A modified genetic algorithm for optimal control problems

Michalewicz, Zbigniew; Janikow, Cezary Z.; Krawczyk, Jacek B.

doi:10.1016/0898-1221(92)90094-x

Cited by 235 publications

(87 citation statements)

References 4 publications

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“…When F is lower thanF, the higher crossover probability is used to raise the chance of emergence of new and improved individuals. The crossover operation used in the proposed algorithm is arithmetic crossover [35].…”

Section: Crossover Operationmentioning

confidence: 99%

“…3: Calculate the fitness of each individual in the initial population E 0 according to Equations 27 and 28; 4: for all =1 to L do 5: Select survivor according to the roulette wheel selection rule [34]; 6: end for 7: for all g = 1 to g max do 8: for all =1 to L do 9: Select randomly two individuals and calculate the crossover probability p c according to Equation 29;10: Generate a random floating-point number n random , n random ∈ (0, 1); 11: if n random ≤ p c then 12: Perform arithmetic crossover operation [35]; 13: end if 14: end for 15: for all =1 to L do 16: Calculate the mutation probability p ,m according to Equation 30; 17: Generate a random floating-point number n random , n random ∈ (0, 1); 18: if n random ≤ p l,m then 19: Perform Gaussian mutation operation [36]; 20: end if 21: end for 22: Calculate the fitness of each individual in the new population E g+1 according to Equations 27 and 28; 23: end for 24: Return the minimum CAPEX, A pan and E max B .…”

Section: Algorithm 1 the Capex Minimization Algorithmmentioning

confidence: 99%

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Modeling, metrics, and optimal design for solar energy-powered base station system

Wang

Tang

et al. 2015

J Wireless Com Network

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Using renewable energy system in powering cellular base stations (BSs) has been widely accepted as a promising avenue to reduce and optimize energy consumption and corresponding carbon footprints and operational expenditures for 4G and beyond cellular communications. However, how to design a reliable and economical renewable energy powering (REPing), while guaranteeing communication reliability, renewable energy utilization, and system durability, is still a great challenge. Motivated by this challenge, we firstly model the dynamic energy flow behavior of solar energy-powered BS by using stochastic queue model, jointly considering instability of solar energy generation, non-linear effects of energy storage, and time varies of traffic load. On the basis of the model, three key performance metrics, including service outage probability (SoP), solar energy utilization efficiency (SEuE), and mean depth of discharge (MDoD), are defined, and close-form expressions of them are derived. Finally, under the guidelines of defined metrics, the sizing optimization problem is formulated, and then we propose the capital expenditure (CAPEX) minimization algorithm to resolve it with considerations of communication reliability, efficiency, and durability. Numerical results conducted to demonstrate the effectiveness of our proposed metrics vividly showed the close relationship between design metrics and system parameters. Simulation results also showed that our proposed algorithm can reduce at least 12.1% CAPEX compared with the classic algorithms and guarantee SoP below 0.82%, SEuE above 97%, and MDoD ranging from 7.2% to 9.1%, which means that the optimal design was achieved in terms of system reliability, efficiency, durability, and investment. The proposed modeling, design metrics, and sizing method provide a theoretical basis for actual designs of REPing BS system, which also can be further applied to the scenario of other forms of renewable energy powered system.

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Section: Crossover Operationmentioning

confidence: 99%

Section: Algorithm 1 the Capex Minimization Algorithmmentioning

confidence: 99%

Modeling, metrics, and optimal design for solar energy-powered base station system

Wang

Tang

et al. 2015

J Wireless Com Network

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“…In the genetic operation, the selection probability determines the probability of individual inheritance to the next generation. The calculation formula proposed by Michalewicz [39] is used here:…”

Section: (2) Initial Populationmentioning

confidence: 99%

The Emergency Vehicle Routing Problem with Uncertain Demand under Sustainability Environments

Qin

Cheng

et al. 2017

Sustainability

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Abstract:The reasonable utilization of limited resources is critical to realize the sustainable developments. In the initial 72-h crucial rescue period after the disaster, emergency supplies have always been insufficient and the demands in the affected area have always been uncertain. In order to improve timeliness, utilization and sustainability of emergency service, the allocation of the emergency supplies and the emergency vehicle routes should be determined simultaneously. Assuming the uncertain demands follow normal distribution, an optimization model for the emergency vehicle routing, by considering the insufficient supplies and the uncertain demands, is developed. The objective function is applied to minimize the total costs, including the penalty costs induced by more or less supplies than the actual demands at all demand points, as well as the constraints of the time windows and vehicle load capacity taken into account. In more details, a solution method for the model, based on the genetic algorithm, is proposed, which solves the problem in two stages. A numerical example is presented to demonstrate the efficiency and validity of the proposed model and algorithm.

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“…[27][28][29], ant colony algorithm [30] and simulated annealing algorithm [31][32]. The simulated annealing algorithm is adopted for control force optimization and distribution in this article.…”

Section: Optimization and Distribution Of Tracking Control Forcementioning

confidence: 99%

Optimal Trajectory Planning and Coordinated Tracking Control Method of Tethered Space Robot Based on Velocity Impulse

Huang

Meng

2014

International Journal of Advanced Robotic Systems

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The tethered space robot (TSR) is a new concept of space robot which consists of a robot platform, space tether and operation robot. This paper presents a multi-objective optimal trajectory planning and a coordinated tracking control scheme for TSR based on velocity impulse in the approaching phase. Both total velocity impulse and flight time are included in this optimization. The non-dominated sorting genetic algorithm is employed to obtain the optimal trajectory Pareto solution using the TSR dynamic model and optimal trajectory planning model. The coordinated tracking control scheme utilizes optimal velocity impulse. Furthermore, the PID controller is designed in order to compensate for the distance measurement errors. The PID control force is optimized and distributed to thrusters and the space tether using a simulated annealing algorithm. The attitude interferential torque of the space tether is compensated a using time-delay algorithm through reaction wheels. The simulation results show that the multi-objective optimal trajectory planning method can reveal the relationships among flight time, fuel consumption, planar view angle and velocity impulse number. This method can provide a series of optimal trajectory according to a number of special tasks. The coordinated control scheme can significantly save thruster fuel for tracking the optimal trajectory, restrain the attitude interferential torque produced by space tether and maintain the relative attitude stability of the operation robot.

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A modified genetic algorithm for optimal control problems

Cited by 235 publications

References 4 publications

Modeling, metrics, and optimal design for solar energy-powered base station system

Modeling, metrics, and optimal design for solar energy-powered base station system

The Emergency Vehicle Routing Problem with Uncertain Demand under Sustainability Environments

Optimal Trajectory Planning and Coordinated Tracking Control Method of Tethered Space Robot Based on Velocity Impulse

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