The design of spacecraft trajectories for missions visiting multiple celestial bodies is here framed as a multi-objective bilevel optimization problem. A comparative study is performed to assess the performance of different Beam Search algorithms at tackling the combinatorial problem of finding the ideal sequence of bodies. Special focus is placed on the development of a new hybridization between Beam Search and the Population-based Ant Colony Optimization algorithm. An experimental evaluation shows all algorithms achieving exceptional performance on a hard benchmark problem. It is found that a properly tuned deterministic Beam Search always outperforms the remaining variants. Beam P-ACO, however, demonstrates lower parameter sensitivity, while offering superior worst-case performance. Being an anytime algorithm, it is then found to be the preferable choice for certain practical applications.
Beam Search @cite_0 @cite_28 has emerged as the standard approach to tackle the combinatorial optimization sub-problems present in most GTOC competitions. Though at times called by other names, it is common to find the general architecture of a tree search that has its computational cost bounded via the selection of a limited number of nodes to branch at each depth-level (non-selected nodes at that depth being immediately discarded). We can find examples of such algorithms in the winning solutions to GTOC4 @cite_23 , GTOC5 @cite_22 , and in the second ranked solution to GTOC7 @cite_6 , which the present research builds on. The Lazy Race Tree Search described in @cite_24 , which at the time presented the best known solution to the GTOC6 problem, can also be seen as a Beam Search variant. In it, the beam'' is composed of all nodes, possibly originating from different tree depths, that fall within a given mission time window. The most promising nodes in that sliding window are branched, and the remaining ones discarded.
@cite_22 @cite_28 @cite_6 @cite_0 @cite_24 @cite_23
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Searching in partially ordered structures has been considered in the context of information retrieval and efficient tree-like indices, as well as in hierarchy based knowledge representation. In this paper we focus on tree-like partial orders and consider the problem of identifying an initially unknown vertex in a tree by asking edge queries: an edge query e returns the component of T - e containing the vertex sought for, while incurring some known cost c ( e ) . The Tree Search Problem with Non-Uniform Cost is the following: given a tree T on n vertices, each edge having an associated cost, construct a strategy that minimizes the total cost of the identification in the worst case.Finding the strategy guaranteeing the minimum possible cost is an NP-complete problem already for input trees of degree 3 or diameter 6. The best known approximation guarantee was an O ( log ź n log ź log ź log ź n ) -approximation algorithm of (2012) 4.We improve upon the above results both from the algorithmic and the computational complexity point of view: We provide a novel algorithm that provides an O ( log ź n log ź log ź n ) -approximation of the cost of the optimal strategy. In addition, we show that finding an optimal strategy is NP-hard even when the input tree is a spider of diameter 6, i.e., at most one vertex has degree larger than 2. We start a systematic study of data structures for the nearest colored node problem on trees. Given a tree with colored nodes and weighted edges, we want to answer queries (v,c) asking for the nearest node to node v that has color c. This is a natural generalization of the well-known nearest marked ancestor problem. We give an O(n)-space O(log log n)-query solution and show that this is optimal. We also consider the dynamic case where updates can change a node's color and show that in O(n) space we can support both updates and queries in O(log n) time. We complement this by showing that O(polylog n) update time implies Omega(log n log log n) query time. Finally, we consider the case where updates can change the edges of the tree (link-cut operations). There is a known (top-tree based) solution that requires update time that is roughly linear in the number of colors. We show that this solution is probably optimal by showing that a strictly sublinear update time implies a strictly subcubic time algorithm for the classical all pairs shortest paths problem on a general graph. We also consider versions where the tree is rooted, and the query asks for the nearest ancestor descendant of node v that has color c, and present efficient data structures for both variants in the static and the dynamic setting. Beam search is commonly used to help maintain tractability in large search spaces at the expense of completeness and optimality. Here we study supervised learning of linear ranking functions for controlling beam search. The goal is to learn ranking functions that allow for beam search to perform nearly as well as unconstrained search, and hence gain computational efficiency without seriously sacrificing optimality. In this paper, we develop theoretical aspects of this learning problem and investigate the application of this framework to learning in the context of automated planning. We first study the computational complexity of the learning problem, showing that even for exponentially large search spaces the general consistency problem is in NP. We also identify tractable and intractable subclasses of the learning problem, giving insight into the problem structure. Next, we analyze the convergence of recently proposed and modified online learning algorithms, where we introduce several notions of problem margin that imply convergence for the various algorithms. Finally, we present empirical results in automated planning, where ranking functions are learned to guide beam search in a number of benchmark planning domains. The results show that our approach is often able to outperform an existing state-of-the-art planning heuristic as well as a recent approach to learning such heuristics. We study resource-limited online learning, motivated by the problem of conditional-branch outcome prediction in computer architecture. In particular, we consider (parallel) time and space-efficient ensemble learners for online settings, empirically demonstrating benefits similar to those shown previously for offline ensembles. Our learning algorithms are inspired by the previously published “boosting by filtering” framework as well as the offline Arc-x4 boosting-style algorithm. We train ensembles of online decision trees using a novel variant of the ID4 online decision-tree algorithm as the base learner, and show empirical results for both boosting and bagging-style online ensemble methods. Our results evaluate these methods on both our branch prediction domain and online variants of three familiar machine-learning benchmarks. Our data justifies three key claims. First, we show empirically that our extensions to ID4 significantly improve performance for single trees and additionally are critical to achieving performance gains in tree ensembles. Second, our results indicate significant improvements in predictive accuracy with ensemble size for the boosting-style algorithm. The bagging algorithms we tried showed poor performance relative to the boosting-style algorithm (but still improve upon individual base learners). Third, we show that ensembles of small trees are often able to outperform large single trees with the same number of nodes (and similarly outperform smaller ensembles of larger trees that use the same total number of nodes). This makes online boosting particularly useful in domains such as branch prediction with tight space restrictions (i.e., the available real-estate on a microprocessor chip).