工业工程最新文献

This paper presents the solutions and results of the 12th edition of the Global Trajectory Optimization Competition (GTOC12) of the National University of Defense and Technology. To address the complex interstellar mining problem proposed by GTOC12, our solution is divided into two stages. The first stage focuses on preliminary work, including the target selection, the establishment of departure and return databases, and the development of methods to estimate transfer costs, with the aim of enhancing planning efficiency during the global planning phase. The second stage involves trajectory optimization for multiple mining ships, including single-mining-ship trajectory optimization and a multiship iterative process. For single-mining-ship trajectory optimization, the method involves three steps: first, employ a heuristic method for planning the first rendezvous sequences; second, utilize an ant colony optimization (ACO) algorithm for planning the second rendezvous sequences; and third, apply a differential evolution (DE) algorithm alongside an indirect method to refine rendezvous times and low-thrust trajectories. Through the implementation of a multiship iterative strategy, the team accomplished trajectory optimization for multiple mining ships that met the constraints. The final score submitted by the team was 15,160.946, which achieved the sixth place in the competition.

In 2023, the 12th edition of Global Trajectory Competition was organized around the problem referred to as “Sustainable Asteroid Mining”. This paper reports the developments that led to the solution proposed by ESA’s Advanced Concepts Team. Beyond the fact that the proposed approach failed to rank higher than fourth in the final competition leader-board, several innovative fundamental methodologies were developed which have a broader application. In particular, new methods based on machine learning as well as on manipulating the fundamental laws of astrodynamics were developed and able to fill with remarkable accuracy the gap between full low-thrust trajectories and their representation as impulsive Lambert transfers. A novel technique was devised to formulate the challenge of optimal subset selection from a repository of pre-existing optimal mining trajectories as an integer linear programming problem. Finally, the fundamental problem of searching for single optimal mining trajectories (mining and collecting all resources), albeit ignoring the possibility of having intra-ship collaboration and thus sub-optimal in the case of the GTOC12 problem, was efficiently solved by means of a novel search based on a look-ahead score and thus making sure to select asteroids that had chances to be re-visited later on.

We present the solution approach developed by the team “TheAntipodes” during the 12th edition of the Global Trajectory Optimization Competition (GTOC12). An overview of the approach is as follows: (1) generate asteroid subsets, (2) chain building with beam search, (3) convex low-thrust trajectory optimization, (4) manual refinement of rendezvous times, and (5) optimal solution set selection. The generation of asteroid subsets involves a heuristic process to find sets of asteroids that are likely to permit high-scoring asteroid chains. Asteroid sequences “chains” are built within each subset through a beam search based on Lambert transfers. Low-thrust trajectory optimization involves the use of sequential convex programming (SCP), where a specialized formulation finds the mass-optimal control for each ship’s trajectory within seconds. Once a feasible trajectory has been found, the rendezvous times are manually refined with the aid of the control profile from the optimal solution. Each ship’s individual solution is then placed into a pool where the feasible set that maximizes the final score is extracted using a genetic algorithm. Our final submitted solution placed fifth with a score of 15,489.

The 12th Global Trajectory Optimization Competition challenged teams to design trajectories for mining asteroids and transporting extracted resources back to the Earth. This paper outlines the methods and results of the runner-up team, BIT-CAS-DFH, highlighting an overall analysis of the approach as well as detailed descriptions of the methods used. The approach begins with building databases to reduce computational costs in trajectory design. Then, asteroid sequences are determined. A segmentation-based approach was adopted to efficiently handle the large dataset. Each sequence was divided into four time-based segments. Segments 1 and 4 were generated forward and backward, respectively, using a breadth-first beam search. Candidates for these segments were refined using genetic and greedy algorithms. Segments 2 and 3 were then generated and selected forward and backward based on the results of Segments 1 and 4. Following this, a matching process paired candidates from Segments 2 and 3. With the asteroid sequences established, low-thrust trajectories were optimized using indirect methods. A local optimization strategy was employed to maximize the collected mass by fine-tuning rendezvous timings. The final solution is presented, with comparative analyses against other teams’ approaches.

Tsinghua University and the Shanghai Institute of Satellite Engineering organized the 12th edition of the Global Trajectory Optimization Competition (GTOC12) on June 19, 2023. The problem for GTOC12, entitled “Sustainable Asteroid Mining”, explores how spacecraft can be dispatched from the Earth to various asteroids for resource extraction. The primary challenge involves designing coupled trajectories for multiple spacecraft to maximize the collected mineral mass. A novel game model is introduced to encourage the mining of rarely mined asteroids. GTOC12 saw significant participation, with 102 teams registered. By the end of the competition, 28 teams provided feasible solutions, highlighting a growing interest in the field. This study describes the design process of the GTOC12 problem and presents a review and analysis of the results from the participating teams.

Establishing a sustainable mining expedition for the asteroids of the main belt over the 2035–2050 horizon is the visionary problem of the 12th Global Trajectory Optimisation Competition. A fleet of mining ships must rendezvous twice with asteroids to deploy miners and collect minerals. In this paper, we describe the approach of the CS Group team, OptimiCS, to solve this challenging problem. We present the symmetrical construction of upstream and downstream semi-sequences of asteroids, maximizing the mining time expectancy via a beam search with tabu iterations, and the composition of these semi-sequences into complete fleet routes, maximizing the total collected mass via simulated annealing. While representative Earth–asteroid legs are precomputed, the delta-V costs of the asteroid-to-asteroid hops composing the sequences are initially approximated during exploration via a method that refines the accuracy of the maximum initial mass. The resulting high-fidelity trajectories are adjusted and optimized via a direct method and nonlinear programming.

Asteroid mining is a potentially lucrative method for extracting resources from space. Water resources found on asteroids can serve as fuel supplies for spacecrafts in deep space, and some asteroids are rich in precious metals, offering immense potential economic value. The 12th Global Trajectory Optimization Competition, held in 2023, introduced a challenge to trajectory design for sustainable asteroid mining. Participating teams were tasked with maximizing the mining quantity over a 15-yr period by utilizing as many mining ships as possible to depart from the Earth, deploy miners on multiple asteroids, recover minerals, and return to the Earth. Σ team devised a strategy in which one ship completes one sequence, enabling the collection of minerals from 203 asteroids using 26 mining ships. This paper outlines the design methodology and outcomes of this approach, encompassing a preliminary analysis of the problem, optimization for the Earth departure and return, flight sequence search, and low-thrust conversion and optimization. Through methods such as asteroid selection and clustering, database building for Earth–asteroid transfers, global search with an impulsive model, local optimization with a low-thrust model, and conversion of remaining fuel into mining time, the computational efficiency was significantly enhanced, fuel consumption per unit mineral collection was reduced, and mining quantity was improved. Finally, the design outcomes of this approach are presented. The proposed trajectory design method enables the completion of multiple asteroid rendezvouses in a short time, providing valuable insights for future missions involving a single spacecraft conducting multiple rendezvouses with multiple asteroids.

This paper presents the results and design methods of team Nanjing University of Aeronautics and Astronautics in the 12th edition of the Global Trajectory Optimization Competition. To address the problem of sustainable asteroid mining, we focus on the following: analyzing the constraints and asteroids involved; selecting a candidate set of asteroids for which mining missions can be performed easily; establishing an algorithmic flow using phasing indicators, multiobjective beam search, and a genetic algorithm to determine the sequence of asteroid visits for mining ships; and optimizing low-thrust trajectories via an indirect method and global optimization. In addition, a central-node method is proposed to simplify the design process and reduce the computational cost of performing repetitive asteroid-rendezvous missions. The methods developed in the competition enable the mining of 161 asteroids via 20 mining ships, with a total collected mass of 11,513 kg.