Uncertain Capacitated Arc Routing Problem Research Articles

Explaining Genetic Programming-Evolved Routing Policies for Uncertain Capacitated Arc Routing Problems

Genetic programming has been successfully used to evolve routing policies that can make real-time routing decisions for uncertain arc routing problems. Although the evolved routing policies are highly effective, they are typically very large and complex, and hard to be understood and trusted by real users. Existing studies have attempted to improve the interpretability by developing new genetic programming approaches to evolve both effective and interpretable (e.g., with smaller program size) routing policies. However, they still have limitations due to the trade-off between effectiveness and interpretability. To address this issue, we propose a new post-hoc explanation approach to explaining the effective but complex routing policies evolved by genetic programming. The new approach includes a local ranking explanation and a global explanation module. The local ranking explanation uses particle swarm optimisation to learn an interpretable linear model that accurately explains the local behaviour of the routing policy for each decision situation. Then, the global explanation module uses a clustering technique to summarise the local explanations into a global explanation. The experimental results and case studies on the benchmark datasets show that the proposed method can obtain accurate and understandable explanations of the routing policies evolved for uncertain arc routing problems. Our explanation approach is not restricted to uncertain arc routing, but has a great potential to be generalised to other optimisation and machine learning problems such as learning classifier systems and reinforcement learning.

A Multi-Objective Genetic Programming Algorithm With α Dominance and Archive for Uncertain Capacitated Arc Routing Problem

The uncertain capacitated arc routing problem is an important combinatorial optimization problem with many applications in the real world. Genetic programming hyper heuristic has been successfully used to automatically evolve routing policies, which can make real-time routing decisions for uncertain capacitated arc routing problems. It is desired to evolve routing policies that are both effective and small/simple to be easily understood. The effectiveness and size are two potentially conflicting objectives. A further challenge is the objective selection bias issue, i.e., it is much more likely to obtain small but ineffective routing policies than the effective ones that are typically large. In this paper, we propose a new multi-objective genetic programming algorithm to evolve effective and small routing policies. The new algorithm employs the α dominance strategy with a newly proposed α adaptation scheme to address the objective selection bias issue. In addition, it contains a new archive strategy to prevent the loss of promising individuals due to the rotation of training instances. The experimental results showed that the newly proposed algorithm can evolve significantly better routing policies than the current state-of-the-art algorithms for uncertain capacitated arc routing problem in terms of both effectiveness and size. We have also analysed the evolved routing policies to show better interpretability.

Learning Heuristics With Different Representations for Stochastic Routing.

Uncertainty is ubiquitous in real-world routing applications. The automated design of the routing policy by hyperheuristic methods is an effective technique to handle the uncertainty and to achieve online routing for dynamic or stochastic routing problems. Currently, the tree representation routing policy evolved by genetic programming is commonly adopted because of the remarkable flexibility. However, numeric representations have never been used. Considering the practicability of the numeric representations and the capability of the numeric optimization methods, in this article, we investigate two numeric representations on a representative stochastic routing problem and uncertain capacitated arc routing problem. Specifically, a linear representation and an artificial neural-network (ANN) representation are implemented and compared with the tree representation to reveal the potential of the numeric representations and the characteristics of their optimization. Experimental results show that the tree representation is the best choice, but on a majority of the test instances, the numeric representations, especially the ANN representation, can provide competitive performance. Further analyses also show that training a good ANN representation policy requires more training data than the tree representation. Finally, a guideline of representation selection is given.

Knowledge Transfer Genetic Programming With Auxiliary Population for Solving Uncertain Capacitated Arc Routing Problem

The uncertain capacitated arc routing problem (UCARP) is an NP-hard combinatorial optimization problem with a wide range of applications in logistics domains. Genetic programming (GP) hyper-heuristic has been successfully applied to evolve routing policies to effectively handle the uncertain environment in this problem. The real world usually encounters different but related instances due to events, such as season change and vehicle breakdowns, and it is desirable to transfer knowledge gained from solving one instance to help solve another related one. However, the solutions found by the GP process can lack diversity, and the existing methods use the transferred knowledge mainly during initialization. Thus, they cannot sufficiently handle the change from the source to the target instance. To address this issue, we develop a novel knowledge transfer GP with an auxiliary population. In addition to the main population for the target instance, we initialize an auxiliary population using the transferred knowledge and evolve it alongside the main population. We develop a novel scheme to carefully exchange the knowledge between the two populations, and a surrogate model to evaluate the auxiliary population efficiently. The experimental results confirm that the proposed method performed significantly better than the state-of-the-art GP approaches for a wide range of uncertain arc routing instances, in terms of both final performance and convergence speed.

Route Stability in the Uncertain Capacitated Arc Routing Problem

Power line inspections in a microgrid can be modeled as the uncertain capacitated arc routing problem, which is a classic combinatorial optimization problem. As an evolutionary computation method, genetic programming is used as a hyper-heuristic method to automatically evolve routing policies that can make real-time decisions in an uncertain environment. Most existing research on genetic programming hyper-heuristic for the uncertain capacitated arc routing problem only focuses on optimizing the total cost of solutions. As a result, the actual routes directed by the routing policies evolved by genetic programming hyper-heuristic are usually not stable, i.e., the routes have large fluctuations in different uncertain environments. However, for marketing or considering the drivers’ and customers’ perspectives, the routes should not be changed too often or too much. Addressing this problem, this study first proposes a method to estimate the similarity between two routes and then extends it for evaluating the stability of the routes in uncertain environments. A novel genetic programming hyper-heuristic, which considers two objectives, i.e., the solution quality (total cost) and the stability of routes, was designed. Experimental studies demonstrate that the proposed genetic programming is hyper-heuristic with stability in consideration and can obtain more stable solutions than the traditional algorithm, without deteriorating the total cost. The approach provided in this study can be easily extended to solving other combinatorial optimization problems in the microgrid.

Genetic Programming With Knowledge Transfer and Guided Search for Uncertain Capacitated Arc Routing Problem

The uncertain capacitated arc routing problem has many real-world applications in logistics domains. Genetic programming (GP) is a promising approach to training routing policies to make real-time decisions and handle uncertain events effectively. In the real world, there are various problem domains and no single routing policy can work effectively in all of them. Instead of training in isolation, we can leverage the relatedness between the problems and transfer knowledge from previously solved source problems to solve the target problem. The existing transfer methods are not effective enough due to the loss of diversity during the knowledge transfer. To increase the diversity of the transferred knowledge, in this article, we propose a novel GP method that removes phenotypic duplicates from the source individuals to initialize the target individuals. Furthermore, assuming that the transferred knowledge used in initialization already includes all the important knowledge explored for the source problem, it is more effective to explore new regions that have not been explored for the source problem. Therefore, we propose novel genetic operators that prohibit the search from revisiting the source individuals when solving the target problem. To speed up the revisit check, we propose to adapt a powerful hashing method for routing policies that greatly improves the efficiency of the genetic operators. Our experimental results show that the proposed method significantly outperforms the existing GP approaches with knowledge transfer in terms of both initial and final solution quality.

A New Cooperative Recourse Strategy for Emergency Material Allocation in Uncertain Environments

Emergency material allocation is an important issue in the urgent handling of public health emergencies. This article models the relief allocation and transportation route planning as an uncertain capacitated arc routing problem, which is a classic combinatorial optimization problem that considers stochastic factors such as uncertain demand and travel time in the service. The stochastic of demand leads to the route failure that the vehicle cannot serve the tasks successfully unexpected. Most existing research uses the independent recourse strategy. That is, each vehicle takes a back-and-forth trip separately when its remaining capacity cannot meet the actual demand of the task. This leads to a considerable recourse cost. However, a few studies have considered vehicular cooperation to deal with route failure, which is beneficial for pooling the capacity of multiple vehicles. In this paper, we propose a new recourse strategy called OneFAll that lets one vehicle take charge of all the failed tasks. In this case, other vehicles can finish the service once they are full. We develop the genetic programming hyper-heuristic with the OneFAll recourse strategy for solving the uncertain capacitated arc routing problem. The experimental studies show that our proposed method outperforms the existing genetic programming hyper-heuristic with the independent recourse strategy to the uncertain capacitated arc routing problem for the ugdb and uval benchmark instances. Moreover, our strategy outperforms the recourse strategy that failed tasks are returned to the unassigned task set for any vehicle to complete. This reflects that there exists resource waste if all vehicles are involved to repair the failed routes.

Genetic Programming With Niching for Uncertain Capacitated Arc Routing Problem

The uncertain capacitated arc routing problem is an important optimization problem with many real-world applications. Genetic programming is considered a promising hyper-heuristic technique to automatically evolve routing policies that can make effective real-time decisions in an uncertain environment. Most existing research on genetic programming hyper-heuristic for the uncertain capacitated arc routing problem only focused on the test performance aspect. As a result, the routing policies evolved by genetic programming are usually too large and complex, and hard to comprehend. To evolve effective, smaller, and simpler routing policies, this article proposes a novel genetic programming approach, which simplifies the routing policies during the evolutionary process using a niching technique. The simplified routing policies are stored in an external archive. We also developed new elitism, parent selection, and breeding schemes for generating offspring from the original population and the archive. The experimental results show that the newly proposed approach can achieve significantly better test performance than the current state-of-the-art genetic programming algorithms for the uncertain capacitated arc routing problem. The evolved routing policies are smaller, and thus potentially more interpretable.

Robust Optimization in Uncertain Capacitated Arc Routing Problems: Progresses and Perspectives [Review Article

The capacitated arc routing problem is an important NP-hard problem with numerous real-world applications. The capacitated arc routing problem with uncertainties refers to those instances where there are uncertainties in decision variables, objective functions and/or constraints. The capacitated arc routing problem with uncertainties captures real-world situations much better than a static capacitated arc routing problem because few real-world problems are static and certain. Uncertainties in the capacitated arc routing problem pose new research challenges. Algorithms that work well for a static and certain capacitated arc routing problem may not work on the version with uncer-tainties. There have been increasing progresses in studying the capacitated arc routing problem with uncertainties during the past two decades. However, the papers on the capacitated arc rout-ing problem with uncertainties have been scattered around in different journals and conferences in artificial intelligence, computer science, and operational research. Different defini-tions and formulations of capacitated arc routing problem with uncertainties are used by different papers, making comparisons difficult. In order to better understand the state-of-the-art in solv-ing the capacitated arc routing problem with uncertainties, this paper presents a comprehensive review of the problem and its key research issues. Not only has the paper summarized the progresses so far, key research issues are identified, including scalability of the algorithms, performance measures, common benchmarks, etc. Future research direc-tions are also identified at the end of this review.

Genetic Programming Hyper-Heuristics with Vehicle Collaboration for Uncertain Capacitated Arc Routing Problems

Due to its direct relevance to post-disaster operations, meter reading and civil refuse collection, the Uncertain Capacitated Arc Routing Problem (UCARP) is an important optimisation problem. Stochastic models are critical to study as they more accurately represent the real world than their deterministic counterparts. Although there have been extensive studies in solving routing problems under uncertainty, very few have considered UCARP, and none consider collaboration between vehicles to handle the negative effects of uncertainty. This article proposes a novel Solution Construction Procedure (SCP) that generates solutions to UCARP within a collaborative, multi-vehicle framework. It consists of two types of collaborative activities: one when a vehicle unexpectedly expends capacity (route failure), and the other during the refill process. Then, we propose a Genetic Programming Hyper-Heuristic (GPHH) algorithm to evolve the routing policy used within the collaborative framework. The experimental studies show that the new heuristic with vehicle collaboration and GP-evolved routing policy significantly outperforms the compared state-of-the-art algorithms on commonly studied test problems. This is shown to be especially true on instances with larger numbers of tasks and vehicles. This clearly shows the advantage of vehicle collaboration in handling the uncertain environment, and the effectiveness of the newly proposed algorithm.

A Predictive-Reactive Approach with Genetic Programming and Cooperative Coevolution for the Uncertain Capacitated Arc Routing Problem.

The uncertain capacitated arc routing problem is of great significance for its wide applications in the real world. In the uncertain capacitated arc routing problem, variables such as task demands and travel costs are realised in real time. This may cause the predefined solution to become ineffective and/or infeasible. There are two main challenges in solving this problem. One is to obtain a high-quality and robust baseline task sequence, and the other is to design an effective recourse policy to adjust the baseline task sequence when it becomes infeasible and/or ineffective during the execution. Existing studies typically only tackle one challenge (the other being addressed using a naive strategy). No existing work optimises the baseline task sequence and recourse policy simultaneously. To fill this gap, we propose a novel proactive-reactive approach, which represents a solution as a baseline task sequence and a recourse policy. The two components are optimised under a cooperative coevolution framework, in which the baseline task sequence is evolved by an estimation of distribution algorithm, and the recourse policy is evolved by genetic programming. The experimental results show that the proposed algorithm, called Solution-Policy Coevolver, significantly outperforms the state-of-the-art algorithms to the uncertain capacitated arc routing problem for the ugdb and uval benchmark instances. Through further analysis, we discovered that route failure is not always detrimental. Instead, in certain cases (e.g., when the vehicle is on the way back to the depot) allowing route failure can lead to better solutions.

Estimation of the Distribution Algorithm With a Stochastic Local Search for Uncertain Capacitated Arc Routing Problems

The uncertain capacitated arc routing problem is a challenging problem in which the demands of tasks, the costs of edges, and the presence of tasks and edges are uncertain. The objective of this problem is to find a robust optimal solution for a finite set of possible scenarios. In this paper, we propose a novel robust optimization approach, called an estimation of distribution algorithm (EDA) with stochastic local search (SLS), to tackle this problem. The proposed method integrates an EDA with a novel two phase SLS procedure to minimize the maximal total cost over a set of different scenarios. The SLS procedure avoids excessive fitness evaluations of unpromising moves in local search. Our experimental results on two sets of benchmark problems (a total of 55 problem instances) showed that the proposed approach outperformed existing state-of-the-art algorithms.