The rapid adoption of electric vehicles (EVs) in modern transport systems has made energy-aware routing a critical task in their successful integration, especially within large-scale transport networks. In cases where an EV's remaining energy is limited and charging locations are not easily accessible, some destinations may only be reachable through an energy-optimal path: a route that consumes less energy than all other alternatives. The feasibility of such energy-efficient paths depends heavily on the accuracy of the energy model used for planning, and thus failing to account for vehicle dynamics can lead to inaccurate energy estimates, rendering some planned routes infeasible in reality. This paper explores the impact of vehicle dynamics on energy-optimal path planning for EVs. We first investigate how energy model accuracy influences energy-optimal pathfinding and, consequently, feasibility of planned trips, using a novel data-driven model that incorporates key vehicle dynamics parameters into energy calculations. Additionally, we introduce two novel online reweighting and energy heuristic functions that accelerate path planning with negative energy costs arise due to regenerative braking, making our approach well-suited for real-time applications. Extensive experiments on real-world transport networks demonstrate that our method significantly improves both the computational efficiency of energy-optimal pathfinding for EVs.

The classic Resource Constrained Shortest Path (RCSP) problem aims to find a cost optimal path between a pair of nodes in a network such that the resources used in the path are within a given limit. Having been studied for over a decade, RCSP has seen recent solutions that utilize heuristic-guided search to solve the constrained problem faster. Building upon the bidirectional A* search paradigm, this paper introduces a novel constrained search framework that uses efficient pruning strategies to allow for accelerated and effective RCSP search in large-scale networks. Results show that, compared to the state of the art, our enhanced framework can significantly reduce the constrained search time, achieving speed-ups of over to two orders of magnitude.

In this experience paper, we present ALAN, a framework to automate the generation of authentic assessment tasks in networking courses (NC). Using ALAN, all students in a cohort complete a set of assessment tasks generated from the same skeleton, with each student having their own parameters as input. The way we run ALAN assessments fosters students' self-regulation and peer learning and activates students' engagement in learning through assessment. We present three different ALAN assessments. We finally report on student perceptions and satisfaction and reflect on our experience.

Abstract The classic problem of constrained pathfinding is a well‐studied, yet challenging, network optimization problem with a broad range of applications in various areas such as communication and transportation. The weight constrained shortest path problem (WCSPP), the base form of constrained pathfinding with only one side constraint, aims to plan a cost‐optimum path with limited weight/resource usage. Given the bi‐criteria nature of the problem (i.e., dealing with the cost and weight of paths), methods addressing the WCSPP have some common properties with bi‐objective search. This article leverages the recent state‐of‐the‐art techniques in both constrained pathfinding and bi‐objective search and presents two new solution approaches to the WCSPP on the basis of A* search, both capable of solving hard WCSPP instances on very large graphs. We empirically evaluate the performance of our algorithms on a set of large and realistic problem instances and show their advantages over the state‐of‐the‐art algorithms in both time and space metrics. This article also investigates the importance of priority queues in constrained search with A*. We show with extensive experiments on both realistic and randomized graphs how bucket‐based queues without tie‐breaking can effectively improve the algorithmic performance of exhaustive A*‐based bi‐criteria searches.

In optimisation problems involving multiple agents (stakeholders) we often want to make sure that the solution is balanced and fair. That is, we want to maximise total utility subject to an upper bound on the statistical dispersion (e.g., spread or the Gini coefficient) of the utility given to different agents, or minimise dispersion subject to some lower bounds on utility. These needs arise in, for example, balancing tardiness in scheduling, unwanted shifts in rostering, and desired resources in resource allocation, or minimising deviation from a baseline in schedule repair, to name a few. These problems are often quite challenging. To solve them efficiently we want to effectively reason about dispersion. Previous work has studied the case where the mean is fixed, but this may not be possible for many problems, e.g., scheduling where total utility depends on the final schedule. In this paper we introduce two log-linear-time dispersion propagators – (a) spread (variance, and indirectly standard deviation) and (b) the Gini coefficient – capable of explaining their propagations, thus allowing effective clause learning solvers to be applied to these problems. Propagators for (a) exist in the literature but do not explain themselves, while propagators for (b) have not been previously studied. We avoid introducing floating-point variables, which are usually not supported by learning solvers, by reasoning about scaled, integer versions of the constraints. We show through experimentation that clause learning can substantially improve the solving of problems where we want to bound dispersion and optimise total utility and vice versa.

Weight constrained path finding, known as a challenging variant of the classic shortest path problem, aims to plan cost optimum paths whose weight/resource usage is limited by a side constraint. Given the bi-criteria nature of the problem (i.e., the presence of cost and weight), solutions to the Weight Constrained Shortest Path Problem (WCSPP) have some properties in common with bi-objective search. This paper leverages the state-of-the-art bi-objective search algorithm BOBA* and presents WC-BA*, an exact A*-based WCSPP method that explores the search space in different objective orderings bidirectionally. We also enrich WC-BA* with two novel heuristic tuning approaches that can significantly reduce the number of node expansions in the exhaustive search of A*. The results of our experiments on a large set of realistic problem instances show that our new algorithm solves all instances and outperforms the state-of-the-art WCSPP algorithms in various scenarios.

User trust plays a key role in determining whether autonomous computer applications are relied upon. It will play a key role in the acceptance of emerging AI applications such as optimisation. Two important factors known to affect trust are system transparency, i.e., how well the user understands how the system works, and system performance. However, in the case of optimisation, it is difficult for the end-user to understand the underlying algorithms or to judge the quality of the solution. Through two controlled user studies, we explore whether the user is better able to calibrate their trust in the system when: (a) They are provided feedback on the system operation in the form of visualisation of intermediate solutions and their quality; (b) They can interactively explore the solution space by modifying the solution returned by the system. We found that showing intermediate solutions can lead to over-trust, while interactive exploration leads to more accurately calibrated trust.

Resource constrained path finding is a well studied topic in AI, with real-world applications in different areas such as transportation and robotics. This paper introduces several heuristics in the resource constrained path finding context that significantly improve the algorithmic performance of the initialisation phase and the core search. We implement our heuristics on top of a bidirectional A* algorithm and evaluate them on a set of large instances. The experimental results show that, for the first time in the context of constrained path finding, our fast and enhanced algorithm can solve all of the benchmark instances to optimality, and compared to the state of the art algorithms, it can improve existing runtimes by up to four orders of magnitude on large-size network graphs.

Electric Vehicles (EVs) are set to replace vehicles based on internal combustion engines. Path planning and vehicle routing for EVs need to take their specific characteristics into account, such as reduced range, long charging times, and energy recuperation. This paper investigates the importance of vehicle dynamics parameters in energy models for EV routing, particularly in the Pickup-and-Delivery Problem (PDP). We use Constraint Programming (CP) technology to develop a complete PDP model with different charger technologies. We adapt realistic instances that consider vehicle dynamics parameters such as vehicle mass, road gradient and driving speed to varying degrees. The results of our experiments show that neglecting such fundamental vehicle dynamics parameters can affect the feasibility of planned routes for EVs, and fewer/shorter charging visits will be planned if we use energy-efficient paths instead of conventional shortest paths in the underlying system model.

Bi-objective search is a well-known algorithmic problem, concerned with finding a set of optimal solutions in a two-dimensional domain. This problem has a wide variety of applications such as planning in transport systems or optimal control in energy systems. Recently, bi-objective A*-based search (BOA*) has shown state-of-the-art performance in large networks. This paper develops a bi-directional and parallel variant of BOA*, enriched with several speed-up heuristics. Our experimental results on 1,000 benchmark cases show that our bi-directional A* algorithm for bi-objective search (BOBA*) can optimally solve all of the benchmark cases within the time limit, outperforming the state of the art BOA*, bi-objective Dijkstra and bi-directional bi-objective Dijkstra by an average runtime improvement of a factor of five over all of the benchmark instances.

Bi-objective search is a problem of finding a set of optimal solutions in a two-dimensional domain. This study proposes several enhancements to the state-of-the-art bi-objective search with A* and develops its bi-directional variant. Our experimental results on benchmark instances show that our enhanced algorithm is on average five times faster than the state of the art bi-objective search algorithms.

Efficient optimisation algorithms have become important tools for finding high-quality solutions to hard, real-world problems such as production scheduling, timetabling, or vehicle routing. These algorithms are typically "black boxes" that work on mathematical models of the problem to solve. However, many problems are difficult to fully specify, and require a "human in the loop" who collaborates with the algorithm by refining the model and guiding the search to produce acceptable solutions. Recently, the Problem-Solving Loop was introduced as a high-level model of such interactive optimisation. Here, we present and evaluate nine recommendations for the design of interactive visualisation tools supporting the Problem-Solving Loop. They range from the choice of visual representation for solutions and constraints to the use of a solution gallery to support exploration of alternate solutions. We first examined the applicability of the recommendations by investigating how well they had been supported in previous interactive optimisation tools. We then evaluated the recommendations in the context of the vehicle routing problem with time windows (VRPTW). To do so we built a sophisticated interactive visual system for solving VRPTW that was informed by the recommendations. Ten participants then used this system to solve a variety of routing problems. We report on participant comments and interaction patterns with the tool. These showed the tool was regarded as highly usable and the results generally supported the usefulness of the underlying recommendations.

Many optimisation problems are of an online—also called dynamic—nature, where new information is expected to arrive and the problem must be resolved in an ongoing fashion to (a) improve or revise previous decisions and (b) take new ones. Typically, building an online decision-making system requires substantial ad-hoc coding to ensure the offline version of the optimisation problem is continually adjusted and resolved. This paper defines a general framework for automatically solving online optimisation problems. This is achieved by extending a model of the offline optimisation problem, from which an online version is automatically constructed, thus requiring no further modelling effort. In doing so, it formalises many of the aspects that arise in online optimisation problems. The same framework can be applied for automatically creating sliding-window solving approaches for problems that have a large time horizon. Experiments show we can automatically create efficient online and sliding-window solutions to optimisation problems.

For many combinatorial problems, finding a single solution is not enough. This is clearly the case for multi-objective optimization problems, as they have no single “best solution” and, thus, it is useful to find a representation of the non-dominated solutions (the Pareto frontier). However, it also applies to single objective optimization problems, where one may be interested in finding several (close to) optimal solutions that illustrate some form of diversity. The same applies to satisfaction problems. This is because models usually idealize the problem in some way, and a diverse pool of solutions may provide a better choice with respect to considerations that are omitted or simplified in the model. This paper describes a general framework for finding k diverse solutions to a combinatorial problem (be it satisfaction, single-objective or multi-objective), various approaches to solve problems in the framework, their implementations, and an experimental evaluation of their practicality.

Stochastic programming is concerned with decision making under uncertainty, seeking an optimal policy with respect to a set of possible future scenarios. This paper looks at multistage decision problems where the uncertainty is revealed over time. First, decisions are made with respect to all possible future scenarios. Secondly, after observing the random variables, a set of scenario specific decisions is taken. Our goal is to develop algorithms that can be used as a back-end solver for high-level modeling languages. In this paper we propose a scenario decomposition method to solve multistage stochastic combinatorial decision problems recursively. Our approach is applicable to general problem structures, utilizes standard solving technology and is highly parallelizable. We provide experimental results to show how it efficiently solves benchmarks with hundreds of scenarios.

The aim of solver-independent modelling is to create a model of a satisfaction or optimisation problem independent of a particular technology. This avoids early commitment to a solving technology and allows easy comparison of technologies. MiniZinc is a solver-independent modelling language, supported by CP, MIP, SAT, SMT, and constraint-based local search (CBLS) backends. Some technologies, in particular CP and CBLS, require not only a model but also a search strategy. While backends for these technologies offer default search strategies, it is often beneficial to include in a model a user-specified search strategy for a particular technology, especially if the strategy can encapsulate knowledge about the problem structure. This is complex since a local-search strategy (comprising a neighbourhood, a heuristic, and a meta-heuristic) is often tightly tied to the model. Hence we wish to use the same language for specifying the model and the local search. We show how to extend MiniZinc so that one can attach a fully declarative neighbourhood specification to a model, while maintaining the solver-independence of the language. We explain how to integrate a model-specific declarative neighbourhood with an existing CBLS backend for MiniZinc.

Constraint programming allows difficult combinatorial problems to be modelled declaratively and solved automatically. Advances in solver technologies over recent years have allowed the successful use of constraint programming in many application areas. However, when a particular solver's search for a solution takes too long, the complexity of the constraint program execution hinders the programmer's ability to profile that search and understand how it relates to their model. Therefore, effective tools to support such profiling and allow users of constraint programming technologies to refine their model or experiment with different search parameters are essential. This paper details the first user-centred design process for visual profiling tools in this domain. We report on: our insights and opportunities identified through an on-line questionnaire and a creativity workshop with domain experts carried out to elicit requirements for analytical and visual profiling techniques; our designs and functional prototypes realising such techniques; and case studies demonstrating how these techniques shed light on the behaviour of the solvers in practice.