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One of the key challenges for operations researchers solving real-world problems is designing and implementing high-quality heuristics to guide their search procedures. In the past, machine learning techniques have failed to play a major role in operations research approaches, especially in terms of guiding branching and pruning decisions. We integrate deep neural networks into a heuristic tree search procedure to decide which branch to choose next and to estimate a bound for pruning the search tree of an optimization problem. We call our approach Deep Learning assisted heuristic Tree Search (DLTS) and apply it to a well-known problem from the container terminals literature, the container pre-marshalling problem (CPMP). Our approach is able to learn heuristics customized to the CPMP solely through analyzing the solutions to CPMP instances, and applies this knowledge within a heuristic tree search to produce the highest quality heuristic solutions to the CPMP to date.

To what extent is it possible to use machine learning to predict the outcome of a relationship, based on the personality of both partners? In the present study, relationship satisfaction, conflicts, and separation (intents) of 192 partners four years after the completion of questionnaires concerning their personality traits was predicted. A 10x10-fold cross-validation was used to ensure that the results of the linear regression models are reproducible. The findings indicate that machine learning techniques can improve the prediction of relationship quality (37% of variance explained), and that the perceived relationship quality of a partner is mostly dependent on his or her own individual personality traits. Additionally, the influences of different sets of variables on predictions are shown: partner and similarity effects did not incrementally predict relationship quality beyond actor effects and general personality traits predicted relationship quality less strongly than relationship-related personality.

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Recently numerous machine learning based methods for combinatorial optimization problems have been proposed that learn to construct solutions in a sequential decision process via reinforcement learning. While these methods can be easily combined with search strategies like sampling and beam search, it is not straightforward to integrate them into a high-level search procedure offering strong search guidance. Bello et al. (2016) propose active search, which adjusts the weights of a (trained) model with respect to a single instance at test time using reinforcement learning. While active search is simple to implement, it is not competitive with state-of-the-art methods because adjusting all model weights for each test instance is very time and memory intensive. Instead of updating all model weights, we propose and evaluate three efficient active search strategies that only update a subset of parameters during the search. The proposed methods offer a simple way to significantly improve the search performance of a given model and outperform state-of-the-art machine learning based methods on combinatorial problems, even surpassing the well-known heuristic solver LKH3 on the capacitated vehicle routing problem. Finally, we show that (efficient) active search enables learned models to effectively solve instances that are much larger than those seen during training.Preprint. Under review.