Hierarchical optimisation for non-linear dynamical systems with non-separable cost functions

In this paper the previous hierarchical optimisation algorithm of Hassan and Singh for non-linear interconnected dynamical systems with separable cost functions is extended to the case of non-linear and non-separable cost functions. This ensures that any decomposition could be used and makes the new algorithm suitable for the optimisation of general non-linear problems.     

一种应用于柔性作业车间成组调度问题的分级优化算法

提出一种求解柔性作业车间成组调度FGJSS(flexible grouped job-shop scheduling)问题的蚁群粒子群求解算法。算法采用主从递阶形式,主级为蚁群优化算法,选择零件加工设备;从级为粒子群优化算法,在主级零件加工设备约束下优化设备作业排序以实现流通时间最小的目标。算法中,以工序加工时间和设备承载的作业族数为启发式信息设计蚂蚁在工序可用设备间转移概率;以粒子向量优先权值和作业族号为依据设计解码方法实现设备上的成组作业排序。最后,通过仿真实验,验证了该算法的有效性。     

A three level costate prediction method for continuous dynamical systems

In this paper a continuous time version of a previous discrete systems optimisation algorithm is developed. The new algorithm uses prediction of costates within a three level structure to provide an efficient organisation of both the storage and the computation. The algorithm which applies to both linear and nonlinear interconnected dynamical systems has been proved to converge to the optimum. A practical example is given to illustrate the approach. In the example which is of a nonlinear synchronous machine the present approach appears to provide faster convergence and smaller storage than with previous hierarchical and global methods.     

Seeker optimisation (human group optimisation) algorithm with chaos

Seeker optimisation algorithm (SOA), also referred to as human group metaheuristic optimisation algorithms form a very hot area of research, is an emerging population-based and gradient-free optimisation tool. It is inspired by searching behaviour of human beings in finding an optimal solution. The principal shortcoming of SOA is that it is easily trapped in local optima and consequently fails to achieve near-global solutions in complex optimisation problems. In an attempt to relieve this problem, in this article, chaos-based strategies are embedded into SOA. Five various chaotic-based SOA strategies with four different chaotic map functions are examined and the best strategy is chosen as the suitable chaotic scheme for SOA. The results of applying the proposed chaotic SOA to miscellaneous benchmark functions confirm that it provides accurate solutions. It surpasses basic SOA, genetic algorithm, gravitational search algorithm variant, cuckoo search optimisation algorithm, firefly swarm optimisation and harmony search the proposed chaos-based SOA is expected successfully solve complex engineering optimisation problems.     

Differential evolution and differential ant-stigmergy on dynamic optimisation problems

Many real-world optimisation problems are of dynamic nature, requiring an optimisation algorithm which is able to continuously track a changing optimum over time. To achieve this, we propose two population-based algorithms for solving dynamic optimisation problems (DOPs) with continuous variables: the self-adaptive differential evolution algorithm (jDE) and the differential ant-stigmergy algorithm (DASA). The performances of the jDE and the DASA are evaluated on the set of well-known benchmark problems provided for the special session on Evolutionary Computation in Dynamic and Uncertain Environments. We analyse the results for five algorithms presented by using the non-parametric statistical test procedure. The two proposed algorithms show a consistently superior performance over other recently proposed methods. The results show that both algorithms are appropriate candidates for DOPs.     

一种解决复合形局部最优及加速计算的方法

对求解非线性约束优化问题的复合形法陷入局部最优的问题进行探讨,给出了一种改进的方法.改进后的方法不仅可以有效地寻找全局最优解,而且计算速度较传统复合形算法快.     

Deep learning driven real time topology optimisation based on initial stress learning

Topology optimisation can facilitate engineers in proposing efficient and novel conceptual design schemes, but the traditional FEM based optimization demands significant computing power and makes the real time optimization impossible. Based on the convolutional neural network (CNN) method, a new deep learning approximate algorithm for real time topology optimisation is proposed. The algorithm learns from the initial stress (LIS), which is defined as the major principal stress matrix obtained from finite element analysis in the first iteration of classical topology optimisation. The initial major principal stress matrix of the structure is used to replace the load cases and boundary conditions of the structure as independent variables, which can produce topological prediction results with high accuracy based on a relatively small number of samples. Compared with the traditional topology optimisation method, the new method can produce a similar result in real time without repeated iterations. A classic short cantilever problem was used as an example, and the optimized topology of the cantilever structure is predicted successfully by the established approximate algorithm. By comparing the prediction results to the structural optimisation results obtained by the classical topology optimisation method, it is discovered that the two results are highly approximate, which verifies the validity of the established algorithm. Furthermore, a new algorithm evaluation method is proposed to evaluate the effects of using different methods to select samples on the prediction performance of the optimized topology, and the results were promising and concluded in the end.     

Chaotic bat swarm optimisation (CBSO)

Bat swarm optimisation (BSO) is a novel heuristic optimisation algorithm that is being used for solving different global optimisation problems. The paramount problem in BSO is that it severely suffers from premature convergence problem, that is, BSO is easily trapped in local optima. In this paper, chaotic-based strategies are incorporated into BSO to mitigate this problem. Ergodicity and non-repetitious nature of chaotic functions can diversify the bats and mitigate premature convergence problem. Eleven different chaotic map functions along with various chaotic BSO strategies are investigated experimentally and the best one is chosen as the suitable chaotic strategy for BSO. The results of applying the proposed chaotic BSO to different benchmark functions vividly show that premature convergence problem has been mitigated efficiently. Actually, chaotic-based BSO significantly outperforms conventional BSO, cuckoo search optimisation (CSO), big bang-big crunch algorithm (BBBC), gravitational search algorithm (GSA) and genetic algorithm (GA).     

A two level prediction algorithm for non-linear systems

In this note the recent algorithm of Hassan and Singh is modified to provide a more powerful approach to the hierarchical optimisation of non-linear systems with quadratic performance indices. The new approach does not use the quadratic penalty terms in the cost function. This allows convergence over a longer time horizon and numerical studies on the synchronous machine example of Hassan and Singh show that the modified algorithm also provides faster convergence.     

Dwell time-based stabilisation of switched delay systems using free-weighting matrices

In this paper, we present a quasi-convex optimisation method to minimise an upper bound of the dwell time for stability of switched delay systems. Piecewise Lyapunov–Krasovskii functionals are introduced and the upper bound for the derivative of Lyapunov functionals is estimated by free-weighting matrices method to investigate non-switching stability of each candidate subsystems. Then, a sufficient condition for the dwell time is derived to guarantee the asymptotic stability of the switched delay system. Once these conditions are represented by a set of linear matrix inequalities , dwell time optimisation problem can be formulated as a standard quasi-convex optimisation problem. Numerical examples are given to illustrate the improvements over previously obtained dwell time bounds. Using the results obtained in the stability case, we present a nonlinear minimisation algorithm to synthesise the dwell time minimiser controllers. The algorithm solves the problem with successive linearisation of nonlinear conditions.     

Distributed optimisation problem with communication delay and external disturbance

This paper investigates the distributed optimisation problem for the multi-agent systems (MASs) with the simultaneous presence of external disturbance and the communication delay. To solve this problem, a two-step design scheme is introduced. In the first step, based on the internal model principle, the internal model term is constructed to compensate the disturbance asymptotically. In the second step, a distributed optimisation algorithm is designed to solve the distributed optimisation problem based on the MASs with the simultaneous presence of disturbance and communication delay. Moreover, in the proposed algorithm, each agent interacts with its neighbours through the connected topology and the delay occurs during the information exchange. By utilising Lyapunov–Krasovskii functional, the delay-dependent conditions are derived for both slowly and fast time-varying delay, respectively, to ensure the convergence of the algorithm to the optimal solution of the optimisation problem. Several numerical simulation examples are provided to illustrate the effectiveness of the theoretical results.     

On an algorithm for combined system optimisation and parameter estimation

The paper is concerned with the determination of optimum steady-state operation of industrial plant where the optimisation is performed using a mathematical model with parameters whose values are estimated by comparing model and real plant measurements. The two associated problems of system optimisation and model parameter estimation are discussed and an algorithm is examined whose purpose is to accomplish the correct steady-state optimum operating condition on the real plant in spite of inaccuracies in the structure of the mathematical model. The aim of the paper is to investigate the performance of the algorithm which is accomplished through a theoretical analysis of its application to a linear process, where the optimisation is performed using a quadratic performance index and a mathematical model of incorrect structure. Particular emphasis is given to the stability and convergence properties of the algorithm and to the effect of real process measurement errors. Simulation results are also presented illustrating the effectiveness of the technique when applied to nonlinear optimisation problems including a study concerned with determining optimum controller set points to maximise the net rate of return from a chemical reactor plant.     

用于求解对称旅行商问题的粒子群算法和蚂蚁算法的融合

近年来,基于仿生学的随机优化技术成为学术界研究的重点问题之一,并在许多领域得到应用。粒子群优化（PSO）算法和蚂蚁算法ACO（Ant Colong Optimization）是随机全局优化的两个重要方法。PSO算法初始收敛速度较快,但在接近最优解时,收敛速度较慢,而ACO正好相反。结合二者的优势,先利用粒子群算法,再结合蚂蚁算法,以对称旅行商问题为例进行了仿真实现。实验结果表明,先利用PSO算法进行初步求解,在利用蚂蚁算法进行精细求解,可以得到较好的效果。     

A new effective operator for the hybrid algorithm for solving global optimisation problems

Hybrid algorithms have been recently used to solve complex single-objective optimisation problems. The ultimate goal is to find an optimised global solution by using these algorithms. Based on the existing algorithms (HP_CRO, PSO, RCCRO), this study proposes a new hybrid algorithm called MPC (Mean-PSO-CRO), which utilises a new Mean-Search Operator. By employing this new operator, the proposed algorithm improves the search ability on areas of the solution space that the other operators of previous algorithms do not explore. Specifically, the Mean-Search Operator helps find the better solutions in comparison with other algorithms. Moreover, the authors have proposed two parameters for balancing local and global search and between various types of local search, as well. In addition, three versions of this operator, which use different constraints, are introduced. The experimental results on 23 benchmark functions, which are used in previous works, show that our framework can find better optimal or close-to-optimal solutions with faster convergence speed for most of the benchmark functions, especially the high-dimensional functions. Thus, the proposed algorithm is more effective in solving single-objective optimisation problems than the other existing algorithms.     

Distributed convex optimisation with event-triggered communication in networked systems

This paper studies the distributed convex optimisation problem over directed networks. Motivated by practical considerations, we propose a novel distributed zero-gradient-sum optimisation algorithm with event-triggered communication. Therefore, communication and control updates just occur at discrete instants when some predefined condition satisfies. Thus, compared with the time-driven distributed optimisation algorithms, the proposed algorithm has the advantages of less energy consumption and less communication cost. Based on Lyapunov approaches, we show that the proposed algorithm makes the system states asymptotically converge to the solution of the problem exponentially fast and the Zeno behaviour is excluded. Finally, simulation example is given to illustrate the effectiveness of the proposed algorithm.     

Enhanced leader PSO (ELPSO): A new PSO variant for solving global optimisation problems

Particle swarm optimisation (PSO) is a well-established optimisation algorithm inspired from flocking behaviour of birds. The big problem in PSO is that it suffers from premature convergence, that is, in complex optimisation problems, it may easily get trapped in local optima. In this paper, a new PSO variant, named as enhanced leader PSO (ELPSO), is proposed for mitigating premature convergence problem. ELPSO is mainly based on a five-staged successive mutation strategy which is applied to swarm leader at each iteration. The experimental results confirm that in all terms of accuracy, scalability and convergence rate, ELPSO performs well.     

Cam shape optimisation by genetic algorithm

This article overviews a genetic algorithm based computer-aided approach for preliminary design and shape optimisation of cam profiles for cam operated mechanisms. The primary objective of the work was to create a complete systematic approach for preliminary cam shape design including cam shape design automation and true cam shape optimisation with respect to the simulated computer models of cam mechanisms. Typically, shape optimisation of a cam cross-section is a multiobjective optimisation problem of two-dimensional geometric shape in a heavily constrained environment. In order to illustrate the genetic algorithm based cam shape optimisation approach, a cam shape design example is described, in which a cam shape designed by genetic algorithm is compared with its more conventionally designed counterpart.     

Dynamic Ant Colony Optimisation

Ant Colony optimisation has proved suitable to solve static optimisation problems, that is problems that do not change with time. However in the real world changing circumstances may mean that a previously optimum solution becomes suboptimal. This paper explores the ability of the ant colony optimisation algorithm to adapt from the optimum solution for one set of circumstances to the optimal solution for another set of circumstances. Results are given for a preliminary investigation based on the classical travelling salesman problem. It is concluded that, for this problem at least, the time taken for the solution adaption process is far shorter than the time taken to find the second optimum solution if the whole process is started over from scratch.     

A memetic particle swarm optimisation algorithm for dynamic multi-modal optimisation problems

Many real-world optimisation problems are both dynamic and multi-modal, which require an optimisation algorithm not only to find as many optima under a specific environment as possible, but also to track their moving trajectory over dynamic environments. To address this requirement, this article investigates a memetic computing approach based on particle swarm optimisation for dynamic multi-modal optimisation problems (DMMOPs). Within the framework of the proposed algorithm, a new speciation method is employed to locate and track multiple peaks and an adaptive local search method is also hybridised to accelerate the exploitation of species generated by the speciation method. In addition, a memory-based re-initialisation scheme is introduced into the proposed algorithm in order to further enhance its performance in dynamic multi-modal environments. Based on the moving peaks benchmark problems, experiments are carried out to investigate the performance of the proposed algorithm in comparison with several state-of-the-art algorithms taken from the literature. The experimental results show the efficiency of the proposed algorithm for DMMOPs.     

An improved particle swarm optimiser based on swarm success rate for global optimisation problems

Inertia weight is one of the control parameters that influences the performance of particle swarm optimisation (PSO) in the course of solving global optimisation problems, by striking a balance between exploration and exploitation. Among many inertia weight strategies that have been proposed in literature are chaotic descending inertia weight (CDIW) and chaotic random inertia weight (CRIW). These two strategies have been claimed to perform better than linear descending inertia weight (LDIW) and random inertia weight (RIW). Despite these successes, a closer look at their results reveals that the common problem of premature convergence associated with PSO algorithm still lingers. Motivated by the better performances of CDIW and CRIW, this paper proposed two new inertia weight strategies namely: swarm success rate descending inertia weight (SSRDIW) and swarm success rate random inertia weight (SSRRIW). These two strategies use swarm success rates as a feedback parameter. Efforts were made using the proposed inertia weight strategies with PSO to further improve the effectiveness of the algorithm in terms of convergence speed, global search ability and improved solution accuracy. The proposed PSO variants, SSRDIW_PSO and SSRRIW_PSO were validated using several benchmark unconstrained global optimisation test problems and their performances compared with LDIW-PSO, CDIW-PSO, RIW-PSO, CRIW-PSO and some other existing PSO variants. Empirical results showed that the proposed variants are more efficient.