PLRTA* conflates all states that differ only in time into a single abstract state. Abstract states inherit the union of all In dynamic environments such as cities, agents often do not the predecessors of their preimage states, so that backups have time to find a complete plan to reach a goal state. Planning can be performed properly. PLRTA* learns a single static in such environment requires an agent to update its plan heuristic value for each abstract state. For dynamic learning, frequently to respond to the changes around it. The setting PLRTA* performs the standard Dijkstra-style backup across of real-time heuristic search models online planning by requiring the LSS, considering only costs arising from the dynamic elements the agent to commit to its next action within a strict of the environment. As presented by Cannon, Rose, time limit. The time bound for planning is set to the time and Ruml (2014), the algorithm commits to only one step at which the actions to which the agent has already committed along the selected path, and then replans using updated information.

The Coalition Structure Generation (CSG) problem is a partitioning of a set of agents into exhaustive and disjoint coalitions to maximize social welfare. This NP-complete problem arises in many practical scenarios. Prominent examples are included in the field of transportation, e-Commerce, distributed sensor networks, and others. The fastest exact algorithm to solve the CSG problem is ODP-IP, which is a hybrid version of two previously established algorithms, namely Improved Dynamic Programming (IDP) and IP. In this paper, we show that the ODP-IP algorithm performs many redundant operations. To improve ODP-IP, we propose a faster abortion mechanism to speed up IP’s search. Our abortion mechanism decides at runtime which of the IP's operations are redundant to skip them. Then, we propose a modified version of IDP (named MIDP) and an improved version of IP (named IIP). Based on these two improved algorithms, we develop a hybrid version (MIDP-IIP) to solve the CSG problem. After a detailed description of the new algorithm MIDP-IIP, an experimental comparison is conducted against ODP-IP. Our analysis shows that MIDP-IIP performs fewer operations than ODP-IP. In addition, MIDP-IIP reduced significantly many problem instances running times (11% to 37 %), and improved drastically some of them.

In this paper, we develop a general interactive method to solve multi-objective combinatorial optimization problems with imprecise preferences. Assuming that preferences can be represented by a parameterized scalarizing function, we iteratively ask preferences queries to the decision maker in order to reduce the uncertainty over the preference parameters until being able to determine her preferred solution. To produce informative preference queries at each step, we generate promising solutions using the extreme points of the polyhedron representing the admissible preference parameters and then we ask the decision maker to compare two of these solutions (we propose different selection strategies). These extreme points are also used to provide a stopping criterion guaranteeing that the returned solution is optimal (or near-optimal) according to the decision maker's preferences. For the multi-objective spanning tree problem with a linear aggregation function, we provide numerical results to demonstrate the practical efficiency of our approach and we compare our results to a recent approach based on minimax regret, where preferences are asked during the construction of a solution. We show that better results are achieved by our method both in terms of running time and number of questions.

In a multi-agent path-finding (MAPF) problem, the task is to find a plan for moving a set of agents from their initial locations to their goals without collisions. Following this plan, however, may not be possible due to unexpected events that delay some of the agents. Guaranteeing that collisions will never occur may be impossible. An important task is to find a plan that is very likely to succeed, even though unexpected delays may occur. We propose an algorithm for finding a plan in which the probability that no collisions will occur is at least a given parameter p (p-robust plan). We show that finding an optimal p-robust plan is significantly more difficult than finding an optimal standard plan. As a practical solution, we propose a greedy algorithm based on the Conflict-Based Search framework. Our experiments show that it finds p-robust plans with cost that is relatively close to the optimal cost of the standard, non-robust plans.

Recent work in bidirectional front-to-end heuristic search has led to the development of novel algorithms that have advanced the state of the art after many years without major developments. In particular, three different algorithms with very different behavior have been proposed: MM, NBS and GBFHS. In this paper we perform a theoretical comparison of these algorithms, defining lower and upper bounds for each of them and analyzing why a given algorithm displays beneficial characteristics that the others lack. With this information, we propose a simple and intuitive near-optimal algorithm to be used as a baseline for comparison in bidirectional front-to-end heuristic search.

The multi-agent pathfinding problem (MAPF) is the fundamental problem of planning paths for multiple agents, where the key constraint is that the agents will be able to follow these paths concurrently without colliding with each other. Applications of MAPF include automated warehouses, autonomous vehicles, and robotics. Research on MAPF has been flourishing in the past couple of years. Different MAPF research papers assume different sets of assumptions, e.g., whether agents can traverse the same road at the same time, and have different objective functions, e.g., minimize makespan or sum of agents' actions costs. These assumptions and objectives are sometimes implicitly assumed or described informally. This makes it difficult for establishing appropriate baselines for comparison in research papers, as well as making it difficult for practitioners to find the papers relevant to their concrete application. This paper aims to fill this gap and facilitate future research and practitioners by providing a unifying terminology for describing the common MAPF assumptions and objectives. In addition, we also provide pointers to two MAPF benchmarks. In particular, we introduce a new grid-based benchmark for MAPF, and demonstrate experimentally that it poses a challenge to contemporary MAPF algorithms.

This paper proves several new properties of the Meet in the Middle (MMe) bidirectional heuristic search algorithm when applied to graphs with unit edge costs. Primarily, it is shown that the length of the first path discovered by MMe never exceeds the optimal length by more than one and that if the length of the first path found is odd, then it must be optimal. These properties suggest that the search strategy should emphasize finding a complete path as soon as possible. Computational experiments demonstrate that fully exploiting these new properties can decrease the number of nodes expanded by anywhere from twofold to over tenfold.

The travelling thief problem (TTP) is a combination of two interdependent NP-hard components: travelling salesman problem (TSP) and knapsack problem (KP). Existing approaches for TTP typically solve the TSP and KP components in an interleaved fashion, where the solution to one component is held fixed while the other component is changed. This indicates poor coordination between solving the two components and may lead to poor quality TTP solutions. For solving the TSP component, the 2-OPT segment reversing heuristic is often used for modifying the tour. We propose an extended and modified form of the reversing heuristic in order to concurrently consider both the TSP and KP components. Items deemed as less profitable and picked in cities earlier in the reversed segment are replaced by items that tend to be equally or more profitable and not picked in the later cities. Comparative evaluations on a broad range of benchmark TTP instances indicate that the proposed approach outperforms existing state-of-the-art TTP solvers.

Weighted A* (wA*) is a widely used algorithm for rapidly, but suboptimally, solving planning and search problems. The cost of the solution it produces is guaranteed to be at most W times the optimal solution cost, where W is the weight wA* uses in prioritizing open nodes. W is therefore a suboptimality bound for the solution produced by wA*. There is broad consensus that this bound is not very accurate, that the actual suboptimality of wA*'s solution is often much less than W times optimal. However, there is very little published evidence supporting that view, and no existing explanation of why W is a poor bound. This paper fills in these gaps in the literature. We begin with a large-scale experiment demonstrating that, across a wide variety of domains and heuristics for those domains, W is indeed very often far from the true suboptimality of wA*'s solution. We then analytically identify the potential sources of error. Finally, we present a practical method for correcting for two of these sources of error and experimentally show that the corrections frequently eliminate much of the error.

Abstraction heuristics are a leading approach for deriving admissible estimates in cost-optimal planning. However, a drawback with respect to other families of heuristics is that they require a preprocessing phase for choosing the abstraction, computing the abstract distances, and/or suitable cost-partitionings. Typically, this is performed in advance by a fixed amount of time, even though some instances could be solved much faster with little or no preprocessing. We interleave the computation of abstraction heuristics with search, avoiding a long precomputation phase and allowing information from the search to be used for guiding the abstraction selection. To evaluate our ideas, we implement them on a planner that uses a single symbolic PDB. Our results show that delaying the preprocessing is not harmful in general even when an important amount of preprocessing is required to obtain good performance.