Abstract-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.

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Abstract-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.Index Terms-Capacitated arc routing problem (CARP), evolutionary optimization, local search, memetic algorithm, metaheuristic search.

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Genetic programming has been a powerful technique for automated design of production scheduling heuristics. Many studies have shown that heuristics evolved by genetic programming can outperform many existing heuristics manually designed in the literature. The flexibility of genetic programming also allows it to discover very sophisticated heuristics to deal with complex and dynamic production environments. However, as compared to other applications of genetic programming or scheduling applications of other evolutionary computation techniques, the configurations and requirements of genetic programming for production scheduling are more complicated. In this paper, a unified framework for automated design of production scheduling heuristics with genetic programming is developed. The goal of the framework is to provide the researchers with the overall picture of how genetic programming can be applied for this task and the key components. The framework is also used to facilitate our discussions and analyses of existing studies in the field. Finally, this paper shows how knowledge from machine learning and operations research can be employed and how the current challenges can be addressed.