The collaborative optimization of platform location and wellbore trajectory for a complex-structure well factory includes platform location/number, platform-target allocation, multi-trajectory parameters and other design variables, under the constraint of platform layout area, drilling extension limits, underground target distribution, and trajectory anti-collision difficulty, involving multiple drilling-mechanics models, such as trajectory design, trajectory complexity, collision risk and drilling extension limits.

Using a multi-objective optimization approach, this paper normalized four engineering objectives of platform-target matching deviation (f₁), anti-collision difficulty (f₂), total drilling footage (f₃), and trajectory complexity (f₄) to dimensionless indices F₁, F₂, F₃ and F₄. These indices were then weighted by coefficients ω₁, ω₂, ω₃, and ω₄ to form the system objective function F, thereby obtaining an optimal solution among all objectives. The model is given as:

Constraints are divided into three categories: constraints on platform-planning variables, constraints on trajectory design variables, and constraints on the objective functions.

For platform planning, ISSA is applied as follows: (1) Each platform-target assignment scheme is encoded as a sparrow individual. Individuals are randomly initialized and extended to a high-dimensional representation to form a large dataset, which constitutes the sparrow population; (2) Each individual is substituted into the objective function to compute the fitness value; (3) Three update strategies, namely producer, follower, and sentinel strategies ^[17], are used to update individual positions in the population, corresponding to global search, local search, and random search in the solution space of platform-target assignments; (4) During iteration, sparrow individuals continuously adjust position parameters and share the current high-quality solutions (assignment schemes), thereby refining the assignment relationship and driving the population to converge toward the optimal region (best fitness); (5) The individual with the best fitness and its corresponding assignment scheme is taken as the optimization result.

Here, each sparrow represents an assignment scheme. Based on the assumption that the dimension of the platform-planning variables is d₁ and the number of sparrows is N_pop, the assignment scheme of the u-th sparrow is given as:

where d_1=p+q

The elements of each sparrow are randomly permuted. Substituting Eq. (18) into Eq. (1) yields the fitness function f(G_u) for each sparrow. The producer, follower, and sentinel strategies are then applied to iteratively update Eq. (18), and the best fitness can be obtained.

Due to the randomness of the initial population, candidate solutions may become overly clustered in the later iterations, which weakens global search capability. This is mainly caused by randomness of the step-size control parameters Δβ and Δρ in the sentinel strategy. Levy flight is a special random walk that combines long range jumps and short moves, enabling natural switching between global and local search spaces and facilitating sufficient exploration toward a global optimum ^[18]. The improved formulation is given as:

where

DABC adopts a data-driven strategy and uses nectar source directional information to guide decision variable updates. For trajectory optimization, design variables such as kickoff point, build-up rate, inclination/azimuth, and reservoir section length are treated as a candidate solution set, encoded as nectar sources and initialized; then employed bee local adjustment, onlooker bee following of high-quality solutions, and scout bee global search are used to adjust nectar source information ^[19]. During iteration, this information is continuously shared and updated to gradually improve the solutions and yield the optimal trajectory design scheme.

Setting the variable dimension as d₂, and the number of nectar-sources as N_sn, the initialization of the s-th design variable h_m,s in the m-th nectar-source $H_{m}=\left[\begin{array}{llllll} h_{m, 1} & h_{m, 2} & \cdots & h_{m, s} & \cdots & h_{m, d_{2}} \end{array}\right]$ is given as:

In the traditional artificial bee colony algorithm, each employed bee selects a nectar source and updates design variables by replacing r₁ in Eq. (20) with r_m,s (a random number in [−1, 1]). However, this update ignores nectar source directional information, which can drive the algorithm search toward worse directions and slow convergence. Therefore, following Zhu et al. ^[20], the current global best term h_s,best is introduced to guide H_m toward a better direction, namely:

Onlooker bees select according to the employed bee strategy and retain the high fitness G_u, namely:

If the current H_m is not improved within the maximum trial limit, the conventional scout bee strategy randomly reinitializes its position using Eq. (20) to replace the local optimum. However, random reinitialization may disrupt the current convergence state and reduce search efficiency. Therefore, considering search directionality, a new scout bee strategy is given as:

ISSA-DABC adopts a two-layer framework of “outer layer platform and inner layer trajectory”. In the outer layer, ISSA performs global search on platform planning variables. At each iteration, the geological information matched to the current assignment scheme is passed to the inner layer to obtain the allowable ranges of trajectory parameters. The inner layer takes the outer layer output as input and uses DABC to conduct guided search on trajectory design variables. Feasible solutions and threshold matching information are then returned to the outer layer to update platform-target matching deviation and platform control range. This feedback guides ISSA to adjust the search direction quickly in subsequent iterations and obtain more reasonable platform planning variables. During algorithm runs, platform planning and trajectory design variables are dynamically coordinated through information exchange to solve the well factory collaborative optimization problem.

To address persistent unconstrained conditions during optimization, after ISSA updates, the assignment scheme is first screened using constraints on platform control range and capacity. If constraints are violated, the fitness is assigned a very large value to avoid ineffective selections in subsequent iterations. After DABC updates, subobjectives including anti-collision difficulty, drilling footage, and trajectory complexity are checked again. If constraints are still violated, penalty terms are added to the corresponding subobjectives to guide candidate solutions toward correct directions. Accordingly, Eq. (1) is rewritten as:

where

Fig. 1 shows the required steps of the ISSA-DABC algorithm, including variable initialization, fitness calculation, platform-target assignment optimization, trajectory design variable update, and information feedback, as follows: (1) Parameter Input. Load model constraint parameters (Eq. (6) to Eq. (17)), optimization variables (platform planning parameter G_u, trajectory design parameter H_m) and algorithm parameters (ISSA, DABC, iteration, etc.). (2) Outer layer initialization. Use GMM clustering analysis to determine potential platform locations, and based on platform and target coordinates, generate multiple platform-target assignment sets G_u using Eq. (18). (3) Inner layer initialization. For each outer layer assignment, the geological conditions corresponding to the platform are obtained, and the constraints for trajectory design variables are defined. Generate H_m using Eq. (20), and calculate the fitness f(G_u) using the drilling models (Eq. (2) to Eq. (5)) and Eq. (1). (4) Ranking. Sort the initial population (G_u, H_m) by fitness f(G_u). Take the minimum as the current global best candidate set, and record the corresponding best objective value f\left[G_{\text{best}}^{(t)}\right], best platform-target assignment G_{\text{best}}^{(t)}, and best trajectory design variables H_{\text{best}}^{\text{(}t\text{)}}. (5) Outer layer ISSA update. Update the platform assignment G_u using producer, follower, sentinel, and Levy flight strategies (Eq. (19)). Update the constraints on trajectory design variables using the geological information corresponding to the new assignment, and provide optimization direction for inner layer DABC. (6) Inner layer DABC update. Update all trajectory optimization variables using the employed bee strategy (Eq. (21)), and carry out constraint checking in time. Use the onlooker bee strategy (Eq. (22)) to select the current high-quality trajectories H_m^{(t)} and the corresponding platform assignments G_u^{(t)}. Use the scout bee strategy (Eq. (23)) to prevent the fitness from becoming stagnated during iteration (local optimum). (7) Feedback and constraint adjustment. Feed the inner layer trajectory optimization results back to outer layer constraints such as compatibility and control range, to guide ISSA to adjust the search direction and update the platform assignment. (8) Iteration. Repeat steps (5)-(7). The outer and inner layers optimize alternately and exchange information until the maximum iteration number (t=T) is reached, then terminate the calculation. (9) Output. Return the final optimal platform-target assignment G_best, optimal trajectory design variables H_best, and the corresponding objective values f(G_{\text{best}}).

Considering uncertainties across different formation intervals (e.g., faults, dip, heterogeneity, and strike), this study, based on candidate platform locations in Fig. 3 and on-site design scheme in Fig. 2b and Fig. 2c, incorporated the intervals to be avoided and sections unfavorable for trajectory adjustment into the constraints, determining the allowable ranges of trajectory design variables. This allows the deployable area and search direction to be directly constrained during optimization. For the constraint set, several parameter values are identical for Platforms P1-P5, namely: (1) Trajectory design variable constraints: target section length 1 000-1 400 m, build-up rate 2°-6°/30 m, inclination angle of kickoff points 0°-5°, inclination angle of target section 86°-92°, azimuth angle of target section 50°-70° and 210°-230°. (2) Engineering objective constraints: maximum drilling footage 4 500 m, maximum trajectory complexity 100, minimum directional separation factor is required to be greater than 1.5. The values of the other parameters are different (Table 2).

During optimization, conflicts may arise between sub-objectives, and it is necessary to first determine the weights for each sub-objective. In this study, the analytic hierarchy process (AHP) method ^[11] was adopted, with pairwise comparison by experts and consistency checking, to obtain a more reasonable weighting of the four sub-objectives. The calculated weighting coefficients ω₁, ω₂, ω₃, and ω₄ in Eq. (1) are 0.35, 0.40, 0.10, and 0.15, respectively.

Simulation tests were conducted for the collaborative optimization of platform locations and wellbore trajectories in Block S using GA, PSO, SSA and ISSA-DABC (Fig. 4). The optimization results of ISSA-DABC outperform the other three algorithms, achieving the best results in the number of platforms, well allocation balance, well depth, trajectory complexity, and anti-collision performance.

Fig. 5 shows that GA, PSO, and SSA tend to suffer from prolonged infeasibility and become trapped in local optima during updates, whereas ISSA-DABC provides better coordination between objectives and constraints to carry out the search. To further compare the four algorithms and identify premature convergence (local optima), the objective function convergence curves (Fig. 5a), drilling footage and trajectory complexity before and after optimization (Fig. 5b, 5c), and collision risk (Fig. 5d) were analyzed. Note that collaborative optimization requires matching between parameter transfer among drilling models and the algorithm update mechanism.

Fig. 5a shows that the optimized objective values of all four algorithms are lower than the initial (pre-optimization) value. ISSA-DABC reaches a stable state after approximately 25 iterations and gives the lowest objective value, improving by 15.93% compared with the on-site design plan. In contrast, the other three algorithms prematurely cluster into a local optimum or suboptimal region. The objective value shows little further improvement in the subsequent iterations, and the local optimum remains after 100 iterations. This is consistent with the unconstrained and local optimum phenomenon observed for GA, PSO, and SSA in Fig. 4, indicating that ISSA- DABC has the strongest global search capability under the problem settings and constraints of this study.

Fig. 5b and Fig. 5c show that among four optimized algorithms, ISSA-DABC is the only algorithm that satisfies both the total trajectory footage and complexity constraints, achieving the minimum values for both. SSA is the second best, while PSO and GA perform the worst. Fig. 5d shows that the minimum directional separation factor of the well group optimized by ISSA-DABC meets the constraint, and the collision risk is reduced by 7.89% compared with the on-site design scheme. In contrast, GA, PSO, and SSA show higher collision risk (with the minimum directional separation factor below 1.5). Overall, Fig. 5b-5d correspond to the convergence behavior in Fig. 5a, confirming that ISSA-DABC provides a better balance among total drilling footage, trajectory complexity, and anti-collision difficulty.

Stability and search efficiency are also important criteria for algorithm evaluation. Stability is assessed by the magnitude of the correction cost for the objective function (Eq. (24)) during search; a smaller correction cost indicates that stable solutions are easier to obtain. Search efficiency is described by computation time; a shorter time indicates faster convergence.

Table 3 records the correction cost and computational time during the search in Fig. 5a. The results show that ISSA-DABC has the lowest mean, minimum, and maximum correction costs, as well as the lowest standard deviation among the four methods, with computational efficiency comparable to that of the other algorithms. The overall performance ranking, from the best to the worst, is ISSA-DABC, SSA, PSO, GA.

Combined with the above analysis, Table 4 presents the final optimized decision variables obtained by ISSA- DABC. After optimization, only three platforms (P1, P3 and P5) are required to deploy 48 wells successfully. This solution satisfies all the set constraints and effectively overcomes the local optimum issues commonly encountered in the traditional “platform first, trajectory second” stepwise optimization, such as “few platforms but complex trajectories” or “optimal trajectories but excessive platforms”. It balances platform layout, trajectory optimization, and engineering-geological constraints, and automatically generates a constraint satisfying global optimal platform-trajectory combination without manual intervention (Fig. 6).