Constraint-based Sequential Pattern Mining with Decision Diagrams

Constrained sequential pattern mining aims at identifying frequent patterns on a sequential database of items while observing constraints defined over the item attributes. We introduce novel techniques for constraint-based sequential pattern mining that rely on a multi-valued decision diagram representation of the database. Specifically, our representation can accommodate multiple item attributes and various constraint types, including a number of non-monotone constraints. To evaluate the applicability of our approach, we develop an MDD-based prefix-projection algorithm and compare its performance against a typical generate-and-check variant, as well as a state-of-the-art constraint-based sequential pattern mining algorithm. Results show that our approach is competitive with or superior to these other methods in terms of scalability and efficiency.Comment: AAAI201

Learning in planning with temporally extended goals and uncontrollable events

Recent contributions to advancing planning from the classical model to more realistic problems include using temporal logic such as LTL to express desired properties of a solution plan. This paper introduces a planning model that combines temporally extended goals and uncontrollable events. The planning task is to reach a state such that all event sequences generated from that state satisfy the problem's temporally extended goal. A real-life application that motivates this work is to use planning to configure a system in such a way that its subsequent, non-deterministic internal evolution (nominal behavior) is guaranteed to satisfy a condition expressed in temporal logic. A solving architecture is presented that combines planning, model checking and learning. An online learning process incrementally discovers information about the problem instance at hand. The learned information is useful both to guide the search in planning and to safely avoid unnecessary calls to the model checking module. A detailed experimental analysis of the approach presented in this paper is included. The new method for online learning is shown to greatly improve the system performance.NICTA is funded by the Australian Government’s Department of Communications, Information Technology, and the Arts and the Australian Research Council through Backing Australia’s Ability and the ICT Research Centre of Excellence program

Discrete Nonlinear Optimization by State-Space Decompositions

This paper investigates a decomposition approach for binary optimization problems with nonlinear objectives and linear constraints. Our methodology relies on the partition of the objective function into separate low-dimensional dynamic programming (DP) models, each of which can be equivalently represented as a shortest-path problem in an underlying state-transition graph. We show that the associated transition graphs can be related by a mixed-integer linear program (MILP) so as to produce exact solutions to the original nonlinear problem. To address DPs with large state spaces, we present a general relaxation mechanism that dynamically aggregates states during the construction of the transition graphs. The resulting MILP provides both lower and upper bounds to the nonlinear function, and it may be embedded in branch-and-bound procedures to find provably optimal solutions. We describe how to specialize our technique for structured objectives (e.g., submodular functions) and consider three problems arising in revenue management, portfolio optimization, and healthcare. Numerical studies indicate that the proposed technique often outperforms state-of-the-art approaches by orders of magnitude in these applications.The research of A. A. Cire was supported by the Natural Sciences and Engineering Research Council of Canada [Discovery Grant RGPIN-2015-04152]

Theoretical insights and algorithmic tools for decision diagram-based optimization

The use of decision diagrams has recently emerged as a viable general solution approach for solving discrete optimization problems. The decision diagram data structure is used to explicitly represent, either exactly or approximately, the set of feasible solutions to a given problem. Techniques based on decision diagrams have been successfully used on a diverse set of applications, ranging from scheduling to combinatorial optimization, and have often outperformed commercial state-of-the-art constraint programming and integer programming technology. Lacking, however, is a thorough theoretical investigation into the quality of approximate decision diagrams, as well as the development of structured techniques for tightening relaxation bounds provided by approximate decision diagrams, analogously to how cutting-planes are used in integer programming. This paper provides an analysis of the strength of approximate decision diagrams, as well as the description of several bound-tightening procedures for problems with linear objective functions

Decomposition Based on Decision Diagrams

In recent years, decision diagrams (DDs) have proven useful for solving a variety of optimization problems, often closing long-standing from classical benchmarks. This success is primarily driven by DDs ability to capture structure. This paper exploits this characteristic proposes a novel solution method which decomposes a problem into-structured portions, where the solution set of each portion can be compactly represented using a DD. This technique is applied to a case of the independent set problem and to unconstrained binary programming. Preliminary computational results suggest that proposed approach can improve upon both standard programming models and a single DD approach

Incremental Heuristic Search for Planning with Temporally Extended Goals and Uncontrollable Events

Planning with temporally extended goals and uncontrollable events has recently been introduced as a formal model for system reconfiguration problems. An important application is to automatically reconfigure a real-life system in such a way that its subsequent internal evolution is consistent with a temporal goal formula. In this paper we introduce an incremental search algorithm and a search-guidance heuristic, two generic planning enhancements. An initial problem is decomposed into a series of subproblems, providing two main ways of speeding up a search. Firstly, a subproblem focuses on a part of the initial goal. Secondly, a notion of action relevance allows to explore with higher priority actions that are heuristically considered to be more relevant to the subproblem at hand. Even though our techniques are more generally applicable, we restrict our attention to planning with temporally extended goals and uncontrollable events. Our ideas are implemented on top of a successful previous system that performs online learning to better guide planning and to safely avoid potentially expensive searches. In experiments, the system speed performance is further improved by a convincing margin

Multiobjective Optimization by Decision Diagrams

In this paper we present a technique for solving multiobjective discrete optimization problems using decision diagrams. The proposed methodology is related to an algorithm designed for multiobjective optimization for dynamic programming, except utilizing decision diagram theory to reduce the state space, which can lead to orders of magnitude performance gains over existing algorithms. The decision diagram-based technique is applied to knapsack, set covering, and set partitioning problems, exhibiting improvements over state-of-the-art general-purpose multiobjective optimization algorithms