Implementation of Digital Pheromones in Particle Swarm Optimization for Constrained Optimization Problems

Kalivarapu, Vijay; Winer, Eliot H.

doi:10.2514/6.2008-1974

Cited by 12 publications

(5 citation statements)

References 20 publications

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“…Albeit less computationally efficient, in the scientific literature [25,52,43,42,22,21,13] the local version of the PSO algorithm, based on the definition of the neighbors of each particle, has been reported to be occasionally capable of avoiding local minima. Additional improvements based on the application of evolutionary operators to the particle swarm methodology are also reported by several researchers [37,47].…”

Section: Numerical Resultsmentioning

confidence: 85%

Orbital transfers: optimization methods and recent results

Pontani¹

2011

Numerical Algebra, Control &Amp; Optimization

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A wide variety of techniques have been employed in the past for optimizing orbital transfers, which represent the trajectories that lead a spacecraft from a given initial orbit to a specified final orbit. This paper describes several original approaches to optimizing impulsive and finite-thrust orbital transfers, and presents some very recent results. First, impulsive transfers between Keplerian trajectories are considered. A new, analytical optimization method applied to these transfers leads to conclusions of a global nature for transfers involving both ellipses and escape trajectories, without any limitation on the number of impulses, and with possible constraints on the radius of closest approach and greatest recession from the attracting body. A direct optimization technique, termed direct collocation with nonlinear programming algorithm, is then applied to finite-thrust transfers between circular orbits. Lastly, low-thrust orbital transfers are optimized through the joint use of the necessary conditions for optimality and of the recently introduced heuristic method referred to as particle swarm optimization. This work offers a complete description and demonstrates the effectiveness of the distinct techniques applied to optimizing orbital transfer problems of different nature.

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Section: Numerical Resultsmentioning

confidence: 85%

Orbital transfers: optimization methods and recent results

Pontani¹

2011

Numerical Algebra, Control &Amp; Optimization

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“…In addition, two different versions of the particle swarm exist [2][3][4]: the global version, where the collective best position (associated with the social term in the velocity updating expression) is selected by considering the entire swarm, and the local version where, for each particle, the collective best position is selected among the particles located in a proper neighborhood of the particle itself. In the scientific literature, additional improvements based on the application of evolutionary operators to the particle swarm methodology are also reported [5].…”

Section: Introductionmentioning

confidence: 98%

Optimal Finite-Thrust Rendezvous Trajectories Found via Particle Swarm Algorithm

Pontani

Conway

2013

Journal of Spacecraft and Rockets

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The particle swarm optimization technique is a population-based stochastic method developed in recent years and successfully applied in several fields of research. The particle swarm optimization methodology aims at taking advantage of the mechanism of information sharing that affects the overall behavior of a swarm, with the intent of determining the optimal values of the unknown parameters of the problem under consideration. This research applies the technique to determining optimal continuous-thrust rendezvous trajectories in a rotating Euler-Hill frame. Five distinct applications, both in two dimensions and in three dimensions, are considered. Hamiltonian methods are employed to translate the related optimal control problems into parameter optimization problems. The transversality condition, which is an analytical condition that arises from the calculus of variations, is proven to be ignorable for these problems, and this property greatly simplifies the solution process. For each of the five applications considered in the paper, despite its simplicity, the swarming algorithm successfully finds the optimal control law corresponding to the minimum-time trajectory with great accuracy. Nomenclature a = thrust acceleration of P with components a x ; a y ; a z in the r T ;θ T ;ĥ T frame, DU∕TU 2 or km∕s 2 a k = lower bound for the kth component of the position vector χ b k = upper bound for the kth component of the position vector χ a P = magnitude of the thrust acceleration of P, DU∕TU 2 or km∕s 2 c = effective exhaust velocity of the propulsive system, DU∕TU or km∕s d k = upper bound for the kth component of the velocity vector w H = Hamiltonian function h i = specific angular momentum of spacecraft i (i P or T) J = objective function J j opt = minimum value of the objective function found by the particle swarm optimization algorithm up to iteration j J = objective function considered by the particle swarm optimization algorithm (in the presence of equality constraints) l r = rth equality constraint function (r 1; : : : ; m) m = number of equality constraints m 0 = initial mass of P N = number of particles N IT = number of iterations n = number of unknown parameters n 0 = initial thrust acceleration, DU∕TU 2 or km∕s 2 P = pursuing spacecraft p = parameter vector r i = inertial position vector of spacecraft i (i P or T) R T = radius of the circular orbit of the target vehicle, DU or km r T , θ T ,ĥ T = orbital reference frame T = target vehiclẽ T = propulsive thrust t = time, TU or s t f = final time, TU or s t 0 = initial time, TU or s u = control vector v i = inertial velocity vector of spacecraft i (i P or T) wi = velocity vector of particle i with components fw k ig x = state vector α = in-plane thrust angle, deg or rad β= out-of-plane thrust angle, deg or rad η r = weighting coefficient for penalty term r Θ = state transition matrix associated with the linear equations of motion λ = adjoint variable conjugate to the dynamics equations with components fλ i g μ = gravitational parameter of the attracting body, ...

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“…The pheromones were used to select next node in graph as waypoint. A combination of PSO with digital pheromones for constrained optimization problems has been described in [5]. In [6] virtual pheromone based communication mechanism to decrease communication cost in the map coverage task was introduced.…”

Section: Introductionmentioning

confidence: 99%

Robot Coordination Based on Biologically Inspired Methods

Masár

Budinská

2013

AMR

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An embedded particle swarm optimization (PSO) technique combined with virtual pheromones deposition and rules for artificial bird flocking is proposed to handle an area coverage problem using a swarm of mobile robots. A simulation tool VERA that was developed to simulate a swarm behavior of a group of mobile agents is described. Results of simulation experiments and tests on Lego robots that prove the concept are presented. Results are discussed and future development is suggested in the end of the paper.

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Implementation of Digital Pheromones in Particle Swarm Optimization for Constrained Optimization Problems

Cited by 12 publications

References 20 publications

Orbital transfers: optimization methods and recent results

Orbital transfers: optimization methods and recent results

Optimal Finite-Thrust Rendezvous Trajectories Found via Particle Swarm Algorithm

Robot Coordination Based on Biologically Inspired Methods

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