We present an approach to couple the resolution of Combinatorial Optimization problems with methods from Machine Learning, applied to the single source, capacitated, facility location problem. Our study is framed in the context where a reference facility location optimization problem is given. Assuming there exist data for many variations of the reference problem (historical or simulated) along with their optimal solution, we study how one can exploit these to make predictions about an unseen new instance. We demonstrate how a classifier can be built from these data to determine whether the solution to the reference problem still applies to a new instance. In case the reference solution is partially applicable, we build a regressor indicating the magnitude of the expected change, and conversely how much of it can be kept for the new instance. This insight, derived from a priori information, is expressed via an additional constraint in the original mathematical programming formulation. We present an empirical evaluation and discuss the benefits, drawbacks and perspectives of such an approach. Although presented through the application to the facility location problem, the approach developed here is general and explores a new perspective on the exploitation of past experience in combinatorial optimization.

Recently there has been increased interest in combining the fields of Model-Driven Engineering (MDE) and Search-Based Software Engineering (SBSE). Such approaches use meta-heuristic search guided by search operators (model mutators and sometimes breeders) implemented as model transformations. The design of these operators can substantially impact the effectiveness and efficiency of the meta-heuristic search. Currently, designing search operators is left to the person specifying the optimisation problem. However, developing consistent and efficient search-operator rules requires not only domain expertise but also in-depth knowledge about optimisation, which makes the use of model-based meta-heuristic search challenging and expensive. In this paper, we propose a generalised approach to automatically generate atomic consistency preserving search operators (aCPSOs) for a given optimisation problem. This reduces the effort required to specify an optimisation problem and shields optimisation users from the complexity of implementing efficient meta-heuristic search mutation operators. We evaluate our approach with a set of case studies, and show that the automatically generated rules are comparable to, and in some cases better than, manually created rules at guiding evolutionary search towards near-optimal solutions. This paper is an extended version of the paper with the same title published in the proceedings of the 22nd International Conference on Model Driven Engineering Languages and Systems (MODELS '19).

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.

NBS is a non-parametric bidirectional search algorithm, proved to expand at most twice the number of node expansions required to verify the optimality of a solution. We introduce new variants of NBS that are aimed at finding all optimal solutions. We then introduce an algorithmic framework that includes NBS as a special case. Finally, we introduce DVCBS, a new algorithm in this framework that aims to further reduce the number of expansions. Unlike NBS, DVCBS does not have any worst-case bound guarantees, but in practice it outperforms NBS in verifying the optimality of solutions.

Designing good heuristic functions for graph search requires adequate domain knowledge. It is often easy to design heuristics that perform well and correlate with the underlying true cost-to-go values in certain parts of the search space but these may not be admissible throughout the domain thereby affecting the optimality guarantees of the search. Bounded suboptimal search using several of such partially good but inadmissible heuristics was developed in Multi-Heuristic A* (MHA*). Although MHA* leverages multiple inadmissible heuristics to potentially generate a faster suboptimal solution, the original version does not improve the solution over time. It is an one shot algorithm that requires careful setting of inflation factors to obtain a desired one time solution. In this work, we tackle this issue by extending MHA* to an anytime version that finds a feasible suboptimal solution quickly and continually improve it until time runs out. Our work is inspired from the Anytime Repairing A* (ARA*) algorithm. We prove that our precise adaptation of ARA* concepts in the MHA* framework preserves the original suboptimal and completeness guarantees and enhances MHA* to perform in an anytime fashion. Furthermore, we report the performance of A-MHA* in 3-D path planning domain and sliding tiles puzzle and compare against MHA* and other anytime algorithms.

It is known that seemingly small details such as tie-breaking among nodes with the same f-cost can significantly affect the performance of a best-first search algorithm on many domains (Asai and Fukunaga 2017). In this paper, we show that low-level algorithmic details of domain-independent planning heuristics can have a surprisingly large impact on search performance. As a case study, we consider the well-known FF heuristic (hff ) (Hoffmann and Nebel 2001).

Empirically, this optimization lead to 0.5 - 2.5% savings on expansions in our experiments A fundamental concern in real-time planning is the presence (Cserna, Gall, and Ruml 2019). of dead-ends in the state space, from which no goal is reachable. SafeRTS interleaves exploration and safety proofs during Providing real-time heuristic search algorithms that are its planning phase. As a direct consequence, it attempts complete in domains with dead-end states is a challenging safety proofs on nodes that become internal to the LSS by problem. Recently, the SafeRTS algorithm was proposed for the end of the search iteration. As shown in Cserna, Gall, and searching in such spaces (Cserna et al. 2018). SafeRTS exploits Ruml (2019), it would be equally or less difficult to achieve a user-provided predicate to identify safe states, from the same or better safety coverage by doing safety proofs after which a goal is likely reachable, and attempts to maintain a all the LSS expansions. SafeRTS has an anytime behavior backup plan for reaching a safe state at all times.

Most real-world project have a deadline and consist of completing tasks. In our setting, each task needs to be executed by a single supplier, chosen from a subset of suppliers that have the required proficiency to handle that task. The suppliers differ in their execution times, which are stochastically taken from known distributions. The Supplier Assignment for Meeting a Deadline (SAMD) problem is the problem of assigning a supplier to each task in a manner that maximizes the chance to meet the overall project deadline. We propose an A*-based approach, along with an efficient admissible heuristic function, that guarantees an optimal solution for this problem. Experimentally, we compare our A*-based approach to an exhaustive brute-force approach and several heuristic methods. The results show that our A*-based approach compares favorably with the heuristic methods, and is orders of magnitude faster than the exhaustive alternative.

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.

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.