Rapid development of the construction sector has accelerated the rise of prefabricated buildings and has changed the traditional concept of cargo transportation. Prefabricated buildings refer to the transfer of numerous on-site operations from traditional construction sites to factories. Prefabricated components (PCs) and accessories, such as precast panels, wall units, shear walls, precast columns, stairs, and balconies, are processed in factories, transported to the construction site, and assembled and installed on the construction site by reliable connections. Heavyweight, bulkiness, and fragility are the characteristics of PCs that pose challenges to the traditional transportation industry. Bulk goods require not only a lot of space but also special vehicles and technicians. It is worth mentioning when the demand for a construction site is greater than the maximum load of the truck, it must be split, and the site must be visited more than once [1]. To ensure that the construction site is constructed according to the plan, strict requirements for the arrival time of such goods are put forward. Multiple trucks travel to and from different construction sites multiple times to meet the requirements for PCs, which makes conflicts in the truck scheduling process more obvious. Against this background, the MFVRP-PC is proposed, considering time window constraints, limited heterogeneous fleet constraints, limited capacity constraints, and loader resource constraints. The goal of this study is to investigate real-life prefabricated component logistics so that transport efficiency is improved and the total transportation cost is reduced.

The split-delivery VRP (SDVRP) is a relaxation of the well-known capacitated VRP that only allows a customer to be served once. Obviously, it has a significantly larger solution space because the split delivery between different vehicles is subject to a combinatorial explosion [2]. As a result, viewing the service time on construction sites as a fixed value does not reflect the realistic logistic system. In contrast, MFVRP-PC considers this. Indeed, the MFVRP-PC is an extension of the SDVRP with time window (SDVRPTW). Dror and Trudeau [3] proved that an SDVRP is an NP-hard problem. Furthermore, MFVRP-PC can be degraded to SDVRPTW when, at the construction site, the number of cranes is sufficient and the precast unloading time is negligible. The limited heterogeneous trucks, time windows, and loader resource constraints on sites also increase the complexity of the MFVRP-PC. The limited heterogeneous trucks and loader resource constraints are the primary contributors to the significant complications of the problem in terms of formulating not only the model but also the solution method. Therefore, MFVRP-PC is also an NP-hard problem. This study differs from the SDVRPTW in the following ways: (1) the truck can only be dispatched to one construction site and then returned during each scheduling process. As a result, multi-frequency dispatch trucks are required, which is not available in the standard VRP and VRP with split delivery. (2) SDVRPTW mainly focuses on the customer being visited multiple times, ignores the dependencies of service time and quantity delivered at the customer point, and only considers the customer's demand to be satisfied. In contrast, MFVRP-PC emphasizes the conflicting costs of multiple-trucks arriving at the construction site at the same time (c.f., Subsection 4.2), considering the additional effect of dynamic service times at construction sites due to changes in quantity delivered and the resource constraints caused by a single loader at the construction site.

While paying attention to transportation costs, in the case of a limited number of trucks, the efficiency and frequency of truck utilization also play an important role in managerial insights. The objective of minimizing the maximum vehicle duration was introduced to enable a balanced workload. Therefore, the MFVRP-PC is modeled as a bi-objective problem, namely, the total transportation cost and makespan. On the one hand, for multiobjective optimization problems (MOPs), the multiobjective evolutionary algorithm (MOEA) is commonly adopted as the main framework, which has been extensively researched and has achieved excellent results in the combinatorial optimization fields [[4], [5], [6], [7], [8], [9], [10], [11], [12], [13]]. The proximity, cardinality, uniformity, and spread of the non-dominated solution are ensured by the MOEA. Therefore, it is straightforward to adopt MOEA as an optimizer for handing non-dominated solutions. On the other hand, the three components of ALNS, namely destroy, repair, and adaptive adjustment mechanisms, prevent it from searching in the poor regions of the solution space. Owing its simplicity and generality, ALNS achieves remarkably excellent performance in non-population, single-objective scenarios [8,[14], [15], [16], [17], [18], [19], [20], [21]]. In addition, it is worth mentioning that each individual in the population-based MOEA can be acquired using ALNS. Therefore, to remedy the MFVRP-PC, a knowledge-driven efficient optimization algorithm is proposed that incorporates an MOEA and ALNS. The hybrid metaheuristic algorithm is hereafter referred to as MOEA-ALNS.

When ALNS is utilized to address MOPs, the grade-setting rules must first be clarified in the adaptive adjustment mechanism. However, there is no reasonable method for dynamically setting the score to reduce the impact of the parameters on this algorithm. For MOPs, it is not only necessary to measure the relationship between the current and new solution, but also the influence of the current solution on the population. Additional parameters have been introduced to complicate this situation. To remedy this issue, motivated by a strength Pareto evolutionary algorithm (SPEA2) [22], a SPEA2-based adaptive weight adjustment mechanism was designed to obtain dynamic scores. The score sets become reasonable and accurately reflect the relationship between the current solution and evolving population.

The main contributions of this study are as follows: (1) it is the first time that the transportation problem of PCs is modeled as a multi-frequency transportation problem with time window, limited heterogeneous fleet, limited capacity, and loader resource constraints; (2) two problem-specific knowledge are proposed as the theoretical basis of coding and operation design; (3) the solution is constructed with effective three-dimensional (3-D) vectors, namely, construction sites visit sequence, vehicle assignment sequence, and PCs number arrangement; (4) for MOPs, a SPEA2-based adaptive weight adjustment mechanism is embedded into adaptive large neighborhood search (ALNS) to dynamically reflect the relationship of solution-solution, and solution-population; (5) ALNS and MOEA are incorporated by a novel approach, which can provide an exploration-exploitation balance.

The remainder of the study is organized as follows. Section II briefly presents a literature review. Section III provides problem definition and problem-specific knowledge in detail. Section IV details the framework of the proposed MOEA-ALNS and its core components. Moreover, computational experiments are presented in Section V. Finally, Section VI concludes this study and presents future research directions.