Papers

Combinatorial optimization problems are ubiquitous for decision making in planning social infrastructures. In real-world scenarios, a decision-maker needs to solve his/her problem iteratively until he/she satisfies solutions, but such an iterative process remains challenging. This paper studies a new explainable framework, particularly for finding meeting points, which is a key optimization problem for designing facility locations. Our framework automatically fills the gap between its input instance and instances from which a user could obtain the desired outcome, where computed solutions are judged by the user. The framework also provides users with explanations, representing the difference of instances for deeply understanding the process and its inside. Explanations are clues for users to understand their situation and implement suggested results in practice (e.g., designing a coupon for free travel). We experimentally demonstrate that our search-based framework is promising to solve instances with generating explanations in a sequential decision-making process.

poster session 2 @ blue 4, poster session 9 @ blue 4, oral session 2 @ blue 4, poster session 2, poster session 9, oral session 2

The Maximum $k$-Defective Clique Problem (MDCP), as a clique relaxation model, has been used to solve various problems. Because it is a computational hard task, previous works can hardly solve the MDCP for massive sparse graphs derived from real-world applications. In this work, we propose a novel branch-and-bound algorithm to solve the MDCP based on several new techniques. First, we propose two new upper bounds of the MDCP as well as corresponding reduction rules to remove redundant vertices and edges. The proposed reduction rules are particularly useful for massive graphs. Second, we present another new upper bound by counting missing edges between fixed vertices and an unfixed vertex for cutting branches. We perform extensive computational experiments to evaluate our algorithm. Experimental results show that our reduction rules are very effective for removing redundant vertices and edges so that graphs are reduced greatly. Also, our algorithm can solve benchmark instances efficiently, and it has significantly better performance than state-of-the-art algorithms.

poster session 2 @ blue 4, poster session 9 @ blue 4, oral session 2 @ blue 4, poster session 2, poster session 9, oral session 2

Column Generation (CG) is an effective method for solving large-scale optimization problems. CG starts by solving a subproblem with a subset of columns (i.e., variables) and gradually includes new columns that can improve the solution of the current subproblem. The new columns are generated as needed by repeatedly solving a pricing problem, which is often NP-hard and is a bottleneck of the CG approach. To tackle this, we propose a Machine-Learning-based Pricing Heuristic (MLPH) that can generate many high-quality columns efficiently. In each iteration of CG, our MLPH leverages an ML model to predict the optimal solution of the pricing problem, which is then used to guide a sampling method to efficiently generate multiple high-quality columns. Using the graph coloring problem, we empirically show that MLPH significantly enhances CG as compared to six state-of-the-art methods, and the improvement in CG can lead to substantially better performance of the branch-and-price exact method.

poster session 2 @ blue 4, poster session 9 @ blue 4, oral session 2 @ blue 4, poster session 2, poster session 9, oral session 2