Multi-dimensional Function Optimization Problem Research Articles

UAV Path Planning Algorithm Based on Improved Harris Hawks Optimization.

In the Unmanned Aerial Vehicle (UAV) system, finding a flight planning path with low cost and fast search speed is an important problem. However, in the complex three-dimensional (3D) flight environment, the planning effect of many algorithms is not ideal. In order to improve its performance, this paper proposes a UAV path planning algorithm based on improved Harris Hawks Optimization (HHO). A 3D mission space model and a flight path cost function are first established to transform the path planning problem into a multidimensional function optimization problem. HHO is then improved for path planning, where the Cauchy mutation strategy and adaptive weight are introduced in the exploration process in order to increase the population diversity, expand the search space and improve the search ability. In addition, in order to reduce the possibility of falling into local extremum, the Sine-cosine Algorithm (SCA) is used and its oscillation characteristics are considered to gradually converge to the optimal solution. The simulation results show that the proposed algorithm has high optimization accuracy, convergence speed and robustness, and it can generate a more optimized path planning result for UAVs.

Fast Trajectory Optimization for Gliding Reentry Vehicle Based on Improved Sparrow Search Algorithm

In order to solve the problem of low convergence accuracy and easy to fall into local optimization when solving the reentry vehicle trajectory optimization problem for existing algorithms, an improved sparrow search algorithm (OTRSSA) is proposed. Firstly, the basic sparrow search algorithm is improved by the methods of opposition-based learning, adaptive T-distribution and random walk to improve the optimization accuracy and stability, and increase the global search ability, and the performance verification is carried out in 12 benchmark functions; secondly, the 3-DOF motion model of reentry trajectory optimization problem is established and transformed into multi-dimensional function optimization problem; finally, OTRSSA is applied to solve the trajectory optimization problem. The simulation results show that the optimization performance and convergence speed of OTRSSA are better, and a reentry trajectory with the farthest range and satisfying constraints can be obtained quickly.

A Modified Sparrow Search Algorithm with Application in 3d Route Planning for UAV.

The unmanned aerial vehicle (UAV) route planning problem mainly centralizes on the process of calculating the best route between the departure point and target point as well as avoiding obstructions on route to avoid collisions within a given flight area. A highly efficient route planning approach is required for this complex high dimensional optimization problem. However, many algorithms are infeasible or have low efficiency, particularly in the complex three-dimensional (3d) flight environment. In this paper, a modified sparrow search algorithm named CASSA has been presented to deal with this problem. Firstly, the 3d task space model and the UAV route planning cost functions are established, and the problem of route planning is transformed into a multi-dimensional function optimization problem. Secondly, the chaotic strategy is introduced to enhance the diversity of the population of the algorithm, and an adaptive inertia weight is used to balance the convergence rate and exploration capabilities of the algorithm. Finally, the Cauchy–Gaussian mutation strategy is adopted to enhance the capability of the algorithm to get rid of stagnation. The results of simulation demonstrate that the routes generated by CASSA are preferable to the sparrow search algorithm (SSA), particle swarm optimization (PSO), artificial bee colony (ABC), and whale optimization algorithm (WOA) under the identical environment, which means that CASSA is more efficient for solving UAV route planning problem when taking all kinds of constraints into consideration.

Optimal measurement area determination algorithm of articulated arm measuring machine based on improved FOA

The determination of the optimal measurement area of the articulated arm measuring machine belongs to the multi-dimensional function optimization problem under complex constraints. To realize high-precision measurement of low-precision articulated arm measuring machine, we analyze the working principle and error source of the measuring machine, and establish the optimization target model of the optimal measurement area in this paper. We propose a method for determining the optimal measurement area of an articulated arm measuring machine based on improved FOA. The basic FOA algorithm is improved, the historical optimal individual and population centroid information are added in the population iteration update process, and the fruit fly individuals in each iteration are directly used as the taste concentration judgment value, which increases cooperation and information sharing among fruit fly individuals, and improves the global optimization ability and stability of the algorithm. In the designated area of the measuring machine, we have carried out comparative experiments on the optimization results of improved FOA and basic FOA, ACO, PSO, AL-SC-FOA, LGMS-FOA, IPGS-FFO. Experimental results show that the improved FOA, ACO, PSO, and IPGS-FFO algorithms do not fall into local optimum, and the optimal measurement area determined by them is consistent with the optimization results of other algorithms, and is superior to other algorithms in convergence speed and stability, so it is more suitable for determining the optimal measurement area of articulated arm measuring machine.

A Novel Fuzzy Inspired Bat Algorithm for Multidimensional Function Optimization Problem

This article introduces Fuzzy Inspired Bat Algorithm (FIBA), which is an improved variant of the original Bat algorithm. The novelty of FIBA lies in the integration of a fuzzy controller with the basic Bat algorithm that tries to bring balance between the degree of explorations and exploitations during the mutation operation. Another novelty of FIBA is the introduction of a step size parameter, maintained separately for every candidate solution, to customize and control the mix of explorative and exploitative operations around each candidate solution. FIBA is tested on a standard benchmark set that includes 10 complex, scalable, high dimensional functions. The results on benchmark functions reveal that FIBA can perform sufficiently well, and often better than the original Bat algorithm and another recently proposed improved Bat variant. Such improvements on the experimental results imply that the fuzzy technique adopted by FIBA might be effective on other existing problems as well, and hence demand further research and investigation.

Parameter optimization of Cuckoo Search Algorithm for Multi Dimensional Function Optimization Problem

Parameter optimization of Cuckoo Search Algorithm for Multi Dimensional Function Optimization Problem

An improved fruit fly optimization algorithm based on knowledge memory

ABSTRACT An improved fruit fly optimization algorithm based on knowledge memory (KM-FOA) is proposed for solving continuous functions problems. It is featured with mechanisms devised for solving the concerned problems: (1) Direction vectors, a novel method, is defined as knowledge. Each fruit fly needs to learn and memorize the direction with the most obvious concentration changes in the search space iteratively; (2) we embedded the direction vectors to guide the procedure of choosing the food. Fruit fly swarm can optimize the search roads on the basis of knowledge. And this approach achieves the goal of locating the global optimal space during early evolution. Furthermore, continuous benchmark functions are used to verify the performance of KM-FOA, and numerical results show that the proposed algorithm not only speeds up the convergence but also has a better convergence precision and better balance searching between global and local. The comparisons among KM-FOA, other improved FOAs and other evolution algorithms also demonstrate that KM-FOA performs much better in solving multi-dimensional function optimization problems.

A Modified Artificial Bee Colony Algorithm for Parameter Estimation of Fractional-Order Nonlinear Systems

In this paper, a modified artificial bee colony (MABC) algorithm is proposed to estimate the unknown fractional-order nonlinear systems. First, the parameter estimation problem can be mathematically transformed into a multi-dimensional continuous function optimization problem, which is solved via the MABC algorithm. The proposed MABC algorithm well combines the original artificial bee colony algorithm (ABC) and the Nelder-Mead simplex method (NMS) in a very simple way, which takes full advantage of the exploration ability of the ABC algorithm and the exploitation ability of the NMS. And in the meanwhile, the proposed algorithm improves the speed of convergence. To evaluate the effectiveness of the proposed MABC algorithm, numerical simulations contain two typical uncertain fractional-order nonlinear systems. The results show that compared with the other population-based algorithm and ABC-variants, the proposed MABC for solving the problem of parameter estimation get the faster convergence speed and higher calculation accuracy.

A set of novel continuous action-set reinforcement learning automata models to optimize continuous functions

Learning automata (LA) as a powerful tool for reinforcement learning which belongs to the subject of Artificial Intelligence, could search for the optimal state adaptively in a random environment. In the past decades quite a few FALA algorithms are maturely developed but exposing critical defects, when they are applied to optimize continuous functions. In order to overcome their shortcomings and explore a higher-performance LA, we propose a novel CALA algorithm to solve the function optimization problems via one kind of LA prototypes, i.e, the continuous action-set reinforcement learning automata, which is abbreviated as CARLA. The key mechanism of the proposed algorithm lies in a combination of equidistant discretization and linear interpolation. Specifically, four categories of application models are constructed. Two of them are created to obtain continuous actions when the priori information is finite ones, thus avoiding the drawbacks of FALA. The realization of this functionality recourses to the so-called cumulative distribution function (CDF) and a new concept of area surrounded by curves (AsbC) respectively. The other two models are modified versions to balance the trade-off between accuracy and speed. Moreover, these models are expanded to their generalized versions so that multidimensional function optimization problems can be handled as well. A massive amount of experiments including four benchmarks and three scenarios are designed to demonstrate the effectiveness and efficiency of the proposed application models. The proposed algorithm outperforms the state of the arts of LA as well as optimization algorithms, with a high accuracy rate, a fast convergence speed, and a competitive time consumption, especially in noised environments.

Fitness Proportionate Random Vector Selection based DE Algorithm (FPRVDE)

Differential Evolution (DE) is a simple, powerful and easy to use global optimization algorithm. DE has been studied in detail by many researchers in the past years. In DE algorithm trial vector generation strategies have a significant influence on its performance. This research studies that whether performance of DE algorithm can be improved by incorporating selection advancement in effective trial vector generation strategies. A novel advancement in DE trial vector generation strategies is proposed in this research to speeds up the convergence speed of DE algorithm. The proposed fitness proportion based random vector selection DE (FPRVDE) is based on the proportion of individual fitness mechanism. FPRVDE reduces the role of poor performing individuals to enhance it performance capability of DE algorithm. To form a trial vector using FPRVDE, individual based on the proportion of their fitness are selected. FPRVDE mechanism is applied to most commonly used set of DE variants. A comprehensive set of multidimensional function optimization problems is used to access the performance of FPRVDE. Experimental result shows that proposed approach accelerates DE algorithm.

A hybrid artificial bee colony algorithm for parameter identification of uncertain fractional-order chaotic systems

It is an important issue to estimate parameters of uncertain fractional-order chaotic systems in nonlinear science. In this paper, fractional orders as well as systematic parameters of fractional-order chaotic systems are all considered as independent variables. Firstly, the parameter estimation problem is transformed into a multi-dimensional function optimization problem. And in the meantime, an effective hybrid artificial bee colony algorithm is proposed to deal with the parameter estimation problem. Numerical simulations are conducted on two typical fractional-order chaotic systems to test the effectiveness of the proposed method. The experiments’ results show that the proposed approach for identification of uncertain fractional-order chaotic systems is a successful and promising method with higher calculation accuracy and faster convergence speed.

Parameter estimation of S-shaped growth model: A modified particle swarm algorithm

Parameter estimation plays a critical role for the application and development of S-shaped growth model in the agricultural sciences and others. In this paper, a modified particle swarm optimization algorithm based on the diffusion phenomenon (DPPSO) was employed to estimate the parameters for this model. Under the sense of least squares, the parameter estimation problem of S-shaped growth model, taking the Gompertz and Logistic models for example, is transformed into a multi-dimensional function optimization problem. The results show that the DPPSO algorithm can effectively estimate the parameters of the S-shaped growth model.