320 research outputs found

    Assessing the resilience of optimal solutions in multiobjective problems

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    Publisher Copyright: © 2023 The AuthorsProcesses and products are multidimensional so researchers and practitioners have to solve problems with multiple objectives frequently. These problems have, in general, responses in conflict so they do not have a unique solution. Different approaches have been proposed in the literature to solve these problems, but many of them, including the popular desirability function approach, are not employed with the focus on the generation of Pareto frontiers. In addition, it is important to stress that some Pareto solutions may not yield the expected outcome(s) when implemented in practice. Thus, to avoid wasting resources and time in implementing a theoretical solution which does not produce the expected outcome(s), in this paper is proposed a novel metric to assess the resilience of Pareto solutions. This way, the decision-maker may identify a solution less sensitive to changes in the variables setting when their values are implemented in production process (equipments) or during its operation. Metric usefulness is illustrated using a case study, and results analysis is complemented with plots that facilitate the decision-making process.publishersversionpublishe

    Robust Mission Design Through Evidence Theory and Multi-Agent Collaborative Search

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    In this paper, the preliminary design of a space mission is approached introducing uncertainties on the design parameters and formulating the resulting reliable design problem as a multiobjective optimization problem. Uncertainties are modelled through evidence theory and the belief, or credibility, in the successful achievement of mission goals is maximised along with the reliability of constraint satisfaction. The multiobjective optimisation problem is solved through a novel algorithm based on the collaboration of a population of agents in search for the set of highly reliable solutions. Two typical problems in mission analysis are used to illustrate the proposed methodology

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

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    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

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

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    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

    On the generation of environmentally efficient flight trajectories

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    To achieve a sustainable future for air transport, the International Civil Aviation Organization has proposed goals for reductions in community noise impact, local air quality and climate impacting emissions. The goals are intended to be achieved through advances in engine design, aircraft design and through improvements in aircraft operational procedures. This thesis focuses on operational procedures, and considers how trajectory generation methods can be used to support flight and airspace planners in the planning and delivery of environmentally efficient flight operations. The problem of planning environmentally efficient trajectories is treated as an optimal control problem that is solved through the application of a direct method of trajectory optimisation combined with a stochastic Non Linear Programming (NLP) solver. Solving the problem in this manner allows decision makers to explore the relationships between how aircraft are operated and the consequent environmental impacts of the flights. In particular, this thesis describes a multi-objective optimisation methodology intended to support the planning of environmentally efficient climb and descent procedures. The method combines environmental, trajectory and NLP methods to generate Pareto fronts between several competing objectives. It is shown how Pareto front information can then be used to allow decision makers to make informed decisions about potential tradeoffs between different environmental goals. The method is demonstrated through its application to a number of real world, many objective procedure optimisation studies. The method is shown to support in depth analysis of the case study problems and was used to identify best balance procedure characteristics and procedures in an objective, data driven approach not achievable through existing methods. Driven by operator specific goals to reduce CO2 emissions, work in this thesis also looks at trajectory based flight planning of CO2 efficient trajectories. The results are used to better understand the impacts of ATM constraints and recommended procedures on both the energy management and fuel efficiency of flights. Further to this, it is shown how trajectory optimisation methods can be applied to the analysis of conventional assumptions on fuel efficient aircraft operations. While the work within is intended to be directly relevant to the current air traffic management system, both consideration and discussion is given over to the evolution and continued relevance of the work to the Single European Sky trajectory based concept of operation

    Identification of key players in networks using multi-objective optimization and its applications

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    Identification of a set of key players, is of interest in many disciplines such as sociology, politics, finance, economics, etc. Although many algorithms have been proposed to identify a set of key players, each emphasizes a single objective of interest. Consequently, the prevailing deficiency of each of these methods is that, they perform well only when we consider their objective of interest as the only characteristic that the set of key players should have. But in complicated real life applications, we need a set of key players which can perform well with respect to multiple objectives of interest. In this dissertation, a new perspective for key player identification is proposed, based on optimizing multiple objectives of interest. The proposed approach is useful in identifying both key nodes and key edges in networks. Experimental results show that the sets of key players which optimize multiple objectives perform better than the key players identified using existing algorithms, in multiple applications such as eventual influence limitation problem, immunization problem, improving the fault tolerance of the smart grid, etc. We utilize multi-objective optimization algorithms to optimize a set of objectives for a particular application. A large number of solutions are obtained when the number of objectives is high and the objectives are uncorrelated. But decision-makers usually require one or two solutions for their applications. In addition, the computational time required for multi-objective optimization increases with the number of objectives. A novel approach to obtain a subset of the Pareto optimal solutions is proposed and shown to alleviate the aforementioned problems. As the size and the complexity of the networks increase, so does the computational effort needed to compute the network analysis measures. We show that degree centrality based network sampling can be used to reduce the running times without compromising the quality of key nodes obtained

    A multi-criteria based selection method using non-dominated sorting for genetic algorithm based design

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    The paper presents a generative design approach, particularly for simulation-driven designs, using a genetic algorithm (GA), which is structured based on a novel offspring selection strategy. The proposed selection approach commences while enumerating the offsprings generated from the selected parents. Afterwards, a set of eminent offsprings is selected from the enumerated ones based on the following merit criteria: space-fillingness to generate as many distinct offsprings as possible, resemblance/non-resemblance of offsprings to the good/bad individuals, non-collapsingness to produce diverse simulation results and constrain-handling for the selection of offsprings satisfying design constraints. The selection problem itself is formulated as a multi-objective optimization problem. A greedy technique is employed based on non-dominated sorting, pruning, and selecting the representative solution. According to the experiments performed using three different application scenarios, namely simulation-driven product design, mechanical design and user-centred product design, the proposed selection technique outperforms the baseline GA selection techniques, such as tournament and ranking selections

    Supporting strategy selection in multiobjective decision problems under uncertainty and hidden requirements

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    Decision-makers are often faced with multi-faceted problems that require making trade-offs between multiple, conflicting objectives under various uncertainties. The task is even more difficult when considering dynamic, non-linear processes and when the decisions themselves are complex, for instance in the case of selecting trajectories for multiple decision variables. These types of problems are often solved using multiobjective optimization (MOO). A typical problem in MOO is that the number of Pareto optimal solutions can be very large, whereby the selection process of a single preferred solution is cumbersome. Moreover, preference between model-based solutions may not be determined only by their objective function values, but also in terms of how robust and implementable these solutions are. In this paper, we develop a methodological framework to support the identification of a small but diverse set of robust Pareto optimal solutions. In particular, we eliminate non-robust solutions from the Pareto front and cluster the remaining solutions based on their similarity in the decision variable space. This enables a manageable visual inspection of the remaining solutions to compare them in terms of practical implementability. We illustrate the framework and its benefits by means of an epidemic control problem that minimizes deaths and economic impacts, and a screening program for colorectal cancer that minimizes cancer prevalence and costs. These examples highlight the general applicability of the framework for disparate types of decision problems and process models

    Algorithm Engineering for Realistic Journey Planning in Transportation Networks

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    Diese Dissertation beschäftigt sich mit der Routenplanung in Transportnetzen. Es werden neue, effiziente algorithmische Ansätze zur Berechnung optimaler Verbindungen in öffentlichen Verkehrsnetzen, Straßennetzen und multimodalen Netzen, die verschiedene Transportmodi miteinander verknüpfen, eingeführt. Im Fokus der Arbeit steht dabei die Praktikabilität der Ansätze, was durch eine ausführliche experimentelle Evaluation belegt wird
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