We develop a heuristic solution method for the Consistent Vehicle Routing Problem with Time Windows (ConVRPTW), motivated by a real-world application at a distribution center of a food company. Additional to standard VRPTW restrictions, ConVRP assigns to each customer just one fixed driver to fulfill their orders during the complete multi-period planning horizon. For each driver and day of the planning horizon, a route has to be determined to serve all their assigned customers with positive demand. The customers do not buy every day and the frequency with which they do so is irregular. Moreover, the quantities ordered change from one order to another. This causes difficulties in the daily routing, negatively impacting the service level of the company. Unlike the previous works on ConVRP, where the number of drivers is fixed a priori and only the total travel time is minimized, we give priority to minimizing the number of drivers. To evaluate the performance of the heuristic, we compare the solution of the heuristic with the routing plan in use by the food company. The results show significant improvements, with a lower number of trucks and a higher rate of orders delivered within the prescribed time window.

We propose prioritized unit propagation with periodic resetting, which is a simple but surprisingly effective algorithm for solving random SAT instances that are meant to be hard. In particular, an evaluation on the Random Track of the 2017 and 2018 SAT competitions shows that a basic prototype of this simple idea already ranks at second place in both years. We share this observation in the hope that it helps the SAT community better understand the hardness of random instances used in competitions and inspire other interesting ideas on SAT solving.

Personal use of this material is permitted. Abstract -- Increasing interest in integrating advanced robotics within manufacturing has spurred a renewed concentration in developing real-time scheduling solutions to coordinate human-robot collaboration in this environment. Traditionally, the problem of scheduling agents to complete tasks with temporal and spatial constraints has been approached either with exact algorithms, which are computationally intractable for large-scale, dynamic coordination, or approximate methods that require domain experts to craft heuristics for each application. We seek to overcome the limitations of these conventional methods by developing a novel graph attention network formulation to automatically learn features of scheduling problems to allow their deployment. T o learn effective policies for combinatorial optimization problems via machine learning, we combine imitation learning on smaller problems with deep Q-learning on larger problems, in a nonparametric framework, to allow for fast, near-optimal scheduling of robot teams. We show that our network-based policy finds at least twice as many solutions over prior state-of-the-art methods in all testing scenarios. I. INTRODUCTION Advances in robotic technology are enabling the introduction of mobile robots into manufacturing environments alongside human workers. By removing the cage around traditional robot platforms and integrating dynamic, final assembly operations with human-robot teams, manufacturers can see improvements in reducing a factory's footprint and environmental costs, as well as increased productivity [1].

In this paper, the extension of the framework of Learning from Constraints (LfC) to a distributed setting where multiple parties, connected over the network, contribute to the learning process is studied. LfC relies on the generic notion of "constraint" to inject knowledge into the learning problem and, due to its generality, it deals with possibly nonconvex constraints, enforced either in a hard or soft way. Motivated by recent progresses in the field of distributed and constrained nonconvex optimization, we apply the (distributed) Asynchronous Method of Multipliers (ASYMM) to LfC. The study shows that such a method allows us to support scenarios where selected constraints (i.e., knowledge), data, and outcomes of the learning process can be locally stored in each computational node without being shared with the rest of the network, opening the road to further investigations into privacy-preserving LfC. Constraints act as a bridge between what is shared over the net and what is private to each node and no central authority is required. We demonstrate the applicability of these ideas in two distributed real-world settings in the context of digit recognition and document classification.

Project scheduling includes various problems of high pract ical relevance. Such problems arise in many areas and include different constraints and objectives. Usually pro ject scheduling problems require scheduling of a set of proj ect activities over a period of time and assignment of resources to these activities. Typical constraints include time windows for activities, precedence constraints between the ac tivities, assignment of appropriate resources etc. The aim is to find feasible schedules that optimize several criteria su ch as the minimization of total completion time. In this paper we investigate solving a real-world project sc heduling problem that arises in an industrial test laborato ry of a large company. This problem, Industrial Test Laborator y Scheduling (TLSP), which is an extension of the well known Resource-Constrained Project Scheduling Problem (R CPSP), was originally described in [1, 2]. It consists of a grouping stage, where smaller activities (tasks) are join ed into larger jobs, and a scheduling stage, where those jobs are scheduled and have resources assigned to them. In this wo rk, we deal with the second stage and assume that a grouping of tasks into jobs is already provided.

Programming by example is the problem of synthesizing a program from a small set of input / output pairs. Recent works applying machine learning methods to this task show promise, but are typically reliant on generating synthetic examples for training. A particular challenge lies in generating meaningful sets of inputs and outputs, which well-characterize a given program and accurately demonstrate its behavior. Where examples used for testing are generated by the same method as training data then the performance of a model may be partly reliant on this similarity. In this paper we introduce a novel approach using an SMT solver to synthesize inputs which cover a diverse set of behaviors for a given program. We carry out a case study comparing this method to existing synthetic data generation procedures in the literature, and find that data generated using our approach improves both the discriminatory power of example sets and the ability of trained machine learning models to generalize to unfamiliar data.

The blocks world is a classic toy domain that has long been used to build and test spatial reasoning systems. Despite its relative simplicity, tackling this domain in its full complexity requires the agent to exhibit a rich set of functional capabilities, ranging from vision to natural language understanding. There is currently a resurgence of interest in solving problems in such limited domains using modern techniques. In this work we tackle spatial question answering in a holistic way, using a vision system, speech input and output mediated by an animated avatar, a dialogue system that robustly interprets spatial queries, and a constraint solver that derives answers based on 3-D spatial modeling. The contributions of this work include a semantic parser that maps spatial questions into logical forms consistent with a general approach to meaning representation, a dialog manager based on a schema representation, and a constraint solver for spatial questions that provides answers in agreement with human perception. These and other components are integrated into a multi-modal human-computer interaction pipeline.

We investigate rules which allow variable elimination in binary CSP (constraint satisfaction problem) instances while conserving satisfiability. We study variable-elimination rules based on the language of forbidden patterns enriched with counting and quantification over variables and values. We propose new rules and compare them, both theoretically and experimentally. We give optimised algorithms to apply these rules and show that each defines a novel tractable class. Using our variable-elimination rules in preprocessing allowed us to solve more benchmark problems than without.

We explore a new approach for training neural networks where all lo ss functions are replaced by hard constraints. The same approach is very successfu l in phase retrieval, where signals are reconstructed from magnitude constraints and gener al characteristics (sparsity, support, etc.). Instead of taking gradient steps, the optimizer in the constraint based approach, called relaxed-reflect-reflect (RRR), derives its step s from projections to local constraints. In neural networks one such projection makes the minimal modification to the inputs x, the associated weights w, and the pre-activation value y at each neuron, to satisfy the equation x · w y . These projections, along with a host of other local projections (constraining pre-and post-activations, etc.) can be partitioned into two sets such that all the projections in each set can be applied concurrently -- across th e network and across all data in the training batch. This partitioning into two sets is analogous to the situation in phase retrieval and the setting for which the general purpose RR R optimizer was designed. Owing to the novelty of the method, this paper also serves as a self-contained tutorial. Starting with a single-layer network that performs nonnegative m atrix factorization, and concluding with a generative model comprising an autoencoder and c lassifier, all applications and their implementations by projections are described in comp lete detail. Although the new approach has the potential to extend the scope of neura l networks (e.g. by defining activation not through functions but constraint sets), most o f the featured models are standard to allow comparison with stochastic gradient descent.

Programming with logic for sophisticated applications must deal with recursion and negation, which have created significant challenges in logic, leading to many different, conflicting semantics of rules. This paper describes a unified language, DA logic, for design and analysis logic, based on the unifying founded semantics and constraint semantics, that support the power and ease of programming with different intended semantics. The key idea is to provide meta constraints, support the use of uncertain information in the form of either undefined values or possible combinations of values, and promote the use of knowledge units that can be instantiated by any new predicates, including predicates with additional arguments.