Constrained Stochastic Shortest Path Problems (CSSPs) model problems with probabilistic effects, where a primary cost is min-imised subject to constraints over secondary costs, e.g., minimise time subject to monetary budget. Current heuristic search algorithms for CSSPs solve a sequence of increasingly larger CSSPs as linear programs until an optimal solution for the original CSSP is found. In this paper, we introduce a novel algorithm CARL, which solves a series of unconstrained Stochastic Shortest Path Problems (SSPs) with efficient heuristic search algorithms. These SSP subproblems are constructed with scalarisations that project the CSSP's vector of primary and secondary costs onto a scalar cost. CARL finds a maximising scalarisation using an optimisation algorithm similar to the subgradient method which, together with the solution to its associated SSP, yields a set of policies that are combined into an optimal policy for the CSSP . Our experiments show that CARL solves 50% more problems than the state-of-the-art on existing benchmarks.

For combinatorial optimization problems, model-based paradigms such as mixed-integer programming (MIP) and constraint programming (CP) aim to decouple modeling and solving a problem: the `holy grail' of declarative problem solving. We propose domain-independent dynamic programming (DIDP), a new model-based paradigm based on dynamic programming (DP). While DP is not new, it has typically been implemented as a problem-specific method. We introduce Dynamic Programming Description Language (DyPDL), a formalism to define DP models based on a state transition system, inspired by AI planning. We show that heuristic search algorithms can be used to solve DyPDL models and propose seven DIDP solvers. We experimentally compare our DIDP solvers with commercial MIP and CP solvers (solving MIP and CP models, respectively) on common benchmark instances of eleven combinatorial optimization problem classes. We show that DIDP outperforms MIP in nine problem classes, CP also in nine problem classes, and both MIP and CP in seven.

The paper presents a comprehensive performance evaluation of some heuristic search algorithms in the context of autonomous systems and robotics. The objective of the study is to evaluate and compare the performance of different search algorithms in different problem settings on the pathfinding domain. Experiments give us insight into the behavior of the evaluated heuristic search algorithms, over the variation of different parameters: domain size, obstacle density, and distance between the start and the goal states. Results are then used to design a selection algorithm that, on the basis of problem characteristics, suggests the best search algorithm to use.

Real-time heuristic search algorithms follow the agent-centered search paradigm wherein the agent has access only to information local to the agent's current position in the environment. This allows agents with constant-bounded computational faculties (e.g., memory) to take on search problems of progressively increasing sizes. As the agent's memory does not scale with the size of the search problem, the heuristic must necessarily be stored externally, in the environment. Storing the heuristic in the environment brings the extra challenge of read/write errors. In video games, introducing error artificially to the heuristics can make the non-player characters (NPC) behave more naturally. In this paper, we evaluate effects of such errors on real-time heuristic search algorithms. In particular, we empirically study the effects of heuristic read redundancy on algorithm performance and compare its effects to the existing technique of using weights in heuristic learning. Finally, we evaluate a recently proposed technique of correcting the heuristic with a one-step error term in the presence of read/write error.

Real-time heuristic search algorithms are used for creating agents that rely on local information and move in a bounded amount of time making them an excellent candidate for video games as planning time can be controlled. Path finding on video game maps has become the de facto standard for evaluating real-time heuristic search algorithms. Over the years researchers have worked to identify areas where these algorithms perform poorly in an attempt to mitigate their weaknesses. Recent work illustrates the benefits of tailoring algorithms for a given problem as performance is heavily dependent on the search space. In order to determine which algorithm to select for solving the search problems on a map the developer would have to run all the algorithms in consideration to obtain the correct choice. Our work extends the previous algorithm selection approach to use a deep learning classifier to select the algorithm to use on new maps without having to evaluate the algorithms on the map. To do so we select a portfolio of algorithms and train a classifier to predict which portfolio member to use on a unseen new map. Our empirical results show that selecting algorithms dynamically can outperform the single best algorithm from the portfolio on new maps, as well provide the lower bound for potential improvements to motivate further work on this approach.

Markov decision processes are of major interest in the planning community as well as in the model checking community. But in spite of the similarity in the considered formal models, the development of new techniques and methods happened largely independently in both communities. This work is intended as a beginning to unite the two research branches. We consider goal-reachability analysis as a common basis between both communities. The core of this paper is the translation from Jani, an overarching input language for quantitative model checkers, into the probabilistic planning domain definition language (PPDDL), and vice versa from PPDDL into Jani. These translations allow the creation of an overarching benchmark collection, including existing case studies from the model checking community, as well as benchmarks from the international probabilistic planning competitions (IPPC). We use this benchmark set as a basis for an extensive empirical comparison of various approaches from the model checking community, variants of value iteration, and MDP heuristic search algorithms developed by the AI planning community. On a per benchmark domain basis, techniques from one community can achieve state-ofthe-art performance in benchmarks of the other community. Across all benchmark domains of one community, the performance comparison is however in favor of the solvers and algorithms of that particular community. Reasons are the design of the benchmarks, as well as tool-related limitations. Our translation methods and benchmark collection foster crossfertilization between both communities, pointing out specific opportunities for widening the scope of solvers to different kinds of models, as well as for exchanging and adopting algorithms across communities.

Many existing boundedly-suboptimal heuristic search algorithms are variants of best-first search. Due to memory limitations, these algorithms are unable to solve problems with extremely large search spaces. In this paper, we present a framework that allows best-first search algorithms to solve problems with such large search spaces given a (reasonable) memory bound while also preserving optimality guarantees in tree-structured search spaces. In our framework, a given algorithm is run several times. In each search episode, the algorithm expands up to a user-defined number of states. After each episode, unless the goal has been found, the heuristic values of the generated states are updated using a linear-time algorithm that preserves consistency in tree-structured search spaces. In subsequent search episodes, only the heuristic values of the states generated in the previous episode need to be kept in memory. We present experimental results where we plug A*, GBFS, and wA* into our framework to solve traveling salesman problems and compare them against benchmark linear-memory algorithms like DFBnB and wDFBnB.

This paper presents a non-manual design engineering method based on heuristic search algorithm to search for candidate agents in the solution space which formed by artificial intelligence agents modeled on the base of bionics.Compared with the artificial design method represented by meta-learning and the bionics method represented by the neural architecture chip,this method is more feasible for realizing artificial general intelligence,and it has a much better interaction with cognitive neuroscience;at the same time,the engineering method is based on the theoretical hypothesis that the final learning algorithm is stable in certain scenarios,and has generalization ability in various scenarios.The paper discusses the theory preliminarily and proposes the possible correlation between the theory and the fixed-point theorem in the field of mathematics.Limited by the author's knowledge level,this correlation is proposed only as a kind of conjecture.

The research area of real-time heuristics search has produced quite many algorithms. In the landscape of real-time heuristics search research, it is not rare to find that an algorithm X that appears to perform better than algorithm Y on a group of problems, performed worse than Y for another group of problems. If these published algorithms are combined to generate a more powerful space of algorithms, then that novel space of algorithms may solve a distribution of problems more efficiently. Based on this intuition, a recent work Bulitko 2016 has defined the task of finding a combination of heuristics search algorithms as a survival task. In this evolutionary approach, a space of algorithms is defined over a set of building blocks published algorithms and a simulated evolution is used to recombine these building blocks to find out the best algorithm from that space of algorithms. In this paper, we extend the set of building blocks by adding one published algorithm, namely lookahead based A-star shaped local search space generation method from LSSLRTA-star, plus an unpublished novel strategy to generate local search space with Greedy Best First Search. Then we perform experiments in the new space of algorithms, which show that the best algorithms selected by the evolutionary process have the following property: the deeper is the lookahead depth of an algorithm, the lower is its suboptimality and scrubbing complexity.

We address the problem of approximating a matrix by the linear combination of a column sparse matrix and a low rank matrix. Two variants of a heuristic search algorithm are described. The first produces an optimal solution but may be slow, as these problems are believed to be NP-hard. The second is much faster, but only guarantees a suboptimal solution. The quality of the approximation and the optimality criterion can be specified in terms of unitarily invariant norms.