Centroid-based memetic algorithm – adaptive Lamarckian and Baldwinian learning

The application of specific learning schemes in memetic algorithms (MAs) can have significant impact on their performances. One main issue revolves around two different learning schemes, specifically, Lamarckian and Baldwinian. It has been shown that the two learning schemes are better suited for different types of problems and some previous studies have attempted to combine both learning schemes as a means to develop a single optimisation framework capable of solving more classes of problems. However, most of the past approaches are often implemented heuristically and have not investigated the effect of different learning scheme on noisy design optimisation. In this article, we introduce a simple probabilistic approach to address this issue. In particular, we investigate a centroid-based approach that combines the two learning schemes within an MA framework (centroid-based MS; CBMA) through the effective allocation of resources (in terms of local search cost) that are based on information obtained during the optimisation process itself. A scheme that applies the right learning scheme (Lamarckian or Baldwinian) at the right time (during search) would lead to higher search performance. We conducted an empirical study to test this hypothesis using two different types of benchmark problems. The first problem set consists of simple benchmark problems whereby the problem landscape is static and gradient information can be obtained accurately. These problems are known to favour Lamarckian learning while Baldwinian learning is known to exhibit slower convergence. The second problem set consists of noisy versions of the first problem set whereby the problem landscape is dynamic as a result of the random noise perturbation injected into the design vector. These problems are known to favour learning processes that re-sample search points such as Baldwinian learning. Our experiments show that CBMA manages to adaptively allocate resources productively according to problem in most of the cases.     

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.     

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.     

A robust optimisation framework in composite generation and transmission expansion planning considering inherent uncertainties

Abstract

This paper presents a robust optimisation framework for long-term composite generation and transmission expansion planning problem which considers inherent uncertainties such as load growth, fuel cost and renewable energy output uncertainties. In this paper, a bi-level robust optimisation framework is proposed to accommodate wind output uncertainty in line with the uncertain demanded loads and uncertain fuel cost. The addressed optimisation problem is modelled as a mixed-integer optimisation framework with the objective of providing a robust expansion plan while maintaining the minimum cost expansion. In order to evaluate the robustness of each plan, an off-line Lattice Monte Carlo simulation technique is adopted in this study. The validity of the proposed method is examined on a simple six-bus and modified IEEE 118-bus test system as a large-scale case study. The simulation results show that the presented method is both satisfactory and consistent with expectation.     

Valve stiction estimation using global optimisation

Valve stiction is the most frequent cause of loop oscillations. Thus, detecting and quantifying this valve problem is essential to ensuring plant profitability. In this work, a novel one-stage procedure to estimate stiction parameters is proposed using a two-parameter stiction model. The optimisation problem is computed using a global optimisation algorithm. These two propositions make the stiction computation more efficient and computationally faster than the currently available method. The applicability of the proposed approach is illustrated using a large number of simulated and industrial valves. Moreover, to isolate the impact of each proposition, the novel method is compared with the currently available technique, which is based on a two-stage scheme. The results show that the global optimisation algorithm is more efficient than the direct search and genetic algorithms, as previously proposed by Jelali (2008). The two-stage procedure provides a better estimate of the apparent stiction, whereas the one-stage procedure provides a better slipjump value.     

Global optimisation in neural network training

This paper presents a new neural network training scheme for pattern recognition applications. Our training technique is a hybrid scheme which involves, firstly, the use of the efficient BFGS optimisation method for locating minima of the total error function and, secondly, the use of genetic algorithms for finding a global minimum. This paper also describes experiments that compare the performance of our scheme with three other hybrid schemes of this kind when applied to challenging pattern recognition problems. Experiments have shown that our scheme gives better results than others.     

Toolbox for super-structured and super-structure free multi-disciplinary building spatial design optimisation

Multi-disciplinary optimisation of building spatial designs is characterised by large solution spaces. Here two approaches are introduced, one being super-structured and the other super-structure free. Both are different in nature and perform differently for large solution spaces and each requires its own representation of a building spatial design, which are also presented here. A method to combine the two approaches is proposed, because the two are prospected to supplement each other. Accordingly a toolbox is presented, which can evaluate the structural and thermal performances of a building spatial design to provide a user with the means to define optimisation procedures. A demonstration of the toolbox is given where the toolbox has been used for an elementary implementation of a simulation of co-evolutionary design processes. The optimisation approaches and the toolbox that are presented in this paper will be used in future efforts for research into- and development of optimisation methods for multi-disciplinary building spatial design optimisation.     

A centre–free approach for resource allocation with lower bounds

Since complexity and scale of systems are continuously increasing, there is a growing interest in developing distributed algorithms that are capable to address information constraints, specially for solving optimisation and decision-making problems. In this paper, we propose a novel method to solve distributed resource allocation problems that include lower bound constraints. The optimisation process is carried out by a set of agents that use a communication network to coordinate their decisions. Convergence and optimality of the method are guaranteed under some mild assumptions related to the convexity of the problem and the connectivity of the underlying graph. Finally, we compare our approach with other techniques reported in the literature, and we present some engineering applications.     

Discussion on some convergence problems in buckling optimisation

This note reports and briefly discusses some of the numerous reasons for bad convergence in linear buckling optimisation. Above all, it highlights that erratic convergence history can be avoided when the design optimisation problem includes enough buckling modes (and not only the first ones as it is the usual case), which keep the whole structure sensitive to the design restriction. This strategy is illustrated with an example and shows that possible significant improvement in the convergence speed can also be achieved by simply considering a large number of buckling modes in the optimisation problem. The selection of a suitable approximation scheme is also discussed.     

The piecewise optimisation method for approximating uncertain optimal control problems under optimistic value criterion

In this paper, we introduce an approximate model and propose a piecewise optimisation method to simplify the expression of optimal control for an uncertain linear quadratic optimal control problem. First, we consider an optimal control problem of uncertain linear quadratic model under optimistic value criterion. Based on the equation of optimality, we deduce an analytic expression of optimal control. Then, we study an approximate model with control parameter and propose a piecewise optimisation method for solving the optimal parameter of such an approximate model. As an application, a four-wheel steering vehicle optimal control problem is given to show the utility of the proposed approximate model and the efficiency of the proposed piecewise optimisation method.     

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.     

A robust optimisation approach to the problem of supplier selection and allocation in outsourcing

We formulate the supplier selection and allocation problem in outsourcing under an uncertain environment as a stochastic programming problem. Both the decision-maker's attitude towards risk and the penalty parameters for demand deviation are considered in the objective function. A service level agreement, upper bound for each selected supplier's allocation and the number of selected suppliers are considered as constraints. A novel robust optimisation approach is employed to solve this problem under different economic situations. Illustrative examples are presented with managerial implications highlighted to support decision-making.     

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.     

Distributed model predictive control with hierarchical architecture for communication: application in automated irrigation channels

This paper is concerned with a distributed model predictive control (DMPC) method that is based on a distributed optimisation method with two-level architecture for communication. Feasibility (constraints satisfaction by the approximated solution), convergence and optimality of this distributed optimisation method are mathematically proved. For an automated irrigation channel, the satisfactory performance of the proposed DMPC method in attenuation of the undesired upstream transient error propagation and amplification phenomenon is illustrated and compared with the performance of another DMPC method that exploits a single-level architecture for communication. It is illustrated that the DMPC that exploits a two-level architecture for communication has a better performance by better managing communication overhead.     

An integrated and dynamic optimisation model for the multi-level emergency logistics network in anti-bioterrorism system

Demand for emergency resources is usually uncertain and varies quickly in anti-bioterrorism system. Besides, emergency resources which had been allocated to the epidemic areas in the early rescue cycle will affect the demand later. In this article, an integrated and dynamic optimisation model with time-varying demand based on the epidemic diffusion rule is constructed. The heuristic algorithm coupled with the MATLAB mathematical programming solver is adopted to solve the optimisation model. In what follows, the application of the optimisation model as well as a short sensitivity analysis of the key parameters in the time-varying demand forecast model is presented. The results show that both the model and the solution algorithm are useful in practice, and both objectives of inventory level and emergency rescue cost can be controlled effectively. Thus, it can provide some guidelines for decision makers when coping with emergency rescue problem with uncertain demand, and offers an excellent reference when issues pertain to bioterrorism.     

An optimisation-oriented model of distributed supply-chain

In this paper, a suitable model of distributed supply-chains (DSCs) is presented with the aim of providing a tool for DSC decentralised optimisation. To cope with this challenge, in the first part of the paper, a general model for distributed supply-chain including suppliers, processing units, assemblers, and transportation systems is presented with the aim of keeping the framework as general as possible. In the second part of the paper, an optimisation algorithm is also discussed.     

A robust scheduling method based on a multi-objective immune algorithm

A robust scheduling method is proposed to solve uncertain scheduling problems. An uncertain scheduling problem is modeled by a set of workflow models, and then a scheduling scheme (solution) of the problem can be evaluated by workflow simulations executed with the workflow models in the set. A multi-objective immune algorithm is presented to find Pareto optimal robust scheduling schemes that have good performance for each model in the set. The two optimization objectives for scheduling schemes are the indices of the optimality and robustness of the scheduling results. An antibody represents a resource allocation scheme, and the methods of antibody coding and decoding are designed to deal with resource conflicts during workflow simulations. Experimental tests show that the proposed method can generate a robust scheduling scheme that is insensitive to uncertain scheduling environments.     

Distributed primal-dual optimisation method with uncoordinated time-varying step-sizes

This paper is concerned with the distributed optimisation problem over a multi-agent network, where the objective function is described by a sum of all the local objectives of agents. The target of agents is to collectively reach an optimal solution while minimising the global objective function. Under the assumption that the information exchange among agents is depicted by a sequence of time-varying undirected graphs, a distributed optimisation algorithm with uncoordinated time-varying step-sizes is presented, which signifies that the step-sizes of agents are not always uniform per iteration. In light of some reasonable assumptions, this paper fully conducts an explicit analysis for the convergence rate of the optimisation method. A striking feature is that the algorithm has a geometric convergence rate even if the step-sizes are time-varying and uncoordinated. Simulation results on two numerical experiments in power systems show effectiveness and performance of the proposed algorithm.     

Bridge topology optimisation with stress, displacement and frequency constraints

The principal stress based evolutionary structural optimisation method is presented herein for topology optimisation of arch, tied arch, cable-stayed and suspension bridges with both stress and displacement constraints. Two performance index formulas are developed to determine the efficiency of the topology design. A refined mesh scheme is proposed to improve the details of the final topology without resorting to the complete analysis of a finer mesh. Furthermore, cable-supported bridges are optimised with frequency constraint incorporating the “nibbling” technique. The applicability, simplicity and effectiveness of the method are demonstrated through the topology optimisation of the four types of bridges.