A Modified Hybrid Genetic Algorithm for Solving Nonlinear Optimal Control Problems

Here, a two-phase algorithm is proposed for solving bounded continuous-time nonlinear optimal control problems (NOCP). In each phase of the algorithm, a modified hybrid genetic algorithm (MHGA) is applied, which performs a local search on offsprings. In first phase, a random initial population of control input values in time nodes is constructed. Next, MHGA starts with this population. After phase 1, to achieve more accurate solutions, the number of time nodes is increased. The values of the associated new control inputs are estimated by Linear interpolation (LI) or Spline interpolation (SI), using the curves obtained from the phase 1. In addition, to maintain the diversity in the population, some additional individuals are added randomly. Next, in the second phase, MHGA restarts with the new population constructed by above procedure and tries to improve the obtained solutions at the end of phase 1. We implement our proposed algorithm on 20 well-known benchmark and real world problems; then the results are compared with some recently proposed algorithms. Moreover, two statistical approaches are considered for the comparison of the LI and SI methods and investigation of sensitivity analysis for the MHGA parameters

A Hybrid Technique applied to the Intermediate-Target Optimal Control Problem

The DoD has introduced the concept of Manned-Unmanned Teaming, a subset of which is the loyal wingman. Optimal control techniques have been proposed as a method for rapidly solving the intermediate-target (mid-point constraint) optimal control problem. Initial results using direct orthogonal collocation and a gradient-based method for solving the resulting nonlinear program reveals a tendency to converge to or to get `stuck’ in locally optimal solutions. The literature suggested a hybrid technique in which a particle swarm optimization is used to quickly find a neighborhood of a more globally minimal solution, at which point the algorithm switches to a gradient-based nonlinear programming solver to converge on the globally optimal solution. The work herein applies the hybrid optimization technique to rapidly solve the loyal wingman optimal control problem. After establishing the background and describing the loyal wingman particle swarm optimization algorithm, the problem is solved first using the gradient-based direct orthogonal collocation method, then re-solved using a hybrid approach in which the results of the particle swarm optimization algorithm are used as the initial guess for the gradient-based direct orthogonal collocation method. Results comparing the final trajectory and convergence time, demonstrate the hybrid technique as a reliable method for producing rapid, autonomous, and feasible solutions to the loyal wingman optimal control problem

Optimal control problems solved via swarm intelligence

Questa tesi descrive come risolvere problemi di controllo ottimo tramite swarm in telligence. Grande enfasi viene posta circa la formulazione del problema di controllo ottimo, in particolare riguardo a punti fondamentali come l’identificazione delle incognite, la trascrizione numerica e la scelta del risolutore per la programmazione non lineare. L’algoritmo Particle Swarm Optimization viene preso in considerazione e la maggior parte dei problemi proposti sono risolti utilizzando una formulazione differential flatness. Quando viene usato l’approccio di dinamica inversa, il problema di ottimo relativo ai parametri di trascrizione è risolto assumendo che le traiettorie da identificare siano approssimate con curve B-splines. La tecnica Inverse-dynamics Particle Swarm Optimization, che viene impiegata nella maggior parte delle applicazioni numeriche di questa tesi, è una combinazione del Particle Swarm e della formulazione differential flatness. La tesi investiga anche altre opportunità di risolvere problemi di controllo ottimo tramite swarm intelligence, per esempio usando un approccio di dinamica diretta e imponendo a priori le condizioni necessarie di ottimalitá alla legge di controllo. Per tutti i problemi proposti, i risultati sono analizzati e confrontati con altri lavori in letteratura. Questa tesi mostra quindi the algoritmi metaeuristici possono essere usati per risolvere problemi di controllo ottimo, ma soluzioni ottime o quasi-ottime possono essere ottenute al variare della formulazione del problema.This thesis deals with solving optimal control problems via swarm intelligence. Great emphasis is given to the formulation of the optimal control problem regarding fundamental issues such as unknowns identification, numerical transcription and choice of the nonlinear programming solver. The Particle Swarm Optimization is taken into account, and most of the proposed problems are solved using a differential flatness formulation. When the inverse-dynamics approach is used, the transcribed parameter optimization problem is solved assuming that the unknown trajectories are approximated with B-spline curves. The Inverse-dynamics Particle Swarm Optimization technique, which is employed in the majority of the numerical applications in this work, is a combination of Particle Swarm and differential flatness formulation. This thesis also investigates other opportunities to solve optimal control problems with swarm intelligence, for instance using a direct dynamics approach and imposing a-priori the necessary optimality conditions to the control policy. For all the proposed problems, results are analyzed and compared with other works in the literature. This thesis shows that metaheuristic algorithms can be used to solve optimal control problems, but near-optimal or optimal solutions can be attained depending on the problem formulation

Hybrid PSOGSA technique for solving dynamic economic emission dispatch problem

In this paper, a new hybrid population-based algorithm is proposed with the combining of particle swarm optimization (PSO) and gravitational search algorithm (GSA) techniques. The main idea is to integrate the ability of exploration in PSO with the ability of exploration in the GSA to synthesize both algorithms’ strength. The new algorithm is implemented to the dynamic economic emission dispatch (DEED) problem to minimize both fuel cost and emission simultaneously under a set of constraints. To demonstrate the efficiency of the proposed algorithm, a 5-unit test system is used. The results show the effectiveness and superiority of the proposed method when compared to the results of other optimization algorithms reported in the literature

Intelligent Tuned Harmony Search for Solving Economic Dispatch Problem with Valve-point Effects and Prohibited Operating Zones

Economic dispatch with valve point effect and Prohibited Operating Zones (POZs) is a non-convex and discontinuous optimization problem. Harmony Search (HS) is one of the recently presented meta-heuristic algorithms for solving optimization problems, which has different variants. The performances of these variants are severely affected by selection of different parameters of the algorithm. Intelligent Tuned Harmony Search (ITHS) is a recently developed variant, which mitigates the drawbacks of parameter initializing by maintaining a proper balance between diversification and intensification throughout the search process. The proposed method is applied to five different cases of power systems and the effectiveness, feasibility, and robustness of method is explored through the comparison with reported results in recent literature. First three case studies are systems with 3, 13, and 40-units, considering valve- point effect. The fourth and fifth cases are six and 15-generation unit taking into account generator constraints including POZs, ramp rate limit and transmission line losses which is a challenging Economic Dispatch (ED) problem due to restriction in search space. Computation results imply the efficiency of the proposed method toward other optimization methods reported in recent literature, judged in terms of the objective function value and solution robustness

A Novel Hybrid Moth Flame Optimization with Sequential Quadratic Programming Algorithm for Solving Economic Load Dispatch Problem

The insufficiency of energy resources, increased cost of generation and rising load demand necessitate optimized economic dispatch. The real world ED (Economic Dispatch) is highly non-convex, nonlinear and discontinuous problem with different equality and inequality constraints. In this research paper, a novel hybrid MFO-SQP (Moth Flame Optimization with Sequential Quadratic Programming) is proposed to solve the ED problem. The MFO is stochastic searching algorithm minimizes by random search and SQP is definite in nature that refines the local search in vicinity of local minima. Proposed technique has been implemented on 6, 15 and 40 units test system with different constraints like valve point loading effect, transmission loss, prohibited zones, generator capacity limits and power balance. Results, obtained from proposed technique are compared with those of the techniques reported in the literature, are proven better in terms of fuel cost and convergence

An investigation into fishing boat optimisation using a hybrid algorithm

The optimisation of high-speed fishing boats is different from the optimisation of other displacement type vessels as, for high-speed fishing boats, the wave-making resistance decreases while the splashed resistance increases sharply. To reduce fuel consumption and operating costs in the current economic climate, this paper presents a fishing boat optimisation approach using a Computational Fluid Dynamics (CFD) technique. The RANS-VoF solver was utilised to calculate total resistance, sinkage and trim for a fishing boat in calm water. The Arbitrary Shape Deformation (ASD) technique was used to smoothly alter the geometry. A hybrid algorithm was presented to solve the complicated nonlinear optimisation problem. Herein, a Design of Experiments (DoE) method was applied to find an optimal global region and a mathematical programme was employed to determine an optimal global solution. Under the same displacement with the original hull, two optimisation loops were built with different design variables. After completion of the optimisation, two optimal hull forms were obtained. The optimisation results show that the optimisation loop presented in this study can be used to design a suitable fishing boat in the reduction of the total resistance in calm water