An evaluation of best compromise search in graphs

This work evaluates two different approaches for multicriteria graph search problems using compromise preferences. This approach focuses search on a single solution that represents a balanced tradeoff between objectives, rather than on the whole set of Pareto optimal solutions. We review the main concepts underlying compromise preferences, and two main approaches proposed for their solution in heuristic graph problems: naive Pareto search (NAMOA ), and a k-shortest-path approach (kA ). The performance of both approaches is evaluated on sets of standard bicriterion road map problems. The experiments reveal that the k-shortest-path approach looses effectiveness in favor of naive Pareto search as graph size increases. The reasons for this behavior are analyzed and discussedPartially funded by P07-TIC-03018, Cons. Innovación, Ciencia y Empresa (Junta Andalucía), and Univ. Málaga, Campus Excel. Int. Andalucía Tec

New Techniques and Algorithms for Multiobjective and Lexicographic Goal-Based Shortest Path Problems

Shortest Path Problems (SPP) are one of the most extensively studied problems in the fields of Artificial Intelligence (AI) and Operations Research (OR). It consists in finding the shortest path between two given nodes in a graph such that the sum of the weights of its constituent arcs is minimized. However, real life problems frequently involve the consideration of multiple, and often conflicting, criteria. When multiple objectives must be simultaneously optimized, the concept of a single optimal solution is no longer valid. Instead, a set of efficient or Pareto-optimal solutions define the optimal trade-off between the objectives under consideration. The Multicriteria Search Problem (MSP), or Multiobjective Shortest Path Problem, is the natural extension to the SPP when more than one criterion are considered. The MSP is computationally harder than the single objective one. The number of label expansions can grow exponentially with solution depth, even for the two objective case. However, with the assumption of bounded integer costs and a fixed number of objectives the problem becomes tractable for polynomially sized graphs. A wide variety of practical application in different fields can be identified for the MSP, like robot path planning, hazardous material transportation, route planning, optimization of public transportation, QoS in networks, or routing in multimedia networks. Goal programming is one of the most successful Multicriteria Decision Making (MCDM) techniques used in Multicriteria Optimization. In this thesis we explore one of its variants in the MSP. Thus, we aim to solve the Multicriteria Search Problem with lexicographic goal-based preferences. To do so, we build on previous work on algorithm NAMOA*, a successful extension of the A* algorithm to the multiobjective case. More precisely, we provide a new algorithm called LEXGO*, an exact label-setting algorithm that returns the subset of Pareto-optimal paths that satisfy a set of lexicographic goals, or the subset that minimizes deviation from goals if these cannot be fully satisfied. Moreover, LEXGO* is proved to be admissible and expands only a subset of the labels expanded by an optimal algorithm like NAMOA*, which performs a full Multiobjective Search. Since time rather than memory is the limiting factor in the performance of multicriteria search algorithms, we also propose a new technique called t-discarding to speed up dominance checks in the process of discarding new alternatives during the search. The application of t-discarding to the algorithms studied previously, NAMOA* and LEXGO*, leads to the introduction of two new time-efficient algorithms named NAMOA*dr and LEXGO*dr , respectively. All the algorithmic alternatives are tested in two scenarios, random grids and realistic road maps problems. The experimental evaluation shows the effectiveness of LEXGO* in both benchmarks, as well as the dramatic reductions of time requirements experienced by the t-discarding versions of the algorithms, with respect to the ones with traditional pruning

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

Memetic Multi-Objective Particle Swarm Optimization-Based Energy-Aware Virtual Network Embedding

In cloud infrastructure, accommodating multiple virtual networks on a single physical network reduces power consumed by physical resources and minimizes cost of operating cloud data centers. However, mapping multiple virtual network resources to physical network components, called virtual network embedding (VNE), is known to be NP-hard. With considering energy efficiency, the problem becomes more complicated. In this paper, we model energy-aware virtual network embedding, devise metrics for evaluating performance of energy aware virtual network-embedding algorithms, and propose an energy aware virtual network-embedding algorithm based on multi-objective particle swarm optimization augmented with local search to speed up convergence of the proposed algorithm and improve solutions quality. Performance of the proposed algorithm is evaluated and compared with existing algorithms using extensive simulations, which show that the proposed algorithm improves virtual network embedding by increasing revenue and decreasing energy consumption.Comment: arXiv admin note: text overlap with arXiv:1504.0684

Multi crteria decision making and its applications : a literature review

This paper presents current techniques used in Multi Criteria Decision Making (MCDM) and their applications. Two basic approaches for MCDM, namely Artificial Intelligence MCDM (AIMCDM) and Classical MCDM (CMCDM) are discussed and investigated. Recent articles from international journals related to MCDM are collected and analyzed to find which approach is more common than the other in MCDM. Also, which area these techniques are applied to. Those articles are appearing in journals for the year 2008 only. This paper provides evidence that currently, both AIMCDM and CMCDM are equally common in MCDM

Multiobjective scheduling for semiconductor manufacturing plants

Scheduling of semiconductor wafer manufacturing system is identified as a complex problem, involving multiple and conflicting objectives (minimization of facility average utilization, minimization of waiting time and storage, for instance) to simultaneously satisfy. In this study, we propose an efficient approach based on an artificial neural network technique embedded into a multiobjective genetic algorithm for multi-decision scheduling problems in a semiconductor wafer fabrication environment

Methodological review of multicriteria optimization techniques: aplications in water resources

Multi-criteria decision analysis (MCDA) is an umbrella approach that has been applied to a wide range of natural resource management situations. This report has two purposes. First, it aims to provide an overview of advancedmulticriteriaapproaches, methods and tools. The review seeks to layout the nature of the models, their inherent strengths and limitations. Analysis of their applicability in supporting real-life decision-making processes is provided with relation to requirements imposed by organizationally decentralized and economically specific spatial and temporal frameworks. Models are categorized based on different classification schemes and are reviewed by describing their general characteristics, approaches, and fundamental properties. A necessity of careful structuring of decision problems is discussed regarding planning, staging and control aspects within broader agricultural context, and in water management in particular. A special emphasis is given to the importance of manipulating decision elements by means ofhierarchingand clustering. The review goes beyond traditionalMCDAtechniques; it describes new modelling approaches. The second purpose is to describe newMCDAparadigms aimed at addressing the inherent complexity of managing water ecosystems, particularly with respect to multiple criteria integrated with biophysical models,multistakeholders, and lack of information. Comments about, and critical analysis of, the limitations of traditional models are made to point out the need for, and propose a call to, a new way of thinking aboutMCDAas they are applied to water and natural resources management planning. These new perspectives do not undermine the value of traditional methods; rather they point to a shift in emphasis from methods for problem solving to methods for problem structuring. Literature review show successfully integrations of watershed management optimization models to efficiently screen a broad range of technical, economic, and policy management options within a watershed system framework and select the optimal combination of management strategies and associated water allocations for designing a sustainable watershed management plan at least cost. Papers show applications in watershed management model that integrates both natural and human elements of a watershed system including the management of ground and surface water sources, water treatment and distribution systems, human demands,wastewatertreatment and collection systems, water reuse facilities,nonpotablewater distribution infrastructure, aquifer storage and recharge facilities, storm water, and land use

Stability Analysis in Multicriteria Discrete Portfolio Optimization.

Almost every problem of design, planning and management in the technical and organizational systems has several conflicting goals or interests. Nowadays, multicriteria decision models represent a rapidly developing area of operation research. While solving practical optimization problems, it is necessary to take into account various kinds of uncertainty due to lack of data, inadequacy of mathematical models to real-time processes, calculation errors, etc. In practice, this uncertainty usually leads to undesirable outcomes where the solutions are very sensitive to any changes in the input parameters. An example is the investment managing. Stability analysis of multicriteria discrete optimization problems investigates how the found solutions behave in response to changes in the initial data (input parameters). This thesis is devoted to the stability analysis in the problem of selecting investment project portfolios, which are optimized by considering different types of risk and efficiency of the investment projects. The stability analysis is carried out in two approaches: qualitative and quantitative. The qualitative approach describes the behavior of solutions in conditions with small perturbations in the initial data. The stability of solutions is defined in terms of existence a neighborhood in the initial data space. Any perturbed problem from this neighborhood has stability with respect to the set of efficient solutions of the initial problem. The other approach in the stability analysis studies quantitative measures such as stability radius. This approach gives information about the limits of perturbations in the input parameters, which do not lead to changes in the set of efficient solutions. In present thesis several results were obtained including attainable bounds for the stability radii of Pareto optimal and lexicographically optimal portfolios of the investment problem with Savage's, Wald's criteria and criteria of extreme optimism. In addition, special classes of the problem when the stability radii are expressed by the formulae were indicated. Investigations were completed using different combinations of Chebyshev's, Manhattan and Hölder's metrics, which allowed monitoring input parameters perturbations differently.Siirretty Doriast