Yi Mei

Abstract Capacitated Arc Routing Problem (CARP) has drawn much attention during the last few years because of its applications in the real world. Recently, we developed a Memetic Algorithm with Extended Neighborhood Search (MAENS), which is powerful in solving ...

Genetic Programming (GP) has been extensively used to automatically design dispatching rules for job shop scheduling problems. However, the previous studies only focus on the performance on the training instances. So far, there is no systematic investigation of the reusability of the GP-evolved rules on unseen instances. In practice, it is desirable to train the rules on smaller job shop instances, and apply them to larger instances with more jobs and machines to save training time. In this case, the reusability of the GP-evolved rules under different numbers of jobs and machines is an important issue. In this paper, a comprehensive investigation is conducted to analyse how the variation in the numbers of jobs and machines from the training set to the test set affects the reusability of the GP-evolved rules. It is found that in terms of minimizing makespan, the reusability of the GP-evolved rules highly depends on variation in the numbers of jobs and machines. A better reusability can be achieved by choosing training instances whose numbers of jobs and machines (or at least the ratio between the numbers of jobs and machines) are closer to that of the test instances. Furthermore, the ratio between the numbers of jobs and machines is demonstrated to be an important factor to reflect the complexity of an instance for dispatching rules. This study is the first systematic investigation on the reusability of GP-evolved dispatching rules.

In this paper, the Uncertain CARP (UCARP) is investigated. In UCARP, the demands of tasks and the deadheading costs of edges are stochastic and one has to design a robust solution for all possible environments. A problem model and a robustness measure for solutions are defined according to the requirements in reality. Three benchmark sets with uncertain parameters are generated by extending existing benchmark sets for static cases. In order to explore the solution space of UCARP, the most competitive algorithms for static CARP are tested on one of the generated uncertain benchmark sets. The experimental results showed that the optimal solution in terms of robustness in uncertain environment may be far away from the optimal one in terms of quality in a static environment and thus, utilizing only the expected value of the random variables can hardly lead to robust solutions.

Capacitated arc routing problem (CARP) has attracted much attention during the last few years due to its wide applications in real life. Since CARP is NP-hard and exact methods are only applicable for small instances, heuristics and metaheuristic methods are widely adopted when solving CARP. This paper demonstrates one major disadvantage encountered by traditional search algorithms and proposes a novel operator named global repair operator (GRO) to address it. We further embed GRO in a recently proposed tabu search algorithm (TSA) and apply the resultant repair-based tabu search (RTS) algorithm to five well-known benchmark test sets. Empirical results suggest that RTS not only outperforms TSA in terms of quality of solutions but also converges to the solutions faster. Moreover, RTS is also competitive with a number of state-of-the-art approaches for CARP. The efficacy of GRO is thereby justified. More importantly, since GRO is not specifically designed for the referred TSA, it might be a potential tool for improving any existing method that adopts the same solution representation.

The capacitated arc routing problem (CARP) has attracted much attention during the last few years due to its wide applications in real life. Since CARP is NP-hard and exact methods are only applicable to small instances, heuristic and metaheuristic methods are widely adopted when solving CARP. In this paper, we propose a memetic algorithm, namely memetic algorithm with extended neighborhood search (MAENS), for CARP. MAENS is distinct from existing approaches in the utilization of a novel local search operator, namely Merge-Split (MS). The MS operator is capable of searching using large step sizes, and thus has the potential to search the solution space more efficiently and is less likely to be trapped in local optima. Experimental results show that MAENS is superior to a number of state-of-the-art algorithms, and the advanced performance of MAENS is mainly due to the MS operator. The application of the MS operator is not limited to MAENS. It can be easily generalized to other approaches.

The capacitated arc routing problem (CARP) is a challenging combinatorial optimization problem with many real-world applications, e.g., salting route optimization and fleet management. There have been many attempts at solving CARP using heuristic and meta-heuristic approaches, including evolutionary algorithms. However, almost all such attempts formulate CARP as a single-objective problem although it usually has more than one objective, especially considering its real-world applications. This paper studies multiobjective CARP (MO-CARP). A new memetic algorithm (MA) called decomposition-based MA with extended neighborhood search (D-MAENS) is proposed. The new algorithm combines the advanced features from both the MAENS approach for single-objective CARP and multiobjective evolutionary optimization. Our experimental studies have shown that such combination outperforms significantly an off-the-shelf multiobjective evolutionary algorithm, namely nondominated sorting genetic algorithm II, and the state-of-the-art multiobjective algorithm for MO-CARP (LMOGA). Our work has also shown that a specifically designed multiobjective algorithm by combining its single-objective version and multiobjective features may lead to competitive multiobjective algorithms for multiobjective combinatorial optimization problems.

This paper investigates the Periodic Capacitated Arc Routing Problem (PCARP), which is often encountered in the waste collection application. PCARP is an extension of the well-known Capacitated Arc Routing Problem (CARP) from a single period to a multi-period horizon. PCARP is a hierarchical optimization problem which has a primary objective (minimizing the number of vehicles ) and a secondary objective (minimizing the total cost ). An important factor that makes PCARP challenging is that its primary objective is little affected by existing operators and thus difficult to improve. We propose a new Memetic Algorithm (MA) for solving PCARP. The MA adopts a new solution representation scheme and a novel crossover operator. Most importantly, a Route-Merging (RM) procedure is devised and embedded in the algorithm to tackle the insensitive objective . The MA with RM (MARM) has been compared with existing meta-heuristic approaches on two PCARP benchmark sets and a real-world data set. The experimental results show that MARM obtained better solutions than the compared algorithms in much less time, and even updated the best known solutions of all the benchmark instances. Further study reveals that the RM procedure plays a key role in the superior performance of MARM.

Cooperative co-evolution has been introduced into evolutionary algorithms with the aim of solving increasingly complex optimization problems through a divide-and-conquer paradigm. In theory, the idea of co-adapted subcomponents is desirable for solving large-scale optimization problems. However, in practice, without prior knowledge about the problem, it is not clear how the problem should be decomposed. In this paper, we propose an automatic decomposition strategy called differential grouping that can uncover the underlying interaction structure of the decision variables and form subcomponents such that the interdependence between them is kept to a minimum. We show mathematically how such a decomposition strategy can be derived from a definition of partial separability. The empirical studies show that such near-optimal decomposition can greatly improve the solution quality on large-scale global optimization problems. Finally, we show how such an automated decomposition allows for a better approximation of the contribution of various subcomponents, leading to a more efficient assignment of the computational budget to various subcomponents.

In this paper, a divide-and-conquer approach is proposed to solve the large-scale capacitated arc routing problem (LSCARP) more effectively. Instead of considering the problem as a whole, the proposed approach adopts the cooperative coevolution (CC) framework to decompose it into smaller ones and solve them separately. An effective decomposition scheme called the route distance grouping (RDG) is developed to decompose the problem. Its merit is twofold. First, it employs the route information of the best-so-far solution, so that the quality of the decomposition is upper bounded by that of the best-so-far solution. Thus, it can keep improving the decomposition by updating the best-so-far solution during the search. Second, it defines a distance between routes, based on which the potentially better decompositions can be identified. Therefore, RDG is able to obtain promising decompositions and focus the search on the promising regions of the vast solution space. Experimental studies verified the efficacy of RDG on the instances with a large number of tasks and tight capacity constraints, where it managed to obtain significantly better results than its counterpart without decomposition in a much shorter time. Furthermore, the best-known solutions of the EGL-G LSCARP instances are much improved.

In this paper, the interdependence between sub-problems in a complex overall problem is investigated using a benchmark problem called Travelling Thief Problem (TTP), which is a combination of Travelling Salesman Problem (TSP) and Knapsack Problem (KP). First, the analysis on the mathematical formulation shows that it is impossible to decompose the problem into independent sub-problems due to the non-linear relationship in the objective function. Therefore, the algorithm for TTP is not straightforward although each sub-problem alone has been investigated intensively. Then, two meta-heuristics are proposed for TTP. One is the Cooperative Co-evolution (CC) that solves the sub-problems separately and transfers the information between them in each generation. The other is the Memetic Algorithm (MA) that solves TTP as a whole. The comparative results showed that MA consistently obtained much better results than both the standard and dynamic versions of CC within comparable computational budget. This indicates the importance of considering the interdependence between sub-problems in an overall problem like TTP.

This paper proposes a competitive divide-and-conquer algorithm for solving large-scale black-box optimization problems, where there are thousands of decision variables, and the algebraic models of the problems are unavailable. We focus on problems that are partially additively separable, since this type of problem can be further decomposed into a number of smaller independent sub-problems. The proposed algorithm addresses two important issues in solving large-scale black-box optimization: (1) the identification of the independent sub-problems without explicitly knowing the formula of the objective function and (2) the optimization of the identified black-box sub-problems. First, a Global Differential Grouping (GDG) method is proposed to identify the independent sub-problems. Then, a variant of the Covariance Matrix Adaptation Evolution Strategy (CMA-ES) is adopted to solve the sub-problems resulting from its rotation invariance property. GDG and CMA-ES work together under the cooperative co-evolution framework. The resultant algorithm named CC-GDG-CMAES is then evaluated on the CEC'2010 large-scale global optimization (LSGO) benchmark functions, which have a thousand decision variables and black-box objective functions. The experimental results show that on most test functions evaluated in this study, GDG manages to obtain an ideal partition of the index set of the decision variables, and CC-GDG-CMAES outperforms the state-of-the-art results. Moreover, the competitive performance of the well-known CMA-ES is extended from low-dimensional to high-dimensional black-box problems.

In particle swarm optimization, the inertia weight is an important parameter for controlling its search capability. There have been intensive studies of the inertia weight in continuous optimization, but little attention has been paid to the binary case. This study comprehensively investigates the effect of the inertia weight on the performance of binary particle swarm optimization, from both theoretical and empirical perspectives. A mathematical model is proposed to analyze the behavior of binary particle swarm optimization, based on which several lemmas and theorems on the effect of the inertia weight are derived. Our research findings suggest that in the binary case, a smaller inertia weight enhances the exploration capability while a larger inertia weight encourages exploitation. Consequently, this paper proposes a new adaptive inertia weight scheme for binary particle swarm optimization. This scheme allows the search process to start first with exploration and gradually move towards exploitation by linearly increasing the inertia weight. The experimental results on 0/1 knapsack problems show that the binary particle swarm optimization with the new increasing inertia weight scheme performs significantly better than that with the conventional decreasing and constant inertia weight schemes. This study verifies the efficacy of increasing inertia weight in binary particle swarm optimization.