaining to multiple issue auctions in the WWW environment. Based on a critical evaluation of existing auctions, we propose NegotiAuction tm , an algorithmic Internet-based auction procedure, which combines certain elements of negotiations and auctions 1. It can be used either in reverse or forward auctions. When defining a multiple issue (multiple attribute) auction, the auction owner has more control over the bidding process than is possible in traditional auctions, signaling bid requirements to the bidders individually. This will result in a preferred set of auction winners. It is believed to reduce the total transaction time and eliminate the necessity of holding subsequent negotiations with the set of winners.