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Convergence Analysis of hidden genes genetic algorithms in Space Trajectory Optimization

JOURNAL OF AEROSPACE INFORMATION SYSTEMS 2018年第4期15卷 228-238页

作者： Darani, Shadi A. Abdelkhalik, Ossama Michigan Technol Univ Dept Mech Engn Engn Mech 815 RL Smith Bldg1400 Townsend Dr Houghton MI 49931 USA

This study presents a convergence analysis that proves hidden genes genetic algorithms (HGGAs) generate a sequence of solutions with the limit value of the global optima. For an analytical proof, the homogeneous finite Markov models of different mechanisms are derived, and the convergence of the HGGAs with tag evolution mechanisms are investigated. The optimization problem is considered a maximization problem with strictly positive values for the objective function. The stochastic dependency between successive populations is created by applying selection, mutation, and crossover operators to the current population to produce the next population. The GA is a stochastic process in which the state of each population only depends on the state of the immediate predecessor population.

关键词： Trajectory Optimization hidden genes genetic algorithms Convergence Analysis Neptune Deep Space Maneuver Interplanetary Trajectories Particle Swarm Optimization Fuel Consumption Space Missions Solar System

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Space Trajectory Optimization Using hidden genes genetic algorithms

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JOURNAL OF SPACECRAFT AND ROCKETS 2018年第3期55卷 764-774页

作者： Darani, Shadi A. Abdelkhalik, Ossama Michigan Technol Univ Mech Engn Engn Mech Dept 815 RL Smith Bldg1400 Townsend Dr Houghton MI 49931 USA

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Multi-Objective hidden genes genetic Algorithm for Multigravity-Assist Trajectory Optimization

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JOURNAL OF GUIDANCE CONTROL AND DYNAMICS 2022年第7期45卷 1269-1285页

作者： Ellithy, Ahmed Abdelkhalik, Ossama Englander, Jacob Iowa State Univ Aerospace Engn Dept 1200 Howe Hall Ames IA 50011 USA Iowa State Univ Dept Aerosp Engn 1200 Howe Hall Ames IA 50011 USA Johns Hopkins Appl Phys Lab Space Explorat Sect 11101 Johns Hopkins Rd Laurel MD 20723 USA

In multigravity-assist trajectory optimization, the size of the design space is a variable itself. The objective functions are usually replete with local minima. This paper presents a multi-objective hidden genes genetic algorithm (MOHGGA) for trajectory optimization. The length of the chromosome is selected large enough to enable modeling a given maximum number of swing-bys and maximum number of deep space maneuvers (DSMs). Binary tags are appended to those genes that control the swing-bys and DSMs. These binary tags are used to remove/add swing-bys and DSMs to a trajectory solution, and hence enable optimization among solutions of different sizes (different topologies). The MOHGGA generates Pareto fronts that have solutions of, in general, different number of swing-bys, swing-by planets, launch and arrival dates, and number of DSMs. Two objectives are considered in this paper: the total mission cost and total time of flight. An elitist nondominated sorting genetic algorithm is used. Local optimization is conducted on one objective function, holding the other objective function constant, to further improve the resulting Pareto front. Numerical results of four benchmark test cases for missions to Mars, Jupiter, Saturn, and Mercury are presented. The results demonstrate the capability of MOHGGA in searching for optimal trajectory topologies while optimizing two objectives.

关键词： hidden genes genetic algorithms Trajectory Optimization Neptune Deep Space Maneuver Pericenter Multi Objective Evolutionary algorithms Interplanetary Trajectories Lambert Algorithm Cassini Mission MATLAB

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hidden genes genetic Algorithm for Multi-Gravity-Assist Trajectories Optimization

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JOURNAL OF SPACECRAFT AND ROCKETS 2011年第4期48卷 629-641页

作者： Gad, Ahmed Abdelkhalik, Ossama Michigan Technol Univ Mech Engn Engn Mech Dept Houghton MI 49931 USA

The problem of optimal design of a multi-gravity-assist space trajectory, with a free number of deep space maneuvers, poses a multimodal cost function. In the general form of the problem, the number of design variables is solution dependent. This paper presents a genetic-based method developed to handle global optimization problems where the number of design variables vary from one solution to another. A fixed length for the design variables is assigned for all solutions. Independent variables of each solution are divided into effective and ineffective segments. Ineffective segments (hidden genes) are excluded in cost function evaluations. Full-length solutions undergo standard genetic operations. This new method is applied to several interplanetary trajectory design problems. This method has the capability to determine the number of swing-bys, the planets to swing by, launch and arrival dates, and the number of deep space maneuvers, as well as their locations, magnitudes, and directions, in an optimal sense. The results presented in this paper show that solutions obtained using this tool match known solutions for complex case studies.

关键词： Gravity Assist Trajectories hidden genes genetic algorithms Deep Space Maneuver Neptune Pericenter Optimization Algorithm Interplanetary Trajectories Trajectory Optimization Lambert's Problem Interplanetary Mission

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hidden genes genetic Optimization for Variable-Size Design Space Problems

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JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 2013年第2期156卷 450-468页

作者： Abdelkhalik, Ossama Michigan Tech Univ Mech Engn Engn Mech Dept Houghton MI 49931 USA

This paper introduces the biologically inspired concept of hidden genes genetic algorithms;they search for optimal solutions to global optimization problems of multimodal objective functions with a variable number of design variables. A fixed chromosome length is assumed for all solutions in the population. Each chromosome is divided into effective and ineffective segments. The effective segment includes the design variables for that solution. The ineffective segment includes only hidden genes. hidden genes are excluded in objective function evaluations. The effect of the hidden genes on the convergence of the genetic algorithm is studied. Two test cases are presented.

关键词： Global optimization Variable length genetic algorithms hidden genes genetic algorithms

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Dynamic-Size Multiple Populations genetic Algorithm for Multigravity-Assist Trajectories Optimization

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JOURNAL OF GUIDANCE CONTROL AND DYNAMICS 2012年第2期35卷 520-529页

作者： Abdelkhalik, Ossama Gadt, Ahmed Michigan Technol Univ Dept Mech Engn & Engn Mech Houghton MI 49931 USA

The problem of the optimal design of a multigravity-assist space trajectory, with a free number of deep space maneuvers, in its general form poses a multimodal objective function in which design space size is variable. This paper presents a genetic-based method developed to handle global, variable-size, design space optimization problems where the number of design variables varies from one solution to another. Subpopulations of fixed-size design spaces are randomly initialized. Standard genetic operations are carried out for a stage of generations. A new population is then created by reproduction from all members in all subpopulations based on their relative fitnesses. The resulting subpopulations have different sizes from their initial sizes in general. The process repeats, leading to an increase in the size of subpopulations of more fit solutions and a decrease in the size of subpopulations of less fit solutions. This method has the capability to determine the number of swing-bys, the planets to swing by, launch and arrival dates, and the number of deep space maneuvers as well as their locations, magnitudes, and directions in an optimal sense. This new method is applied to several interplanetary trajectory design problems. The results presented in this paper show that solutions obtained using this tool match known solutions for complex case studies.

关键词： hidden genes genetic algorithms Trajectory Optimization Deep Space Maneuver Neptune Interplanetary Trajectories Interplanetary Mission Pericenter Gravity Assist Maneuver Particle Swarm Optimization Lambert's Problem

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Mutation Operator for Resonance Flybys in Moon Tour Design Optimization

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JOURNAL OF GUIDANCE CONTROL AND DYNAMICS 2024年第11期47卷 2287-2300页

作者： Ellithy, Ahmed Englander, Jacob Abdelkhalik, Ossama Iowa State Univ Aerosp Engn Dept 1200 Howe Hall Ames IA 50011 USA Johns Hopkins Appl Phys Lab Space Explorat Sect 11101 Johns Hopkins Rd Laurel MD 20723 USA

The global optimization of the moon tour design problem is addressed in this paper. These missions are usually designed using graphical methods or grid search, which require simplifying assumptions, and a skillful mission designer. The grid search methods are computationally intense. Trajectories with a high number of flybys and multiple resonance flybys are usually hard to optimize, especially with small-size/short-period flyby moons. This work proposes a new mutation operator that is incorporated with the Monotonic Basin Hopping in the Evolutionary Mission Trajectory Generator tool;this mutation operator increases the exploration of resonance flybys to improve convergence in moon tour design optimization problems. In this work, the hidden genes genetic Algorithm is used to optimize the undetermined number of moon flybys. A Europa Clipper-like mission is optimized assuming two-body dynamics, and a validation study for the proposed resonance mutation operator is presented. The results include an optimized baseline solution and a new solution with a different sequence of flybys with a different sequence of flybys for the Europa Clipper-like mission, in addition to an optimized moon tour in the Saturnian system.

关键词： Multidisciplinary Design Optimization hidden genes genetic algorithms Astrodynamics Moon Tours Orbital Mechanics Europa Clipper Multiple-Flyby Mission Exploration of Saturn Trajectory Optimization Analytic Trajectory Optimization Model Space Mission Design

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Structured-Chromosome Evolutionary algorithms for Variable-Size Autonomous Interplanetary Trajectory Planning Optimization

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JOURNAL OF AEROSPACE INFORMATION SYSTEMS 2015年第3期12卷 314-328页

作者： Nyew, Hui Meen Abdelkhalik, Ossama Onder, Nilufer Michigan Technol Univ Dept Comp Sci Houghton MI 49931 USA Michigan Technol Univ Dept Mech Engn Engn Mech Houghton MI 49931 USA

In interplanetary trajectory optimization, events such as planetary gravitational-assist maneuvers (swingbys) and deep-space maneuvers can be added/removed from the trajectory plan to reduce the cost or the flight time. This renders the number of design variables in the optimization problem variable. Global optimization methods that optimize this type of multimodal objective function can only handle problems with a fixed number of design variables. This paper presents the structured-chromosome evolutionary algorithm framework that is developed to handle variable-size design space optimization problems. In this framework, a solution (chromosome) is represented by a hierarchical data structure where the genes in the chromosome are classified as dependent and nondependent genes. This structure provides the capability to apply genetic operations between solutions of different lengths, and thus to automatically determine the number of swingbys, the planets to swingby, launch and arrival dates, and the number of deep-space maneuvers, as well as their locations, magnitudes, and directions, in an optimal sense. This new method is applied to several interplanetary trajectory design problems. Results show that solutions obtained using this tool match known solutions for some complex problems. A comparison between genetic algorithms and differential evolution in the structured-chromosome framework is presented.

关键词： Interplanetary Trajectories Structured Chromosome Evolutionary algorithms Saturn Optimal Impulsive Maneuvers hidden genes genetic algorithms Iterative Algorithm Jupiter Europa Orbiter Trajectory Optimization Nonlinear Programming Statistical Analysis

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