Jimmy Ho-Man Lee’s research while affiliated with The University of Hong Kong and other places

Dominance breaking is a powerful technique in improving the solving efficiency of Constraint Optimization Problems (COPs) by removing provably suboptimal solutions with additional constraints. While dominance breaking is effective in a range of practical problems, it is usually problem specific and requires human insights into problem structures to come up with correct dominance breaking constraints. Recently, a framework is proposed to generate nogood constraints automatically for dominance breaking, which formulates nogood generation as solving auxiliary Constraint Satisfaction Problems (CSPs). However, the framework uses a pattern matching approach to synthesize the auxiliary generation CSPs from the specific forms of objectives and constraints in target COPs, and is only applicable to a limited class of COPs. This paper proposes a novel rewriting system to derive constraints for the auxiliary generation CSPs automatically from COPs with nested function calls, significantly generalizing the original framework. In particular, the rewriting system exploits functional constraints flattened from nested functions in a high-level modeling language. To generate more effective dominance breaking nogoods and derive more relaxed constraints in generation CSPs, we further characterize how to extend the system with rewriting rules exploiting function properties, such as monotonicity, commutativity, and associativity, for specific functional constraints. Experimentation shows significant runtime speedup using the dominance breaking nogoods generated by our proposed method. Studying patterns of generated nogoods also demonstrates that our proposal can reveal dominance relations in the literature and discover new dominance relations on problems with ineffective or no known dominance breaking constraints.

Predict+Optimize is a recently proposed framework which combines machine learning and constrained optimization, tackling optimization problems that contain parameters that are unknown at solving time. The goal is to predict the unknown parameters and use the estimates to solve for an estimated optimal solution to the optimization problem. However, all prior works have focused on the case where unknown parameters appear only in the optimization objective and not the constraints, for the simple reason that if the constraints were not known exactly, the estimated optimal solution might not even be feasible under the true parameters. The contributions of this paper are two-fold. First, we propose a novel and practically relevant framework for the Predict+Optimize setting, but with unknown parameters in both the objective and the constraints. We introduce the notion of a correction function, and an additional penalty term in the loss function, modelling practical scenarios where an estimated optimal solution can be modified into a feasible solution after the true parameters are revealed, but at an additional cost. Second, we propose a corresponding algorithmic approach for our framework, which handles all packing and covering linear programs. Our approach is inspired by the prior work of Mandi and Guns, though with crucial modifications and re-derivations for our very different setting. Experimentation demonstrates the superior empirical performance of our method over classical approaches.

Restart-based Branch-and-Bound Search (BBS) is a standard algorithm for solving Constraint Optimization Problems (COPs). In this paper, we propose an approach to find good partial assignments to jumpstart search at each restart for general COPs, which are identified by comparing different best solutions found in different restart runs. We consider information extracted from historical solutions to evaluate the quality of the partial assignments. Thus the good partial assignments are dynamically updated as the current best solution evolves. Our approach makes restart-based BBS explore different promising sub-search-spaces to find high-quality solutions. Experiments on the MiniZinc benchmark suite show how our approach brings significant improvements to a black-box COP solver equipped with the state of the art search techniques. Our method finds better solutions and proves optimality for more instances.

Combining machine learning and constrained optimization, Predict+ Optimize tackles optimization problems containing parameters that are unknown at the time of solving. Prior works focus on cases with unknowns only in the objectives. A new framework was recently proposed to cater for unknowns also in constraints by introducing a loss function, called Post-hoc Regret, that takes into account the cost of correcting an unsatisfiable prediction. Since Post-hoc Regret is non-differentiable, the previous work computes only its approximation. While the notion of Post-hoc Regret is general, its specific implementation is applicable to only packing and covering linear programming problems. In this paper, we first show how to compute Post-hoc Regret exactly for any optimization problem solvable by a recursive algorithm satisfying simple conditions. Experimentation demonstrates substantial improvement in the quality of solutions as compared to the earlier approximation approach. Furthermore, we show experimentally the empirical behavior of different combinations of correction and penalty functions used in the Post-hoc Regret of the same benchmarks. Results provide insights for defining the appropriate Post-hoc Regret in different application scenarios.KeywordsConstraint OptimizationMachine LearningPredict+Optimize

Combining machine learning and constrained optimization, Predict+Optimize tackles optimization problems containing parameters that are unknown at the time of solving. Prior works focus on cases with unknowns only in the objectives. A new framework was recently proposed to cater for unknowns also in constraints by introducing a loss function, called Post-hoc Regret, that takes into account the cost of correcting an unsatisfiable prediction. Since Post-hoc Regret is non-differentiable, the previous work computes only its approximation. While the notion of Post-hoc Regret is general, its specific implementation is applicable to only packing and covering linear programming problems. In this paper, we first show how to compute Post-hoc Regret exactly for any optimization problem solvable by a recursive algorithm satisfying simple conditions. Experimentation demonstrates substantial improvement in the quality of solutions as compared to the earlier approximation approach. Furthermore, we show experimentally the empirical behavior of different combinations of correction and penalty functions used in the Post-hoc Regret of the same benchmarks. Results provide insights for defining the appropriate Post-hoc Regret in different application scenarios.

Predict+Optimize is a recently proposed framework which combines machine learning and constrained optimization, tackling optimization problems that contain parameters that are unknown at solving time. The goal is to predict the unknown parameters and use the estimates to solve for an estimated optimal solution to the optimization problem. However, all prior works have focused on the case where unknown parameters appear only in the optimization objective and not the constraints, for the simple reason that if the constraints were not known exactly, the estimated optimal solution might not even be feasible under the true parameters. The contributions of this paper are two-fold. First, we propose a novel and practically relevant framework for the Predict+Optimize setting, but with unknown parameters in both the objective and the constraints. We introduce the notion of a correction function, and an additional penalty term in the loss function, modelling practical scenarios where an estimated optimal solution can be modified into a feasible solution after the true parameters are revealed, but at an additional cost. Second, we propose a corresponding algorithmic approach for our framework, which handles all packing and covering linear programs. Our approach is inspired by the prior work of Mandi and Guns, though with crucial modifications and re-derivations for our very different setting. Experimentation demonstrates the superior empirical performance of our method over classical approaches.

This paper proposes Branch & Learn, a framework for Predict+Optimize to tackle optimization problems containing parameters that are unknown at the time of solving. Given an optimization problem solvable by a recursive algorithm satisfying simple conditions, we show how a corresponding learning algorithm can be constructed directly and methodically from the recursive algorithm. Our framework applies also to iterative algorithms by viewing them as a degenerate form of recursion. Extensive experimentation shows better performance for our proposal over classical and state-of-the-art approaches.

This presentation gives the pedagogical innovations and experience of the co-development of three MOOCs on the subject of “Modeling and Solving Discrete Optimization Problems” by The Chinese University of Hong Kong and the University of Melbourne. In a nutshell, the MOOCs feature the Fable-based Learning approach, which is a form of problem-based learning encapsulated in a coherent story plot. Each lecture video begins with an animation that tells a story based on a classic novel. The protagonists of the story encounter a problem requiring technical assistance from the two professors from modern time via a magical tablet granted to them by a fairy god. The new pedagogy aims at increasing learners’ motivation and interests as well as situating the learners in a coherent learning context. In addition to scriptwriting, animation production and embedding the teaching materials in the story plot, another challenge of the project is the remote distance between the two institutions as well as the need to produce all teaching materials in both (Mandarin) Chinese and English to cater for different geographic learning needs. The MOOCs have been running recurrently on Coursera since 2017. We present learner statistics and feedback, and discuss our experience with and preliminary observations of adopting the online materials in a Flipped Classroom setting.

Dominance breaking is shown to be an effective technique to improve the solving speed of Constraint Optimization Problems (COPs). The paper proposes separate techniques to generalize and make more efficient the nogood generation phase of an automated dominance breaking framework by Lee and Zhong's. The first contribution is in giving conditions that allow skipping the checking of non-efficiently checkable constraints and yet still produce sufficient useful nogoods, thus opening up possibilities to apply the technique on COPs that were previously impractical. The second contribution identifies and avoids the generation of dominance breaking nogoods that are both logically and propagation redundant. The nogood generation model is strengthened using the notion of Common Assignment Elimination to avoid generation of nogoods that are subsumed by other nogoods, thus reducing the search space substantially. Extensive experimentation confirms the benefits of the new proposals.