Enhanced Multi-Objective A* with Partial Expansion

The Multi-Objective Shortest Path Problem (MO-SPP), typically posed on a graph, determines a set of paths from a start vertex to a destination vertex while optimizing multiple objectives. In general, there does not exist a single solution path that can simultaneously optimize all the objectives and the problem thus seeks to find a set of so-called Pareto-optimal solutions. To address this problem, several Multi-Objective A* (MOA*) algorithms were recently developed to quickly compute solutions with quality guarantees. However, these MOA* algorithms often suffer from high memory usage, especially when the branching factor (i.e. the number of neighbors of any vertex) of the graph is large. This work thus aims at reducing the high memory consumption of MOA* with little increase in the runtime. By generalizing and unifying several single- and multi-objective search algorithms, we develop the Runtime and Memory Efficient MOA* (RME-MOA*) approach, which can balance between runtime and memory efficiency by tuning two user-defined hyper-parameters.Comment: 8 pages, 4 figure

Optimal Placement of Water Quality Monitoring Stations in Sewer Systems: An Information Theory Approach

A core problem associated with the water quality monitoring in the sewer system is the optimal placement of a limited number of monitoring sites. A methodology is provided for optimally design water quality monitoring stations in sewer networks. The methodology is based on information theory, formulated as a multi-objective optimization problem and solved using NSGA-II. Computer code is written to estimate two entropy quantities, namely Joint Entropy, a measure of information content, and Total Correlation, a measure of redundancy, which are maximized and minimized, respectively. The test on a real sewer network suggests the effectiveness of the proposed methodology

Multi-objective optimization in graphical models

Many real-life optimization problems are combinatorial, i.e. they concern a choice of the best solution from a finite but exponentially large set of alternatives. Besides, the solution quality of many of these problems can often be evaluated from several points of view (a.k.a. criteria). In that case, each criterion may be described by a different objective function. Some important and well-known multicriteria scenarios are: · In investment optimization one wants to minimize risk and maximize benefits. · In travel scheduling one wants to minimize time and cost. · In circuit design one wants to minimize circuit area, energy consumption and maximize speed. · In knapsack problems one wants to minimize load weight and/or volume and maximize its economical value. The previous examples illustrate that, in many cases, these multiple criteria are incommensurate (i.e., it is difficult or impossible to combine them into a single criterion) and conflicting (i.e., solutions that are good with respect one criterion are likely to be bad with respect to another). Taking into account simultaneously the different criteria is not trivial and several notions of optimality have been proposed. Independently of the chosen notion of optimality, computing optimal solutions represents an important current research challenge. Graphical models are a knowledge representation tool widely used in the Artificial Intelligence field. They seem to be specially suitable for combinatorial problems. Roughly, graphical models are graphs in which nodes represent variables and the (lack of) arcs represent conditional independence assumptions. In addition to the graph structure, it is necessary to specify its micro-structure which tells how particular combinations of instantiations of interdependent variables interact. The graphical model framework provides a unifying way to model a broad spectrum of systems and a collection of general algorithms to efficiently solve them. In this Thesis we integrate multi-objective optimization problems into the graphical model paradigm and study how algorithmic techniques developed in the graphical model context can be extended to multi-objective optimization problems. As we show, multiobjective optimization problems can be formalized as a particular case of graphical models using the semiring-based framework. It is, to the best of our knowledge, the first time that graphical models in general, and semiring-based problems in particular are used to model an optimization problem in which the objective function is partially ordered. Moreover, we show that most of the solving techniques for mono-objective optimization problems can be naturally extended to the multi-objective context. The result of our work is the mathematical formalization of multi-objective optimization problems and the development of a set of multiobjective solving algorithms that have been proved to be efficient in a number of benchmarks.Muchos problemas reales de optimización son combinatorios, es decir, requieren de la elección de la mejor solución (o solución óptima) dentro de un conjunto finito pero exponencialmente grande de alternativas. Además, la mejor solución de muchos de estos problemas es, a menudo, evaluada desde varios puntos de vista (también llamados criterios). Es este caso, cada criterio puede ser descrito por una función objetivo. Algunos escenarios multi-objetivo importantes y bien conocidos son los siguientes: · En optimización de inversiones se pretende minimizar los riesgos y maximizar los beneficios. · En la programación de viajes se quiere reducir el tiempo de viaje y los costes. · En el diseño de circuitos se quiere reducir al mínimo la zona ocupada del circuito, el consumo de energía y maximizar la velocidad. · En los problemas de la mochila se quiere minimizar el peso de la carga y/o el volumen y maximizar su valor económico. Los ejemplos anteriores muestran que, en muchos casos, estos criterios son inconmensurables (es decir, es difícil o imposible combinar todos ellos en un único criterio) y están en conflicto (es decir, soluciones que son buenas con respecto a un criterio es probable que sean malas con respecto a otra). Tener en cuenta de forma simultánea todos estos criterios no es trivial y para ello se han propuesto diferentes nociones de optimalidad. Independientemente del concepto de optimalidad elegido, el cómputo de soluciones óptimas representa un importante desafío para la investigación actual. Los modelos gráficos son una herramienta para la represetanción del conocimiento ampliamente utilizados en el campo de la Inteligencia Artificial que parecen especialmente indicados en problemas combinatorios. A grandes rasgos, los modelos gráficos son grafos en los que los nodos representan variables y la (falta de) arcos representa la interdepencia entre variables. Además de la estructura gráfica, es necesario especificar su (micro-estructura) que indica cómo interactúan instanciaciones concretas de variables interdependientes. Los modelos gráficos proporcionan un marco capaz de unificar el modelado de un espectro amplio de sistemas y un conjunto de algoritmos generales capaces de resolverlos eficientemente. En esta tesis integramos problemas de optimización multi-objetivo en el contexto de los modelos gráficos y estudiamos cómo diversas técnicas algorítmicas desarrolladas dentro del marco de los modelos gráficos se pueden extender a problemas de optimización multi-objetivo. Como mostramos, este tipo de problemas se pueden formalizar como un caso particular de modelo gráfico usando el paradigma basado en semi-anillos (SCSP). Desde nuestro conocimiento, ésta es la primera vez que los modelos gráficos en general, y el paradigma basado en semi-anillos en particular, se usan para modelar un problema de optimización cuya función objetivo está parcialmente ordenada. Además, mostramos que la mayoría de técnicas para resolver problemas monoobjetivo se pueden extender de forma natural al contexto multi-objetivo. El resultado de nuestro trabajo es la formalización matemática de problemas de optimización multi-objetivo y el desarrollo de un conjunto de algoritmos capaces de resolver este tipo de problemas. Además, demostramos que estos algoritmos son eficientes en un conjunto determinado de benchmarks

A deterministic agent-based path optimization method by mimicking the spreading of ripples

Inspirations from nature have fundamentally contributed to the development of evolutionary computation (EC). This paper, by learning from the natural ripple-spreading phenomenon, proposes a novel ripple-spreading algorithm (RSA) for the path optimization problem (POP). In nature, a ripple spreads at a constant speed in all directions, and the node closest to the source will be the first to be reached. This very simple principle forms the foundation of the proposed RSA. In contrast to most deterministic top-down centralized path optimization methods, such as Dijkstra's algorithm, the RSA is a bottom-up decentralized agent-based simulation model. Moreover, it is distinguished from other agent-based algorithms, such as genetic algorithms and ant colony optimization, by being a deterministic method that can always guarantee the global optimal solution with very good scalability. Here, the RSA is specifically applied to four different POPs. The comparative simulation results presented clearly illustrate the advantages of the RSA in terms of effectiveness and efficiency. Thanks to the combination of both agent-based and deterministic features, the RSA opens new opportunities to attack some problems, such as calculating the exact complete Pareto front in multi-objective optimization and determining the kth shortest project time in project management, which are very difficult, if not impossible, for existing methods to resolve. The ripple-spreading optimization principle, aswell as the new distinguishing features and capacities of RSA, enriches the theoretical foundations of EC

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Multi-objective design of post-tensioned concrete road bridges using artificial neural networks

[EN] In order to minimize the total expected cost, bridges have to be designed for safety and durability. This paper considers the cost, the safety, and the corrosion initiation time to design post-tensioned concrete box-girder road bridges. The deck is modeled by finite elements based on problem variables such as the cross-section geometry, the concrete grade, and the reinforcing and post-tensioning steel. An integrated multi-objective harmony search with artificial neural networks (ANNs) is proposed to reduce the high computing time required for the finite-element analysis and the increment in conflicting objectives. ANNs are trained through the results of previous bridge performance evaluations. Then, ANNs are used to evaluate the constraints and provide a direction towards the Pareto front. Finally, exact methods actualize and improve the Pareto set. The results show that the harmony search parameters should be progressively changed in a diversification-intensification strategy. This methodology provides trade-off solutions that are the cheapest ones for the safety and durability levels considered. Therefore, it is possible to choose an alternative that can be easily adjusted to each need.The authors acknowledge the financial support of the Spanish Ministry of Economy and Competitiveness, along with FEDER funding (BRIDLIFE Project: BIA2014-56574-R) and the Research and Development Support Program of Universitat Politecnica de Valencia (PAID-02-15).García-Segura, T.; Yepes, V.; Frangopol, D. (2017). Multi-objective design of post-tensioned concrete road bridges using artificial neural networks. Structural and Multidisciplinary Optimization. 56(1):139-150. doi:10.1007/s00158-017-1653-0S139150561Alberdi R, Khandelwal K (2015) Comparison of robustness of metaheuristic algorithms for steel frame optimization. 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Ministerio de Fomento, MadridGarcía-Segura T, Yepes V (2016) Multiobjective optimization of post-tensioned concrete box-girder road bridges considering cost, CO2 emissions, and safety. Eng Struct 125:325–336. doi: 10.1016/j.engstruct.2016.07.012García-Segura T, Yepes V, Alcalá J (2014a) Life cycle greenhouse gas emissions of blended cement concrete including carbonation and durability. Int J Life Cycle Assess 19:3–12. doi: 10.1007/s11367-013-0614-0García-Segura T, Yepes V, Martí JV, Alcalá J (2014b) Optimization of concrete I-beams using a new hybrid glowworm swarm algorithm. Lat Am J Solids Struct 11:1190–1205. doi: 10.1590/S1679-78252014000700007García-Segura T, Yepes V, Alcalá J, Pérez-López E (2015) Hybrid harmony search for sustainable design of post-tensioned concrete box-girder pedestrian bridges. Eng Struct 92:112–122. doi: 10.1016/j.engstruct.2015.03.015Geem ZW, Kim JH, Loganathan GV (2001) A new heuristic optimization algorithm: harmony search. 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An Analysis of Some Algorithms and Heuristics for Multiobjective Graph Search

Muchos problemas reales requieren examinar un número exponencial de alternativas para encontrar la elección óptima. A este tipo de problemas se les llama de optimización combinatoria. Además, en problemas reales normalmente se evalúan múltiples magnitudes que presentan conflicto entre ellas. Cuando se optimizan múltiples obje-tivos simultáneamente, generalmente no existe un valor óptimo que satisfaga al mismo tiempo los requisitos para todos los criterios. Solucionar estos problemas combinatorios multiobjetivo deriva comúnmente en un gran conjunto de soluciones Pareto-óptimas, que definen los balances óptimos entre los objetivos considerados. En esta tesis se considera uno de los problemas multiobjetivo más recurrentes: la búsqueda de caminos más cortos en un grafo, teniendo en cuenta múltiples objetivos al mismo tiempo. Se pueden señalar muchas aplicaciones prácticas de la búsqueda multiobjetivo en diferentes dominios: enrutamiento en redes multimedia (Clímaco et al., 2003), programación de satélites (Gabrel & Vanderpooten, 2002), problemas de transporte (Pallottino & Scutellà, 1998), enrutamiento en redes de ferrocarril (Müller-Hannemann & Weihe, 2006), planificación de rutas en redes de carreteras (Jozefowiez et al., 2008), vigilancia con robots (delle Fave et al., 2009) o planificación independiente del dominio (Refanidis & Vlahavas, 2003). La planificación de rutas multiobjetivo sobre mapas de carretera realistas ha sido considerada como un escenario de aplicación potencial para los algoritmos y heurísticos multiobjetivo considerados en esta tesis. El transporte de materias peligrosas (Erkut et al., 2007), otro problema de enrutamiento multiobjetivo relacionado, ha sido también considerado como un escenario de aplicación potencial interesante. Los métodos de optimización de un solo criterio son bien conocidos y han sido ampliamente estudiados. La Búsqueda Heurística permite la reducción de los requisitos de espacio y tiempo de estos métodos, explotando el uso de estimaciones de la distancia real al objetivo. Los problemas multiobjetivo son bastante más complejos que sus equivalentes de un solo objetivo y requieren métodos específicos. Éstos, van desde técnicas de solución exactas a otras aproximadas, que incluyen los métodos metaheurísticos aproximados comúnmente encontrados en la literatura. Esta tesis se ocupa de algoritmos exactos primero-el-mejor y, en particular, del uso de información heurística para mejorar su rendimiento. Esta tesis contribuye análisis tanto formales como empíricos de algoritmos y heurísticos para búsqueda multiobjetivo. La caracterización formal de estos algoritmos es importante para el campo. Sin embargo, la evaluación empírica es también de gran importancia para la aplicación real de estos métodos. Se han utilizado diversas clases de problemas bien conocidos para probar su rendimiento, incluyendo escenarios realistas como los descritos más arriba. Los resultados de esta tesis proporcionan una mejor comprensión de qué métodos de los disponibles sonmejores en situaciones prácticas. Se presentan explicaciones formales y empíricas acerca de su comportamiento. Se muestra que la búsqueda heurística reduce considerablemente los requisitos de espacio y tiempo en la mayoría de las ocasiones. En particular, se presentan los primeros resultados sistemáticos mostrando las ventajas de la aplicación de heurísticos multiobjetivo precalculados. Esta tesis también aporta un método mejorado para el precálculo de los heurísticos, y explora la conveniencia de heurísticos precalculados más informados.Many real problems require the examination of an exponential number of alternatives in order to find the best choice. They are the so-called combinatorial optimization problems. Besides, real problems usually involve the consideration of several conflicting magnitudes. When multiple objectives must be simultaneously optimized, there is generally not an optimal value satisfying the requirements for all the criteria at the same time. Solving these multiobjective combinatorial problems commonly results in a large set of Pareto-optimal solutions, which define the optimal tradeoffs between the objectives under consideration. One of most recurrent multiobjective problems is considered in this thesis: the search for shortest paths in a graph, taking into account several objectives at the same time. Many practical applications of multiobjective search in different domains can be pointed out: routing in multimedia networks (Clímaco et al., 2003), satellite scheduling (Gabrel & Vanderpooten, 2002), transportation problems (Pallottino & Scutellà, 1998), routing in railway networks (Müller-Hannemann & Weihe, 2006), route planning in road maps (Jozefowiez et al., 2008), robot surveillance (delle Fave et al., 2009) or domain independent planning (Refanidis & Vlahavas, 2003). Multiobjective route planning over realistic road maps has been considered as a potential application scenario for the multiobjective algorithms and heuristics considered in this thesis. Hazardous material transportation (Erkut et al., 2007), another related multiobjective routing problem, has also been considered as an interesting potential application scenario. Single criterion shortest path methods are well known and have been widely studied. Heuristic Search allows the reduction of the space and time requirements of these methods, exploiting estimates of the actual distance to the goal. Multiobjective problems are much more complex than their single-objective counterparts, and require specific methods. These range from exact solution techniques to approximate ones, including the metaheuristic approximate methods usually found in the literature. This thesis is concerned with exact best-first algorithms, and particularly, with the use of heuristic information to improve their performance. This thesis contributes both formal and empirical analysis of algorithms and heuristics for multiobjective search. The formal characterization of algorithms is important for the field. However, empirical evaluation is also of great importance for the real application of these methods. Several well known classes of problems have been used to test their performance, including some realistic scenarios as described above. The results of this thesis provide a better understanding of which of the available methods are better in practical situations. Formal and empirical explanations of their behaviour are presented. Heuristic search is shown to reduce considerably space and time requirements in most situations. In particular, the first systematic results showing the advantages of the application of precalculated multiobjective heuristics are presented. The thesis also contributes an improved method for heuristic precalculation, and explores the convenience of more informed precalculated heuristics.This work is partially funded by / Este trabajo está financiado por: Consejería de Economía, Innovación, Ciencia y Empresa. Junta de Andalucía (España) Referencia: P07-TIC-0301

Reservoir management under consideration of stratification and hydraulic phenomena

Reservoirs are the most important components in a water resources system. They are used to store water to extend its temporal availability. The physical, chemical and biological characteristics of water change when impounded in reservoirs. This implies the possibility of using reservoirs for the control of the quality of water besides merely satisfying the quantity requirement. This study presents several techniques formulated to manage a reservoir when both quantity and quality of water are of interest. In this study salinity is selected to characterize the water quality status. The approaches are demonstrated using data from the Jarreh Reservoir on the Shapur river in Iran.Water in a reservoir is stratified for most of a year due to difference in density caused by temperature, dissolved and suspended solids. Therefore, in a stratified reservoir the quality of water that is interrelated to density varies with depth. Consequently, this feature could be used in the process of reservoir operational policy determination to improve the quality of water supply. The aim of this research is to analyze different approaches regarding the incorporation of this phenomenon into reservoir operational policies and to propose those which require the least increase in mathematical and computational complexity.Initially, two techniques that rely on the natural process of stratification occurring in a reservoir are presented. The first methodology proceeds stepwise in time alternating optimization and simulation of reservoir operation at each time step. A one-dimensional reservoir dynamics simulation model is employed to simulate the stratification of the reservoir. A constrained nonlinear optimization model is used to identify optimum releases. In the optimization step the reservoir is assumed to be equivalent to the parallel configuration of several smaller hypothetical reservoirs, the number of which being equal to the number of outlets. There is no communication among these hypothetical reservoirs. The applicability of the technique is tested for three hydrologically different years and for a continuous period of five years. Incorporation of inflow stochasticity into the methodology is devised through the integration of an optimization model based on Stochastic Dynamic Programming technique.Next, an iterative technique, in which an optimization model and a reservoir stratification simulation model operate interactively, is presented. One iteration cycle comprises the run of the optimization model and the simulation model: i) Reservoir operation is optimized over the entire time period (year); ii) Simulation of stratification is applied over the entire time period. The optimization model is based on Incremental Dynamic Programming technique. In the optimization model, the hypothetical reservoir concept used in the above model is adopted. However, communication between any two adjoining hypothetical reservoirs is allowed in the model. The one-dimensional reservoir dynamics simulation model simulates the stratification of the reservoir. The applicability of the technique is examined for three hydrologically different years.Reservoirs could also be modelled by assuming that complete mixing of water is occurring throughout its entire volume during a year. It is a simplification as compared with the real behaviour of stratification occurring in reservoirs. Two models are developed based on this assumption to improve the quality of water supply. In one model only the releases are controlled. In the other, both inflows and releases are controlled. Optimization is based on Incremental Dynamic Programming technique. The results from both models show improvements in the quality of water supplied from the reservoir. However, the improvements obtained by manipulating both inflows and releases are more profound.Improving the quality of water supplied from a reservoir by diverting poor quality inflows and satisfying downstream quantity demands are two conflicting objectives. This problem is studied under the multiobjective analysis framework. The reservoir is assumed to be completely mixed throughout its volume during the whole annual cycle. The results show that a cautious balance between the quantity of water supplied for downstream and the volume of inflows diverted would lead to marked reduction in the supply salinity.The study reveals that the quality of reservoir releases could be improved by withdrawals from different elevations in a stratified reservoir. However, the benefits obtained in this way are marginal for the case study reservoir. Similar improvements are observed under the assumption that the reservoir is completely mixed throughout a year. On the other hand, by manipulating the inflows to the Jarreh reservoir these improvements could be enhanced significantly. That is, by-passing of poor quality inflows seems to be a very promising management alternative for improving the quality of water supplied from the reservoir. The assumption of reservoir's complete mixing is warranted for the stratified reservoir by the obtained results. Hence, a relatively simple and straightforward methodology based on the non-stratification assumption proves to be suitable in managing a density stratified reservoir