Multi-solution problems extensively exist in practice. Particularly, the traveling salesman problem may possess multiple shortest tours, from which travelers can choose one according to their specific requirements. However, very few efforts have been devoted to the multi-solution problems in the discrete domain. In order to fill this research gap and to effectively tackle the multi-solution traveling salesman problem, we propose a niching memetic algorithm in this paper. The proposed algorithm is characterized by a niche preservation technique to enable the parallel search of multiple optimal solutions; an adaptive neighborhood strategy to balance the exploration and exploitation; a critical edge-aware method to provide effective guidance to the reproduction; and a selective local search strategy to improve the search efficiency. To evaluate the performance of the proposed algorithm, we conduct comprehensive experiments on a recently published multi-solution optimization test suite. The experimental results show that our algorithm outperforms other compared algorithms. Furthermore, the proposed algorithm is adopted to tackle problems from the well-known TSPLIB library to obtain a set of distinct but good solutions.

Automatic itinerary planning is a crucial and challenging issue in tourism. This paper proposes a novel automatic planning method to suggest multiple itineraries that satisfy the specific demands of tourists. First, a multiple-itinerary planning model is developed, which provides three customized goals for a tourist to choose and supports generating multiple D-day trips. The model makes fewer assumptions than the literature works did, while it provides more flexibility to the tourists. Then, based on the multiple-itinerary planning model, we design a niching genetic evolution approach to accomplish the automatic itinerary planning task. The genetic evolution approach guarantees a high search efficiency, while the niching strategy facilitates maintaining the population diversity. Consequently, the resultant algorithm can finally provide a number of diverse and superior solutions. Experimental results on real-world datasets show that our proposed algorithm not only outperforms state-of-the-art methods in considering different user-specified goals, but it is also capable of generating a set of diverse itineraries for the tourist to select. Additional experiments further verify the scalability of the proposed algorithm in terms of the problem size and the optimization objective.

Trajectory planning is a crucial task in designing the navigation systems of automatic underwater vehicles (AUVs). Due to the complexity of underwater environments, decision makers may hope to obtain multiple alternative trajectories in order to select the best. This paper focuses on the multiple-trajectory planning (MTP) problem, which is a new topic in this field. First, we establish a comprehensive MTP model for AUVs, by taking into account the complex underwater environments, the efficiency of each trajectory, and the diversity among different trajectories, simultaneously. Then, to solve the MTP, we develop an ant colony-based trajectory optimizer, which is characterized by a niching strategy, a decayed alarm pheromone measure, and a diversified heuristic measure. The niching strategy assists in identifying and maintaining a diverse set of high-quality solutions. The use of decayed alarm pheromone and diversified heuristic further improves the search effectiveness and efficiency of the algorithm. Experimental results on practical datasets show that our proposed algorithm not only provides multiple AUV trajectories for a flexible choice, but it also outperforms the state-of-the-art algorithms in terms of the single trajectory efficiency.

Multimodal optimization problems have multiple satisfactory solutions to identify. Most of the existing works conduct the search based on the information of the current population, which can be inefficient. This article proposes a probabilistic niching evolutionary computation framework that guides the future search based on more sufficient historical information, in order to locate diverse and high-quality solutions. A binary space partition tree is built to structurally organize the space visiting information. Based on the tree, a probabilistic niching strategy is defined to reinforce exploration and exploitation by making full use of the structural historical information. The proposed framework is universal for incorporating various baseline niching algorithms. In this article, we integrate the proposed framework with two niching algorithms: 1) a distance-based differential evolution algorithm and 2) a topology-based particle swarm optimization algorithm. The two new algorithms are evaluated on 20 multimodal optimization test functions. The experimental results show that the proposed framework helps the algorithms obtain competitive performance. They outperform a number of state-of-the-art niching algorithms on most of the test functions.

The significance of maritime transportation highlights the need to enhance the efficiency of container terminals. This study addresses a challenge within maritime transportation, specifically the continuous berth allocation and time-variant quay crane assignment problem (C/T-V BACAP). We formulate a comprehensive mathematical model of C/T-V BACAP. To solve the problem, we propose an effective memetic algorithm with a heuristic decoding method, named HMA, which comprises three essential components: a three-stage heuristic decoding method, a clustering-based evolutionary strategy, and a target-guided local search operator. The three-stage heuristic decoding method guarantees solution feasibility and high quality through the entire optimization, allowing the following strategies to fully utilize their search capabilities. The clustering-based evolutionary strategy refines the search space and diversifies the promising candidates. Meanwhile, the target-guided local search operator rapidly optimizes the allocation for the challenging vessel. The experimental results demonstrate that the proposed algorithm delivers excellent performance, especially in handling large-scale instances (up to 60 vessels). Our proposed method outperforms the state-of-the-art BACAP algorithms by an average margin of 150% in terms of berth offset and waiting time in most problem instances.

Solving multimodal optimization problems (MMOP) requires finding all optimal solutions, which is challenging in limited function evaluations. Although existing works strike the balance of exploration and exploitation through hand-crafted adaptive strategies, they require certain expert knowledge, hence inflexible to deal with MMOP with different properties. In this paper, we propose RLEMMO, a Meta-Black-Box Optimization framework, which maintains a population of solutions and incorporates a reinforcement learning agent for flexibly adjusting individual-level searching strategies to match the up-to-date optimization status, hence boosting the search performance on MMOP. Concretely, we encode landscape properties and evolution path information into each individual and then leverage attention networks to advance population information sharing. With a novel reward mechanism that encourages both quality and diversity, RLEMMO can be effectively trained using a policy gradient algorithm. The experimental results on the CEC2013 MMOP benchmark underscore the competitive optimization performance of RLEMMO against several strong baselines.