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

Multi-agent collaborative search : an agent-based memetic multi-objective optimization algorithm applied to space trajectory design

This article presents an algorithm for multi-objective optimization that blends together a number of heuristics. A population of agents combines heuristics that aim at exploring the search space both globally and in a neighbourhood of each agent. These heuristics are complemented with a combination of a local and global archive. The novel agent-based algorithm is tested at first on a set of standard problems and then on three specific problems in space trajectory design. Its performance is compared against a number of state-of-the-art multi-objective optimization algorithms that use the Pareto dominance as selection criterion: non-dominated sorting genetic algorithm (NSGA-II), Pareto archived evolution strategy (PAES), multiple objective particle swarm optimization (MOPSO), and multiple trajectory search (MTS). The results demonstrate that the agent-based search can identify parts of the Pareto set that the other algorithms were not able to capture. Furthermore, convergence is statistically better although the variance of the results is in some cases higher

A bi-objective genetic algorithm approach to risk mitigation in project scheduling

A problem of risk mitigation in project scheduling is formulated as a bi-objective optimization problem, where the expected makespan and the expected total cost are both to be minimized. The expected total cost is the sum of four cost components: overhead cost, activity execution cost, cost of reducing risks and penalty cost for tardiness. Risks for activities are predefined. For each risk at an activity, various levels are defined, which correspond to the results of different preventive measures. Only those risks with a probable impact on the duration of the related activity are considered here. Impacts of risks are not only accounted for through the expected makespan but are also translated into cost and thus have an impact on the expected total cost. An MIP model and a heuristic solution approach based on genetic algorithms (GAs) is proposed. The experiments conducted indicate that GAs provide a fast and effective solution approach to the problem. For smaller problems, the results obtained by the GA are very good. For larger problems, there is room for improvement

Multi agent collaborative search based on Tchebycheff decomposition

This paper presents a novel formulation of Multi Agent Collaborative Search, for multi-objective optimization, based on Tchebycheff decomposition. A population of agents combines heuristics that aim at exploring the search space both globally (social moves) and in a neighborhood of each agent (individualistic moves). In this novel formulation the selection process is based on a combination of Tchebycheff scalarization and Pareto dominance. Furthermore, while in the previous implementation, social actions were applied to the whole population of agents and individualistic actions only to an elite sub-population, in this novel formulation this mechanism is inverted. The novel agent-based algorithm is tested at first on a standard benchmark of difficult problems and then on two specific problems in space trajectory design. Its performance is compared against a number of state-of-the-art multi objective optimization algorithms. The results demonstrate that this novel agent-based search has better performance with respect to its predecessor in a number of cases and converges better than the other state-of-the-art algorithms with a better spreading of the solutions

On green routing and scheduling problem

The vehicle routing and scheduling problem has been studied with much interest within the last four decades. In this paper, some of the existing literature dealing with routing and scheduling problems with environmental issues is reviewed, and a description is provided of the problems that have been investigated and how they are treated using combinatorial optimization tools

The crew-scheduling module in the GIST system

The public transportation is gaining importance every year basically due the population growth, environmental policies and, route and street congestion. Too able an efficient management of all the resources related to public transportation, several techniques from different areas are being applied and several projects in Transportation Planning Systems, in different countries, are being developed. In this work, we present the GIST Planning Transportation Systems, a Portuguese project involving two universities and six public transportation companies. We describe in detail one of the most relevant modules of this project, the crew-scheduling module. The crew-scheduling module is based on the application of meta-heuristics, in particular GRASP, tabu search and genetic algorithm to solve the bus-driver-scheduling problem. The metaheuristics have been successfully incorporated in the GIST Planning Transportation Systems and are actually used by several companies.Integrated transportation systems, crew scheduling, metaheuristics

Differential Evolution for Multiobjective Portfolio Optimization

Financial portfolio optimization is a challenging problem. First, the problem is multiobjective (i.e.: minimize risk and maximize profit) and the objective functions are often multimodal and non smooth (e.g.: value at risk). Second, managers have often to face real-world constraints, which are typically non-linear. Hence, conventional optimization techniques, such as quadratic programming, cannot be used. Stochastic search heuristic can be an attractive alternative. In this paper, we propose a new multiobjective algorithm for portfolio optimization: DEMPO - Differential Evolution for Multiobjective Portfolio Optimization. The main advantage of this new algorithm is its generality, i.e., the ability to tackle a portfolio optimization task as it is, without simplifications. Our empirical results show the capability of our approach of obtaining highly accurate results in very reasonable runtime, in comparison with quadratic programming and another state-of-art search heuristic, the so-called NSGA II.Portfolio Optimization, Multiobjective, Real-world Constraints, Value at Risk, Expected Shortfall, Differential Evolution