As the complexity of logistics scenarios continues to increase, numerous new challenges have emerged. In multi-depots pickup and delivery path planning (MDPDP) scenario, these challenges include cross-depot resource coordination, spatio-temporal dependencies of pickup-delivery pairs, and generalization across problem scales. To address these challenges, this paper proposes a deep reinforcement learning framework with a Heterogeneous Collaborative Multi-Attention (HCMA) mechanism. The HCMA framework has three key features. 1) HCMA comprises a three-level heterogeneous attention architecture: an inter-depot collaborative attention module for cross-depot resource allocation, a pickup-delivery pairing attention module that explicitly learns sequential and pairwise relationships between task nodes, and a global attention module to capture long-range node dependencies. 2) HCMA dynamically integrates real-time vehicle status with multi-type node features through attention weighting to balance vehicle resource utilization across depots. 3) HCMA adopts multi-start training and instance augmentation strategies to enhance generalization capability and obtain the global optimal solution. Extensive experiments conducted on random datasets, benchmark datasets, and a real-world Shenzhen logistics dataset demonstrate that the proposed HCMA method outperforms state-of-the-art heuristic algorithms and deep reinforcement learning baselines, while exhibiting superior generalization capability. The source code is publicly available at:https://github.com/CIA-SZU/LAQ

The multifactorial evolutionary algorithm (MFEA) is one of the most widely used evolutionary multitasking (EMT) algorithms. The MFEA implements knowledge transfer among optimization tasks via crossover and mutation operators and it obtains high-quality solutions more efficiently than single-task evolutionary algorithms. Despite the effectiveness of MFEA in solving difficult optimization problems, there is no evidence of population convergence or theoretical explanations of how knowledge transfer increases algorithm performance. To fill this gap, we propose a new MFEA based on diffusion gradient descent (DGD), namely, MFEA-DGD in this article. We prove the convergence of DGD for multiple similar tasks and demonstrate that the local convexity of some tasks can help other tasks escape from local optima via knowledge transfer. Based on this theoretical foundation, we design complementary crossover and mutation operators for the proposed MFEA-DGD. As a result, the evolution population is endowed with a dynamic equation that is similar to DGD, that is, convergence is guaranteed, and the benefit from knowledge transfer is explainable. In addition, a hyper-rectangular search strategy is introduced to allow MFEA-DGD to explore more underdeveloped areas in the unified express space of all tasks and the subspace of each task. The proposed MFEA-DGD is verified experimentally on various multitask optimization problems, and the results demonstrate that MFEA-DGD can converge faster to competitive results compared to state-of-the-art EMT algorithms. We also show the possibility of interpreting the experimental results based on the convexity of different tasks.

Evolutionary multitasking (EMT) is one of the emerging topics in evolutionary computation. EMT can solve multiple related optimization tasks simultaneously and enhance the optimization of each task via knowledge sharing among tasks. Many EMT algorithms have been proposed and achieved success in various problems, yet EMT for multiobjective optimization remains a big challenge. The existing multiobjective EMT algorithms tend to suffer from slow convergence and difficulty in generating high-quality knowledge. To alleviate these issues, this article proposes a new EMT algorithm, namely, EMT-GS for multiobjective optimization based on two generative strategies. Particularly, generative adversarial networks (GANs) and inertial differential evolution (IDE) are introduced to generate transferable knowledge and offspring, respectively. A GAN is trained periodically for each source-target task pair, based on which helpful knowledge is generated from the source task and transferred to boost the solving of the target task. To accelerate the population convergence, the IDE strategy is put forward to generate offspring in a promising direction according to the individuals from the previous generation and the transferred knowledge. The performance of EMT-GS is validated on three multitasking multiobjective benchmark problems. The experimental results highlight the excellent competitiveness of EMT-GS compared to other state-of-the-art multiobjective EMT algorithms.

In contrast to the traditional single-tasking evolutionary algorithms, evolutionary multitasking (EMT) travels in the search space of multiple optimization tasks simultaneously. Through sharing knowledge across the tasks, EMT is able to enhance solving the optimization tasks. However, if knowledge transfer is not properly carried out, the performance of EMT might become unsatisfactory. To address this issue and improve the quality of knowledge transfer among the tasks, a novel multiobjective EMT algorithm based on subspace alignment and self-adaptive differential evolution (DE), namely, MOMFEA-SADE, is proposed in this article. Particularly, a mapping matrix obtained by subspace learning is used to transform the search space of the population and reduce the probability of negative knowledge transfer between tasks. In addition, DE characterized by a self-adaptive trial vector generation strategy is introduced to generate promising solutions based on previous experiences. The experimental results on multiobjective multi/many-tasking optimization test suites show that MOMFEA-SADE is superior or comparable to other state-of-the-art EMT algorithms. MOMFEA-SADE also won the Competition on Evolutionary Multitask Optimization (the multitask multiobjective optimization track) within IEEE 2019 Congress on Evolutionary Computation.

In recent years, dynamic multiobjective optimization problems (DMOPs) have drawn increasing interest. Many dynamic multiobjective evolutionary algorithms (DMOEAs) have been put forward to solve DMOPs mainly by incorporating diversity introduction or prediction approaches with conventional multiobjective evolutionary algorithms. Maintaining a good balance of population diversity and convergence is critical to the performance of DMOEAs. To address the above issue, a DMOEA based on decision variable classification (DMOEA-DVC) is proposed in this article. DMOEA-DVC divides the decision variables into two and three different groups in static optimization and changes response stages, respectively. In static optimization, two different crossover operators are used for the two decision variable groups to accelerate the convergence while maintaining good diversity. In change response, DMOEA-DVC reinitializes the three decision variable groups by maintenance, prediction, and diversity introduction strategies, respectively. DMOEA-DVC is compared with the other six state-of-the-art DMOEAs on 33 benchmark DMOPs. The experimental results demonstrate that the overall performance of the DMOEA-DVC is superior or comparable to that of the compared algorithms.

Multitask optimization aims to solve two or more optimization tasks simultaneously by leveraging intertask knowledge transfer. However, as the number of tasks increases to the extent of many-task optimization, the knowledge transfer between tasks encounters more uncertainty and challenges, thereby resulting in degradation of optimization performance. To give full play to the many-task optimization framework and minimize the potential negative transfer, this article proposes an evolutionary many-task optimization algorithm based on a multisource knowledge transfer mechanism, namely, EMaTO-MKT. Particularly, in each iteration, EMaTO-MKT determines the probability of using knowledge transfer adaptively according to the evolution experience, and balances the self-evolution within each task and the knowledge transfer among tasks. To perform knowledge transfer, EMaTO-MKT selects multiple highly similar tasks in terms of maximum mean discrepancy as the learning sources for each task. Afterward, a knowledge transfer strategy based on local distribution estimation is applied to enable the learning from multiple sources. Compared with the other state-of-the-art evolutionary many-task algorithms on benchmark test suites, EMaTO-MKT shows competitiveness in solving many-task optimization problems.

Multitasking optimization can achieve better performance than traditional single-tasking optimization by leveraging knowledge transfer between tasks. However, the current multitasking optimization algorithms suffer from some deficiencies. Particularly, on high similar problems, the existing algorithms might fail to take full advantage of knowledge transfer to accelerate the convergence of the search, or easily get trapped in the local optima. Whereas, on low similar problems, they tend to suffer from negative transfer, resulting in performance degradation. To solve these issues, this article proposes an evolutionary multitasking optimization algorithm for multiobjective/many-objective optimization with two-stage adaptive knowledge transfer based on population distribution. The resultant algorithm named EMT-PD can improve the convergence performance of the target optimization tasks based on the knowledge extracted from the probability model that reflects the search trend of the whole population. At the first stage of knowledge transfer, an adaptive weight is used to adjust the search step size of each individual, which can reduce the impact of negative transfer. At the second stage of knowledge transfer, the search range of each individual is further adjusted dynamically, which can improve the population diversity and be beneficial for jumping out of the local optima. Experimental results on multitasking multiobjective optimization test suites show that EMT-PD is superior to other state-of-the-art evolutionary multitasking/single-tasking algorithms. To further investigate the effectiveness of EMT-PD on many-objective optimization problems, a multitasking many-objective optimization test suite is also designed in this article. The experimental results on the new test suite also demonstrate the competitiveness of EMT-PD.

Mobile edge computing (MEC) can supplement cloud computing by helping to overcome the limitations of long physical transmission distances and accelerating the responsiveness of edge computing servers. In 5G (fifth generation) cellular networks, adopting MEC can guarantee ultralow latency. To enhance the MEC quality, optimization of the user service profile migration according to the user mobility is essential. However, this optimization establishes an NP-hard problem. Moreover, high-speed 5G base stations with MEC servers often experience high energy consumption. As conventional service migration algorithms such as those based on profile tracking and game theory tend to fall in local optima and neglect energy consumption constraints, we propose a memetic algorithm based on community detection local search (MA-CDLS) to continuously optimize the service migration in 5G MEC scenarios. During busy periods or in crowded areas, MA-CDLS adopts a single-objective optimization of user-perceived latency to achieve high-performance 5G services. During light-load periods or in uncrowded areas, MA-CDLS uses two measures, namely the user-perceived latency and energy consumption, to realize energy-efficient 5G services. MA-CDLS effectively reduces the search space and speeds up the elite selection in the meme operator. Experiments in simulated scenarios show that MA-CDLS achieves a lower user-perceived latency and energy consumption, than the traditional profile tracking and game theory methods, especially during congestion.

Balancing population diversity and convergence is critical for evolutionary algorithms to solve many-objective optimization problems (MaOPs). In this paper, a two-round environmental selection strategy is proposed to pursue good tradeoff between population diversity and convergence for many-objective evolutionary algorithms (MaOEAs). Particularly, in the first round, the solutions with small neighborhood density are picked out to form a candidate pool, where the neighborhood density of a solution is calculated based on a novel adaptive position transformation strategy. In the second round, the best solution in terms of convergence is selected from the candidate pool and inserted into the next generation. The procedure is repeated until a new population is generated. The two-round selection strategy is embedded into an MaOEA framework and the resulting algorithm, namely, 2REA, is compared with eight state-of-the-art MaOEAs on various benchmark MaOPs. The experimental results show that 2REA is very competitive with the compared MaOEAs and the two-round selection strategy works well on balancing population diversity and convergence.

Many-objective optimization problems (MaOPs) pose a big challenge to the traditional Pareto-based multiobjective evolutionary algorithms (MOEAs). As the number of objectives increases, the number of mutually nondominated solutions explodes and MOEAs become invalid due to the loss of Pareto-based selection pressure. Indicator-based many-objective evolutionary algorithms (MaOEAs) have been proposed to address this issue by enhancing the environmental selection. Indicator-based MaOEAs are easy to implement and of good versatility, however, they are unlikely to maintain the population diversity and coverage very well. In this article, a new indicator-based MaOEA with boundary protection, namely, MaOEA-IBP, is presented to relieve this weakness. In MaOEA-IBP, a worst elimination mechanism based on the${I}_{{\epsilon }^{+}}$indicator and boundary protection strategy is devised to enhance the balance of population convergence, diversity, and coverage. Specifically, a pair of solutions with the smallest${I}_{{\epsilon }^{+}}$value are first identified from the population. If one solution dominates the other, the dominated solution is eliminated. Otherwise, one solution is eliminated by the boundary protection strategy. MaOEA-IBP is compared with four indicator-based algorithms (i.e.,${I}_{{{ {SDE}}}^{+}}$, SRA, MaOEAIGD, and ARMOEA) and other five state-of-the-art MaOEAs (i.e., KnEA, MaOEA-CSS, 1by1EA, RVEA, and EFR-RR) on various benchmark MaOPs. The experimental results demonstrate that MaOEA-IBP can achieve competitive performance with the compared algorithms.

Multi-tasking optimization (MTO) has attracted increasing attention in the domain of evolutionary computation. Different from single-tasking optimization, MTO can solve multiple optimization tasks simultaneously to improve the performance of solving each optimization task by inter-task knowledge transfer. Multifactorial evolutionary algorithm (MFEA) is one of the most widely used MTO algorithm based on assortative mating and vertical cultural transmission. This work extends MFEA by integrating bone route and large neighborhood local search to solve multi-objective vehicle routing problem with time window (VRPTW). The VRPTW is modeled as two related tasks, i.e., one is a multi-objective version of VRPTW (the main task), and the other is a single-objective version of VRPTW (the auxiliary task). The resultant new algorithm namely multi-objective multi-factorial memetic algorithm (MOMFMA) solve the two tasks simultaneously where the information between the tasks is exchanged in the evolutionary process. In addition to the implicit information transfer of MFEA, the bone route is introduced to enable explicit information transfer between tasks. Particularly, bone routes are constructed as semi-finished product solutions and used in large neighborhood local search. The bone route and the large neighborhood local search work together to speed up the convergence of the algorithm. MOMFMA is tested on Solomon's 56 datasets and the experimental results demonstrate that the efficiency of MOMFMA.

The first cooperative co-evolutionary algorithm (CCEA) was proposed by Potter and De Jong in 1994 and since then many CCEAs have been proposed and successfully applied to solving various complex optimization problems. In applying CCEAs, the complex optimization problem is decomposed into multiple subproblems, and each subproblem is solved with a separate subpopulation, evolved by an individual evolutionary algorithm (EA). Through cooperative co-evolution of multiple EA subpopulations, a complete problem solution is acquired by assembling the representative members from each subpopulation. The underlying divide-and-conquer and collaboration mechanisms enable CCEAs to tackle complex optimization problems efficiently, and hence CCEAs have been attracting wide attention in the EA community. This paper presents a comprehensive survey of these CCEAs, covering problem decomposition, collaborator selection, individual fitness evaluation, subproblem resource allocation, implementations, benchmark test problems, control parameters, theoretical analyses, and applications. The unsolved challenges and potential directions for their solutions are discussed.