Assessing the resilience of optimal solutions in multiobjective problems

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

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

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

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

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

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

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