Dik Barton, the first British man to dive to the Titanic wreck, speculates what could have happened to the Titan submersible missing in the North Atlantic. The U.S. Coast Guard announced Thursday that the Canadian vessel Horizon Arctic deployed a remotely operated vehicle (ROV) "that has reached the sea floor and began its search" for the missing OceanGate Titan submarine. It is the first time during the search that a vessel is combing the floor of the Atlantic Ocean for the missing vessel and its five passengers. Previous search efforts have involved the use of aircraft and sonar. "The French vessel L'Atalante is preparing their ROV to enter the water," the Coast Guard also said.

Anytime search algorithms are useful for planning problems where a solution is desired under a limited time budget. Anytime algorithms first aim to provide a feasible solution quickly and then attempt to improve it until the time budget expires. On the other hand, parallel search algorithms utilize the multithreading capability of modern processors to speed up the search. One such algorithm, ePA*SE (Edge-Based Parallel A* for Slow Evaluations), parallelizes edge evaluations to achieve faster planning and is especially useful in domains with expensive-to-compute edges. In this work, we propose an extension that brings the anytime property to ePA*SE, resulting in A-ePA*SE. We evaluate A-ePA*SE experimentally and show that it is significantly more efficient than other anytime search methods. The open-source code for A-ePA*SE, along with the baselines, is available here: https://github.com/shohinm/parallel_search

Recent work aimed at developing a deeper understanding of suboptimal heuristic search has demonstrated that the use of a cost-based heuristic function in the presence of large operator cost ratio and the decision to allow re-opening of visited nodes can have a significant effect on search effort. In parallel research, phase transitions in problem solubility have proved useful in the study of problem difficulty for many computational problems and have recently been shown to exist in heuristic search problems. In this paper, we show that the impact on search effort associated with a larger operator cost ratio and the number of node re-expansions is concentrated almost entirely in the phase transition region. Combined with previous work connecting local minima in the search space with such behavior, these observations lead us to hypothesize a relationship between the phase transition and the existence of local minima.

Incremental graph search algorithms, such as D* Lite, reuse previous search efforts to speed up subsequent similar path planning tasks. These algorithms have demonstrated their efficiency in comparison with search from scratch, and have been leveraged in many applications such as navigation in unknown terrain. On the other hand, path planning typically involves optimizing multiple conflicting objectives simultaneously, such as travel risk, arrival time, etc. Multi-objective path planning is challenging as the number of "Pareto-optimal" solutions can grow exponentially with respect to the size of the graph, which makes it computationally burdensome to plan from scratch each time when similar planning tasks needs to be solved. This article presents a new multi-objective incremental search algorithm called Multi-Objective Path-Based D* Lite (MOPBD*) which reuses previous search efforts to speed up subsequent planning tasks while optimizing multiple objectives. Numerical results show that MOPBD* is more efficient than search from scratch and runs an order of magnitude faster than existing incremental method for multi-objective path planning.

Incremental graph search algorithms, such as D* Lite, reuse previous search efforts to speed up subsequent similar path planning tasks. These algorithms have demonstrated their efficiency in comparison with search from scratch, and have been leveraged in many applications such as navigation in unknown terrain. On the other hand, path planning typically involves optimizing multiple conflicting objectives simultaneously, such as travel risk, arrival time, etc. Multi-objective path planning is challenging as the number of "Pareto-optimal" solutions can grow exponentially with respect to the size of the graph, which makes it computationally burdensome to plan from scratch each time when similar planning tasks needs to be solved. This article presents a new multi-objective incremental search algorithm called Multi-Objective Path-Based D* Lite (MOPBD*) which reuses previous search efforts to speed up subsequent planning tasks while optimizing multiple objectives. Numerical results show that MOPBD* is more efficient than search from scratch and runs an order of magnitude faster than existing incremental method for multi-objective path planning.

Recent work aimed at developing a deeper understanding of suboptimal heuristic search has demonstrated that the use of a cost-based heuristic function in the presence of large operator cost ratio and the decision to allow re-opening of visited nodes can have a significant effect on search effort. In parallel research, phase transitions in problem solubility have proved useful in the study of problem difficulty for many computational problems and have recently been shown to exist in heuristic search problems. In this paper, we show that the impact on search effort associated with a larger operator cost ratio and the number of node re-expansions is concentrated almost entirely in the phase transition region. Combined with previous work connecting local minima in the search space with such behavior, these observations lead us to hypothesize a relationship between the phase transition and the existence of local minima.

In the recent years, there has been significant work on the difficulty of heuristic search problems, identifying different problem instance characteristics that can have a significant impact on search effort. Phase transitions in the solubility of random problem instances have proved useful in the study of problem difficulty for other classes of computational problems, notably SAT and CSP, and it has been shown that the hardest problems typically occur during this rapid transition. In this work, we perform the first empirical investigation of the phase transition phenomena for heuristic search. We establish the existence of a rapid transition in the solubility of an abstract model of heuristic search problems and show that, for greedy best first search, the hardest instances are associated with the phase transition region. We then perform a novel investigation of the behavior of heuristics of different strength across the solubility spectrum. Finally, we demonstrate that the behavior of our abstract model carries over to commonly used benchmark problems including the Pancake Problem, Grid Navigation, TopSpin, and the Towers of Hanoi. An interesting deviation is observed and explained in the Sliding Puzzle.

In empirical studies we observed that caching can have very little impact in reducing the search effort in Branch and Bound search over context-minimal OR spaces. For example, in one of the problem domains used in our experiments we reduce only by 1% the number of nodes expanded when using caching in context-minimal OR spaces. By contrast, we reduce by 74% the number of nodes expanded when using caching in context-minimal AND/OR spaces on the same instances. In this work we document this unexpected empirical finding and provide explanations for the phenomenon.

Many important problems are too difficult to solve optimally. A traditional approach to such problems is bounded suboptimal search, which guarantees solution costs within a user-specified factor of optimal. Recently, a complementary approach has been proposed: bounded-cost search, where solution cost is required to be below a user-specified absolute bound. In this paper, we show how bounded-cost search can incorporate inadmissible estimates of solution cost and solution length. This information has previously been shown to improve bounded suboptimal search and, in an empirical evaluation over five benchmark domains, we find that our new algorithms surpass the state-of-the-art in bounded-cost search as well, particularly for domains where action costs differ.

We introduce a new bidirectional search algorithm, Single-Frontier Bidirectional Search (SFBDS). Unlike traditional BDS which keeps two frontiers, SFBDS uses a single frontier. At a particular node we can decide to search from start to goal or from goal to start, choosing the direction with the highest potential for minimizing the total work done. We provide theoretical analysis that explains when SFBDS will work validated by experimental results.