Large-scale engineering projects, such as offshore platform and shipbuilding projects, are often affected by factors such as extreme weather and supplier tardiness. The complex operating environment often reduces the efficiency of offshore platform construction.

In offshore production, the resources used during manufacturing include field resources, material resources, human resources, equipment resources, technical resources and service resources. Achieving a reasonable schedule under the constraints of sequence relationships and critical resources has become a focus of current research. Multi-resource limit problems and priority rules were described by Browning et al. [6]. In recent years, most research on RCPSP has focused on adding specific constraints to make the problem more realistic. Ma et al. [7] studied a proactive project scheduling problem with flexible resource constraints. On the basis of the RCPSP problem, Cai et al. [8] considered delivery times and proposed a corresponding heuristic algorithm. Asadujjaman et al. [9] proposed a concurrent project-scheduling and material-ordering problem and proposed a hybrid immune GA solution. Ghamginzadeh et al. [10] studied a multi-objective, multi-skill, project-scheduling model.

To solve resource-constrained problems, the general exact algorithm [11,12], heuristic rules [13] and intelligent optimization algorithm can be used. The exact algorithm can only solve minor problems and remains at the theoretical stage. Heuristic rules, in addition to simple problems (such as single resources), guarantee an optimal solution but are unable to prove its optimality. Due to the large number of production operations during the execution of offshore projects, the complex logical relationship between activities, and the complex resources constraints [14], it is difficult to solve such problems with general exact algorithm and heuristic rules. Therefore, there are many studies using intelligent optimization algorithms to solve this problem.

Intelligent algorithms [15,16] have been validated as feasible solutions, and involve searching several iterations that gradually converge to the global optimal solution. The biological and evolutionary foraging swarm intelligence algorithm has been developed, which is very suitable for solving large-scale problems, especially in multi-mode and multi-resource-constrained project scheduling problems. Therefore, it has gradually become a research hotspot.

Liu et al. [13] tried to solve an RCPSP using a heuristic algorithm with the objective of minimizing activities. Hartmann [17,18], Alcaraz et al. [19], Gonçalves et al. [20], Proon et al. [21], Hindi et al. [22] and Valls et al. [23] used genetic algorithms for their approaches. Cai et al. [8] and Afshar-Nadjafi et al. [24] made improvements for certain genetic algorithms and designed a fitness function and coding rules to solve multi-mode resource-constrained project scheduling problems. Kim et al. [25] and Zhang et al. [26] proposed an adaptive hybrid genetic algorithm and particle swarm optimization for solving resource-constrained scheduling problems, obtaining very good results. Gonzalez-Pardo et al. [27] elaborated on ant colony optimization (ACO) algorithms with a novel CSP-graph-based model to solve RCPSPs. Zhao et al. [28] proposed a genetic simulated annealing algorithm based on population stability to determine the shortest construction period under the resource constraint of a single project with renewable resources. Coric et al. [29] compared the time complexity of IP formulations and genetic algorithms in solving RCPSPs and presented two different solution representations for genetic algorithms: a permutation vector and vector of floating numbers. Snauwaert et al. [30] addressed a multi-skilled extension of RCPSP (MSRCPSP) and developed a genetic algorithm to solve it. In addition to the above algorithms, the particle swarm optimization heuristic has drawn increasing attention [31,32].

Currently, there is a research foundation for multi-mode and multi-resource constrained scheduling problems. However, since marine project scheduling problems are usually large-scale, there is usually some room for optimization. This requires a higher search ability of the algorithm. To minimize the duration of a project, this article integrates a local search into a genetic algorithm and adds an elitist strategy and adaptive crossover/mutation operations to greatly reduce the computation time and ensure the quality of the search solutions. Moreover, comparisons with the classical genetic algorithm and simulated annealing algorithm are made, and the feasibility of the proposed algorithm is validated.

However, since marine project scheduling problems are usually large-scale, there are many feasible solutions during project construction.

In complex projects, the project execution plan is usually graded and the enterprise needs to formulate and decompose it according to contract constraints and production capacity. After making practical investigations into an offshore enterprise, we found that offshore companies usually use Oracle Primavera P6 or Microsoft Project software for project planning and task decomposition. Such software is oriented towards large-scale engineering projects, linking the plans involved in the project execution process with enterprise resources, making it easier for enterprises to manage and control their projects.

In the process of offshore engineering construction, planning and dispatching, four-stage plans are used to guide operations. Some four-level plans are able to be decomposed into a single plan, while other four-level plans cannot be decomposed. Therefore, decomposed fourth-level plans can be regarded as a complete network plan and include all operation items, the logical relationship, etc. A model of such problems requires four preprocessing schemes to form a viable network scheme, as shown in Fig. 1.

In Fig. 1, S₄ and E₄ represent the beginning and end of the fourth-level network activities. These can be taken as two virtual activities with corresponding periods, direct costs, and resource consumptions of zero. Now, we assume that other activities added to activities outside J₄ cannot continue to be broken down into fifth-level activities. Points S₅ and E₅ indicate the beginning and the end of the 5-stage plan, as well as two virtual activities. The earliest start times of J₄₁ and J₄₃ can be considered as the start times S₅, J₄₂, J₄₃’s latest end time as the end time E₅, and pretreatment is shown in Fig. 2.

A complete offshore project can correspond to a complete network diagram, including the complete logical relationship. Engineers use professional software to decompose a complete project into a network plan of four levels to guide the actual operations. In this paper, a single-node network diagram is defined as G=(V,E). In graph G, E there is a set of directed arcs that can connect each node in set V. We define J as an activity, then j can be considered as a subset of J, where j=1,…,J. The network also contains node 0 and node J+1, which represent the beginning and end of the virtual activities, respectively. Activity J cannot start until the predecessor activities of Pj have been completed.

Each activity j may be performed under several different modes Mj={1,…,Mj}. In the execution modem∈Mj, the demand for renewable resources in activity j per unit time can be represented by rjmk, and the duration of activity j, which is under execution mode m, is expressed by djm. Assuming that once activity j starts in mode m, it cannot be allowed to change due to activity interruptions or behaviour patterns. Similarly, all of the activities must be executed continuously.

Bearing this in mind, in order to establish a multi-mode resource-constrained project scheduling optimization model, the following assumptions are made: (1) Once an activity is started, it cannot be interrupted until completion; (2) during the scheduling period considered, the resource supply capacity is evenly distributed; and (3) each operation’s resource demand per unit time must be less than the upper limit of the resource supply.

In this paper, EFTj and LFTj represent the beginning and end times of activity j, respectively, while Mj indicates a set of alternative execution modes. Furthermore, rjmk is activity j in m—the execution mode, which is required for the first k kinds of resource demands (such as personnel, cranes, plates, money, barges, and oil, in which human and oil resources are renewable and non-renewable resources, respectively). Rk indicates that k largest species of renewable resources supply. The mathematical model of the problem can be described as follows:

(1)Minimize∑m=1Mj∑t=EFTjLFTjtxjmt

(2)∑m=1Mj∑t=EFTjLFTjxjmt=1,j=1,…,J

(3)∑m=1Mi∑t=EFTiLFTitximt≤∑m=1Mj∑t=EFTjLFTj(t−djm)txjmt,j=2,….J,i∈Pj

(4)∑j=2J−1∑m=1Mjrjmk∑τ=tt+djm−1xjmτ≤Rk,k∈R,t=1,….,T

(5)∑j=2J−1∑m=1Mjrjmk∑t=EFTjLFTjxjmt≤Rk,k∈NR

(6)xjmt∈{0,1},j=1,…,J,m=1,…,Mj,t=EFTj,…,LFTj

In this model, Eq. (1) is the objective function, while Eqs. (2)–(6) describe the constraint conditions. Eq. (1) indicates the duration of the project; Eq. (2) represents that activity j can only be carried out in an execution mode; in Eq. (3), activity i is the tight predecessor activity before activity j, which only starts after its before-tight-activities event set Pj; Eq. (4) indicates the demand for renewable resources per unit time, which cannot exceed the capacity of resource supply Rk; Eq. (5) means that the demand for non-renewable resources cannot exceed its supply, and we assume that each activity’s demand per unit time is fixed; and Eq. (6) is a 0–1 decision variable, indicating whether activity j can be carried out under execution mode m at time t.

Usually, offshore projects require operating items in large amounts, which results in extremely large execution modes and solution spaces. This directly leads to low efficiency and effectiveness in the general convergence speed. Genetic algorithms have a strong global cable capacity, and crossover/mutation methods protect the diversity of the population to some extent; however, the latter’s convergence results may also undermine the optimal solution that has already been searched, which is likely trapped in a local convergence optimum. Meanwhile, a local search algorithm can generate field solutions by random perturbation and accept inferior solutions of a certain probability, giving it strong local searchability. Therefore, to balance the advantages and disadvantages of these two algorithms, this paper proposes a fused hybrid genetic algorithm to solve multi-mode multi-resource-constrained project scheduling problems. The main improvements are as follows. (1) It adopts an elitist strategy to speed up convergence; (2) it uses adaptive crossover/variability to improve search quality and speed up convergence; (3) it integrates local search into the genetic algorithm and uses a maintenance population to protect the diversity of the population and come to a global optimal solution; and (4) it uses the function calibration method to accommodate the use of roulette rules.

For a higher quality solution and faster speed, in this article, a mixed genetic algorithm is used, which integrates a local search algorithm with an iterative search performed only once into the genetic algorithm for iterative search. The flow chart of the algorithm is shown in Fig. 7. The specific steps are as follows:

Step 1: Initialization. Set the maximum number of iterations G, coefficient k, initial temperature T, and largest provider of resource k values, Rk.

Step 2: Randomly generated initial solution. According to the network diagram for meeting the tight relationship between the former premise randomly generated initial solution of N, where the execution mode for each activity from Mj is randomly selected.

Step 3: Decode. Obtain the initial population of each individual period T, and use the inverse calibration method for the fitness function to convert T′.

Step 4: Select the size of N, respectively, the parent and parent on behalf of Father/Mother according to roulette rules.

Step 5: Adaptive crossover and mutation operations. Conduct crossover and mutation to produce offspring children.

Step 6: Add a local search to the solution for maintenance.

Step 6.1: Crossover and mutation to produce offspring children as its parent X;

Step 6.2: Use the mutation probability of generating a field solution Y;

Step 6.3: Sequence comparison of individuals X and Y. If the individual is superior to the corresponding Y of individual X, Y is replaced by the individual out of individual X; otherwise, keep the X in the individual unchanged.

Step 7: Carry out the elitist operation.

Step 8: Determine whether the convergence condition is satisfied, if yes, go to Step 9; otherwise, go to Step 3.

Step 9: Output the shortest duration and iterative convergence curve.

This article refers to the network in Fig. 8, a data validation instance from the literature, assuming that there is only one kind of renewable resource and one non-renewable resource. The network diagram has 12 events, in which 0 and 11 are starting and ending events, while the execution modes are mode 1 and mode 2 executive. Renewable resources are represented by R and R_k max = 12. Non-renewable resources are represented by NR. This article assumes that workers consume a certain value of non-renewable resources each day, and its total NR_k is 25.

In this example, the size of the initial population of the genetic algorithms is 20; the maximum number of iterations is 500; the renewable resources (HR) Rk limit is 40; the function calibration coefficient k is 400; the adaptive crossover and mutation probabilities k1 and k2 are 0.7 and 0.95; the mutation probabilities k3 and k4 are 0.02 and 0.05; and 1 local search iteration is used. The specific network and data are illustrated in Table 3 and Fig. 12 [35].

It should be noted that renewable resources include human resources, while non-renewable resources are, by their nature, more certain in their supply. Therefore, non-renewable resources are not considered in this verification example. The basic data (onshore construction process of an offshore structure ) in the offshore project network diagram were provided by an offshore company, drawn by project2007.

By the comparative analysis of the hybrid genetic, classical genetic, and simulated annealing algorithms, we know that the classical genetic algorithm easily finds a local optimal solution because of its weakness in local search capability. The simulated annealing algorithm converges very slowly and large fluctuations still exist after 500 iterations, indicating that it does not achieve convergence. The hybrid genetic algorithm iterations have already converged after about 110 times, and the quality of the convergence solution is better than those of the other two. As a result, the optimal duration is 375 days, as shown in Fig. 13, which verifies that the hybrid genetic algorithm can solve the offshore project scheduling optimization problem.