Optimal Continuous Thrust Orbit Transfer Using Evolutionary Algorithms

Nowadays, orbital transfer has a significant role in any space mission, and it can be firmly said that there is no space mission that does not need to the orbital transfer. On the other hand, since the cost of each space mission is very important and the mass of fuel directly related to the cost, decreasing the fuel usage has always been an important issue. So the discussion of minimization of fuel consumption in orbital transfer has always been considered important. Hence, the problem of fuel optimization in orbital transfer has a long history and many scientists have worked on this problem and solved many special and simple cases. To solve the problems with more complex geometry, such as optimal impulsive orbital transfer among coplanar non co-axial orbits, numerical solution of nonlinear equations is required which is extracted from the optimization. Numerical solution of these equations is very sensitive to initial guess values and the convergence process is very slow. Also solving these equations lead only to a local minimum and there is no assurance for global minimum. In this paper, to extract the optimization equations, some explicit equations have been extracted so the process to reach all solutions will be possible. These equations are not provided in other articles. Our method is implemented on two numerical examples. Results have shown acceptable accuracy and high speed calculation of this method.

Optimal debris removal using debris-tether-tug system considering attitude–orbit coupling effects

The well known primer of Lawden is used for the analysis of optimal coplanar orbital transfers in general central force fields. Two first-integrals, which hold for singular thrusting arcs as well as impulsive thrusts, are shown to become linearly dependent if a circular coasting arc forms part of an optimal trajectory. In the time-free case, the two sets of state and adjoint equations can then be integrated analytically. Optimality conditions for a Hohmann transfer in a general central force field are derived. The theory will be applied to an approximate determination of optimum thrust transfers between a circular parking orbit around the Moon and the L2 libration point.

In the present research, optimal control problem for low thrust spacecraft orbital transfer is investigated by combination of analytical method and Artificial Bee Colony (ABC) algorithm, which is a population-based method. Spacecraft trajectory optimization is defined for orbital transfer from Low Earth Orbit (LEO) to Geosynchronous Earth Orbit (GEO). In the proposed analytical method co-state variables are simplified by employing concepts of optimal control and specific conditions which are considered for the problem, consequently, an adjoint differential equation is added to set of differential equations and these equations are solved simultaneously that result in optimum transfer trajectory. Dynamic modeling of the problem is represented based on Edelbaum equations and trajectory design is carried out considering circular orbits. Optimization problem is defined for different kinds of objective functions such as minimum time, minimum control effort, minimum time with minimum control effort as well as both minimum time and minimum control effort considering different optimal weighted coefficients. These coefficients are searched by means of artificial bee colony algorithm in weighted minimum time minimum effort scheme. Initial values of control variable and terminal time for all defined objective functions are foraged through artificial bee colony algorithm. The rate of changes of the states and control variables are obtained and depicted during orbit transfer. The obtained results demonstrate considerable convergence as well as sufficient accuracy.

A fast calculation method for asteroid exploration window based on optimal and sub-optimal two-impulse transfer orbits

Multi-objective evolutionary simulation-optimisation of a real-world manufacturing problem

In this paper, the optimal low thrust planar orbit transfer problem is solved utilizing a fuzzy optimal control algorithm. Firstly, dynamic equations are presented in a discretized form, then all the design variables and constraints are transformed to fuzzy space, while minimizing the performance index and also satisfying transversallity conditions. Applying the concept of membership functions based on expert experience, the designed cost function associated with operational constraints are transformed to fuzzy relations through specific membership functions. Applying Bellman-Zadeh approach, the optimal control problem can be converted to a parameter optimization. Combining the performance index and problem's constraints in a scalar function, necessary optimality conditions are achieved in a form of nonlinear algebraic equations. Finally, to solve this set of equations, the gradient-based method is used. In comparison with the exact form of the problem, the efficiency of the proposed algorithm is highlighted in terms of time and accuracy. In the fuzzy optimal control, a control designer could take advantage of determining the allowed limit for cost function. This algorithm could be successfully extended to fixed state or fixed control problems which is time-consuming in scope of the classical optimal control.

In order to overcome the limitation of traditional single-objective optimal operation method for the multiple energy flows system combined cooling, heat and power (CCHP), this paper presents a multi-objective comprehensive optimization model for CCHP with renewable energy resources and energy storage devices based on the fuzzy theory and PSO. The model utilizes the membership function to fuzzify each objective function. Then linearly weighted sums the objective functions with coefficient of variation method and solve the model by PSO algorithm. The simulation results based on the case of a real district show that compared with traditional optimization method, the comprehensive optimization model established in this paper can take each important performance index into account and effectively optimize the dispatch of energy resources of the CCHP system with renewable energy.

Because of the complexity of some optimization problems, evolutionary and meta-heuristic algorithms are sometimes more applicable than the traditional optimization methods. Some difficulties in solving design-operation problems in the field of engineering are due to the multi-modality of the solution region of these problems. Since the design variables usually are specified as discrete variables and other continuous decision variables have to be set according to the range of the discrete ones, the possibility of trapping the final solution into some local optimum increases. In such cases, the capability of both traditional and evolutionary algorithms decreases. Thus, the development of a strategy to overcome this problem is the subject of this paper. For water utilities, one of the greatest potential areas for energy cost-savings is the effective scheduling of daily pump operations. Optimum design operation of pumping stations is a potential problem in this area that performs a wide background of solutions to this problem with different methods. Computation in all methods is driven by an objective function that includes operating and capital costs subject to various performances and hydraulic constraints. This paper achieves the optimal control and operation of an irrigation pumping station system by one of the latest tools used in optimization problems, which is the honey-bees mating optimization (HBMO) algorithm and is tested with a practical design. The HBMO algorithm with dynamic penalty function is presented and compared with two other well-known optimization tools which are the Lagrange multipliers (LM) method and genetic algorithms (GA) as well as with the previous results of the HBMO algorithm with constant penalty function for the same problem. The LM, GA and HBMO approaches simultaneously determine the least total annual cost of the pumping station and its operation. The solution includes the selection of pump type, capacity and the number of units, as well as scheduling the operation of irrigation pumps that results in minimum design and operating cost for a set of water demand curves. In this paper, the HBMO algorithm is applied and the dynamic penalty function is tested to demonstrate the efficiency of this combination simultaneously. The results are very promising and prove the ability of combining the dynamic penalty function with the HBMO algorithm for solving combinatorial design–operation optimization problems. Application of all these models to a real-world project shows not only considerable savings in cost and energy but also highlights the efficiency and capability of the dynamic penalty function in the HBMO algorithm for solving complex problems of this type.

Active contour models, colloquially known as snakes, are quite popular for several applications such as object boundary detection, image segmentation, object tracking and classification. A snake is an energy minimizing curve that, starting from an initial contour, deforms iteratively thereby gradually moving towards the desired object boundary. Finally, it shrinks and wraps around the object. Therefore, the problem at hand is to find the contour that minimizes the snake energy. While energy minimization may be accomplished using traditional optimization methods, approaches based on nature-inspired evolutionary algorithms have been developed in recent years. One such evolutionary algorithm that has been used extensively in active contours is the particle swarm optimization (PSO). However, conventional PSO converges slowly and gets trapped in local minimum easily. The problem of local minimum results in inaccurate detection of concavities in the object boundary. This is taken care of by using multi-swarm PSO in which a swarm is set for every control point in the snake and then all the swarms search for their best points simultaneously and collaboratively through information sharing among them. The performance of the search process is further enhanced by using dynamic adaptation of the inertia factor. Inertia factor is used to balance the global and local search ability. In this paper, we propose to use a set of fuzzy rules to adjust the inertia weight on the basis of the current normalized snake energy and the current value of inertia. This improves the search for object concavities. Experimental results demonstrate the effectiveness of the proposed method compared to conventional approaches.

Active contour models, colloquially known as snakes, are quite popular for several applications such as object boundary detection, image segmentation, object tracking, and classification via energy minimization. While energy minimization may be accomplished using traditional optimization methods, approaches based on nature-inspired evolutionary algorithms have been developed in recent years. One such evolutionary algorithm that has been used extensively in active contours is the particle swarm optimization (PSO). However, conventional PSO converges slowly and gets trapped in local minimum easily which results in inaccurate detection of concavities in the object boundary. This is taken care of by using proposed multiswarm PSO in which a swarm is set for every control point in the snake and then all the swarms search for their best points simultaneously through information sharing among them. The performance of the multiswarm PSO-based search process is further enhanced by using dynamic adaptation of the inertia factor. In this paper, we propose using a set of fuzzy rules to adjust the inertia weight on the basis of the current normalized snake energy and the current value of inertia. Experimental results demonstrate the effectiveness of the proposed method compared to conventional approaches.

DNA computing relies on biochemical reactions of DNA molecules and may result in incorrect or undesirable computations. Therefore, much work has focused on designing the DNA sequences to make the molecular computation more reliable. Sequence design involves with a number of heterogeneous and conflicting design criteria and traditional optimization methods may face difficulties. In this paper, we formulate the DNA sequence design as a multiobjective optimization problem and solve it using a constrained multiobjective evolutionary algorithm (EA). The method is implemented into the DNA sequence design system, NACST/Seq, with a suite of sequence-analysis tools to help choose the best solutions among many alternatives. The performance of NACST/Seq is compared with other sequence design methods, and analyzed on a traveling salesman problem solved by bio-lab experiments. Our experimental results show that the evolutionary sequence design by NACST/Seq outperforms in its reliability the existing sequence design techniques such as conventional EAs, simulated annealing, and specialized heuristic methods.

This paper deals with the implementation techniques of an implicit integrator to achieve fast and accurate analyses of spacecraft dynamics. For this purpose, the pseudospectral method is adopted to directly integrate the second-order system of equations for both the spacecraft dynamics and corresponding state transition matrix. Various implementation techniques are proposed to enhance the numerical efficiency and integration accuracy, which include a moving horizon approach, the decoupled integration of the second-order dynamics for the state transition matrix, and the grid adaptation method. The numerical features of the proposed techniques are investigated through their applications to a spacecraft’s motion around highly eccentric elliptic orbits, and the resultant numerical errors and computing times are compared with those from the Runge-Kutta method to show the relative efficiency and accuracy of the presented methods. In addition, an optimal two-impulse orbit transfer from the Earth to the Moon is analyzed by implementing the proposed methods using a multiple-shooting framework. The results show that the proposed techniques are extremely effective for dynamical problems requiring intensive and accurate time integrations, and can provide much better accuracy and efficiency than the explicit Runge-Kutta integrator.

Optimal low-thrust lunar orbit transfers with shadowing effect using a multiple-arc formulation

Calibration of exponential Hawkes processes using a Modified Bionomic Algorithm