Fuzzy adaptive teaching–learning-based optimization for global numerical optimization

Teaching–learning-based optimization (TLBO) is one of the latest metaheuristic algorithms being used to solve global optimization problems over continuous search space. Researchers have proposed few variants of TLBO to improve the performance of the basic TLBO algorithm. This paper presents a new variant of TLBO called fuzzy adaptive teaching–learning-based optimization (FATLBO) for numerical global optimization. We propose three new modifications to the basic scheme of TLBO in order to improve its searching capability. These modifications consist, namely of a status monitor, fuzzy adaptive teaching–learning strategies, and a remedial operator. The performance of FATLBO is investigated on four experimental sets comprising complex benchmark functions in various dimensions and compared with well-known optimization methods. Based on the results, we conclude that FATLBO is able to deliver excellence and competitive performance for global optimization.

     

A tutorial on event-based optimization—a new optimization framework

In many practical systems, the control or decision making is triggered by certain events. The performance optimization of such systems is generally different from the traditional optimization approaches, such as Markov decision processes or dynamic programming. The goal of this tutorial is to introduce, in an intuitive manner, a new optimization framework called event-based optimization. This framework has a wide applicability to aforementioned systems. With performance potential as building blocks, we develop two intuitive optimization algorithms to solve the event-based optimization problem. The optimization algorithms are proposed based on an intuitive principle, and theoretical justifications are given with a performance sensitivity based approach. Finally, we provide a few practical examples to demonstrate the effectiveness of the event-based optimization framework. We hope this framework may provide a new perspective to the optimization of the performance of event-triggered dynamic systems.     

An orthogonal opposition-based-learning Yin–Yang-pair optimization algorithm for engineering optimization

Yin–Yang-pair Optimization (YYPO) is a recently developed philosophy-inspired meta-heuristic algorithm, which works with two main points for exploitation and exploration, respectively, and then generates more points via splitting to search the global optimum. However, it suffers from low quality of candidate solutions in its exploration process owing to the lack of elitism. Inspired by this, a new modified algorithm named orthogonal opposition-based-learning Yin–Yang-pair Optimization (OOYO) is proposed to enhance the performance of YYPO. First, the OOYO retains the normalization operation in YYPO and starts with a single point to exploit. A set of opposite points is designed by a method of opposition-based learning with split points generated from the current optimum for exploration. Then, the points, i.e., candidate solutions, are constructed by the randomly selected split point and opposite points through the idea of orthogonal experiment design to make full use of information from the space. The proposed OOYO does not add additional time complexity and eliminates a user-defined parameter in YYPO, which facilitates parameter adjustment. The novel orthogonal opposition-based learning strategy can provide inspirations for the improvement of other optimization algorithms. Extensive test functions containing a classic test suite of 23 standard benchmark functions and 2 test suites of Swarm Intelligence Symposium 2005 and Congress on Evolutionary Computation 2020 from Institute of Electrical and Electronics Engineers are employed to evaluate the proposed algorithm. Non-parametric statistical results demonstrate that OOYO outperforms YYPO and furnishes strong competitiveness compared with other state-of-the-art algorithms. In addition, we apply OOYO to solve four well-known constrained engineering problems and a practical problem of parameters optimization in a rainstorm intensity model.

     

FRPSO: Fletcher–Reeves based particle swarm optimization for multimodal function optimization

Particle swarm optimization (PSO) is a population-based optimization tool that is inspired by the collective intelligent behavior of birds seeking food. It can be easily implemented and applied to solve various function optimization problems. However, relatively few researchers have explored the potential of PSO for multimodal problems. Although PSO is a simple, easily implemented, and powerful technique, it has a tendency to get trapped in a local optimum. This premature convergence makes it difficult to find global optimum solutions for multimodal problems. A hybrid Fletcher–Reeves based PSO (FRPSO) method is proposed in this paper. It is based on the idea of increasing exploitation of the local optimum, while maintaining a good exploration capability for finding better solutions. In FRPSO, standard PSO is used to update the particle’s current position, which is then further refined by the Fletcher–Reeves conjugate gradient method. This enhances the performance of standard PSO. The results of experiments conducted on seventeen benchmark test functions demonstrate that the proposed method shows superior performance on a set of multimodal functions when compared with standard PSO, a genetic algorithm (GA) and fitness distance ratio PSO (FDRPSO).     

Multi-objective optimization of machining and micro-machining processes using non-dominated sorting teaching–learning-based optimization algorithm

Selection of optimum machining parameters is vital to the machining processes in order to ensure the quality of the product, reduce the machining cost, increasing the productivity and conserve resources for sustainability. Hence, in this work a posteriori multi-objective optimization algorithm named as Non-dominated Sorting Teaching–Learning-Based Optimization (NSTLBO) is applied to solve the multi-objective optimization problems of three machining processes namely, turning, wire-electric-discharge machining and laser cutting process and two micro-machining processes namely, focused ion beam micro-milling and micro wire-electric-discharge machining. The NSTLBO algorithm is incorporated with non-dominated sorting approach and crowding distance computation mechanism to maintain a diverse set of solutions in order to provide a Pareto-optimal set of solutions in a single simulation run. The results of the NSTLBO algorithm are compared with the results obtained using GA, NSGA-II, PSO, iterative search method and MOTLBO and are found to be competitive. The Pareto-optimal set of solutions for each optimization problem is obtained and reported. These Pareto-optimal set of solutions will help the decision maker in volatile scenarios and are useful for real production systems.     

Recent advances on distributed online optimization

Online optimization has received numerous attention in recent two decades, mostly inspired by its potential applications to auctions, smart grids, portfolio management, dictionary learning, neural networks, and so on. Generally, online optimization is a sequence of decision making processes, where a sequence of time-varying loss functions are gradually revealed in a dynamic environment which may be adversarial. At each time instant, the loss function information at current time is revealed to the decision maker only after her/his decision is made. The objective of online optimization is to choose the best decision at each time step as far as possible, but unfortunately, this goal is generally diffcult or impossible to achieve. As such, to measure the performance for an algorithm, two metrics are usually exploited, i.e., regret and competitive ratio, for which the former one is leveraged more frequently in the literature. Moreover, two kinds of regrets, i.e., static and dynamic regrets, are usually considered by researchers, where the static regret is to compare the performance with a cumulative loss with respect to the same best decision through all the time horizons, while the dynamic regret is with respect to the best decision at each time instant. More recently, another regret, called adaptive regret , has been proposed and investigated as a suitable metric for changing environments, as dynamic regret does. Historically, centralized online optimization is first addressed, that is, there is a centralized decision maker who can access all the information on the revealed loss function at each time. Along this line, a wide range of results have thus far been reported in the literature. For example, online optimization was studied subject to feasible set constraints, where it has been shown that the optimal bound is O( √ T) for static regret....     

Multi-objective optimization of two stage thermoelectric cooler using a modified teaching–learning-based optimization algorithm

Teaching–learning-based optimization (TLBO) is a recently developed heuristic algorithm based on the natural phenomenon of teaching–learning process. In the present work, a modified version of the TLBO algorithm is introduced and applied for the multi-objective optimization of a two stage thermoelectric cooler (TEC). Two different arrangements of the thermoelectric cooler are considered for the optimization. Maximization of cooling capacity and coefficient of performance of the thermoelectric cooler are considered as the objective functions. An example is presented to demonstrate the effectiveness and accuracy of the proposed algorithm. The results of optimization obtained by using the modified TLBO are validated by comparing with those obtained by using the basic TLBO, genetic algorithm (GA), particle swarm optimization (PSO) and artificial bee colony (ABC) algorithms.     

Cross-layer optimization in ultra wideband networks

Ultra wideband (UWB) network brings both chance and challenge to personal area wireless communications. Compared with other IEEE 802 small range wireless protocols (such as WLAN and Bluetooth), UWB has both extremely high bandwidth (up to 480 Mbps) and low radiation. Moreover, the structured MAC layer of UWB is the fundamental difference to WLAN. The top one is that only when two UWB de-vices belong to the same piconet can they communicate with each other directly, which means that we must jointly consider topology formation and routing when deploying UWB networks because the interaction between routing and topology formation makes separate optimization ineffective. This paper tries to optimize UWB network from a cross-layer point of view. Specifically, given device spatial distribution and traffic requirement, we want to form piconets and determine rout-ing jointly, to maximize the overall throughput. We formulate the problem of joint optimization to mixed-integer programming and give a practical lower bound that is very close to the theoretical upper bound in our simulation. Furthermore, our lower bound is much better than an algorithm that only considers topology formation in UWB networks.     

Structural shape optimization—A survey

This paper is a survey of structural shape optimization with an emphasis on techniques dealing with shape optimization of the boundaries of two- and three-dimensional bodies. Attention is focused on the special problems of structural shape optimization which are due to a finite element model which must change during the optimization process. These problems include the requirement for sophisticated automated mesh generation techniques and careful choice of design variables. They also include special problems in obtaining sufficiently accurate sensitivity derivatives.     

ε-relaxed approach in structural topology optimization

This paper presents a so-called -relaxed approach for structural topology optimization problems of discrete structures. The distinctive feature of this new approach is that unlike the typical treatment of topology optimization problems based on the ground structure approach, we eliminate the singular optima from the problem formulation and thus unify the sizing and topology optimization within the same framework. As a result, numerical methods developed for sizing optimization problems can be applied directly to the solution of topology optimization problems without any further treatment. The application of the proposed approach and its effectiveness are illustrated with several numerical examples.     

A Lyapunov characterization of robust policy optimization

In this paper, we study the robustness property of policy optimization (particularly Gauss–Newton gradient descent algorithm which is equivalent to the policy iteration in reinforcement learning) subject to noise at each iteration. By invoking the concept of input-to-state stability and utilizing Lyapunov’s direct method, it is shown that, if the noise is sufficiently small, the policy iteration algorithm converges to a small neighborhood of the optimal solution even in the presence of noise at each iteration. Explicit expressions of the upperbound on the noise and the size of the neighborhood to which the policies ultimately converge are provided. Based onWillems’ fundamental lemma, a learning-based policy iteration algorithm is proposed. The persistent excitation condition can be readily guaranteed by checking the rank of the Hankel matrix related to an exploration signal. The robustness of the learning-based policy iteration to measurement noise and unknown system disturbances is theoretically demonstrated by the input-to-state stability of the policy iteration. Several numerical simulations are conducted to demonstrate the efficacy of the proposed method.     

An optimization problem in distributed parameter systems†

The optimal control problem for a furnace heating a one-dimensional slab with a quadratic performance index is analysed. This system is a typical distributed parameter system. The Hamiltonian is defined and the canonical equations are obtained. A Riccati type matrix partial differential equation is obtained from the canonical equations. An approximate method to solve these equations is derived and an example is presented to illustrate this method.     

Implementable L ∞ penalty-function method for semi-infinite optimization

This paper considers general non-linear semi-infinite programming problems and presents an implementable method which employs an exact L _∞ penalty function. Since the L _∞ penalty function is continuous even if the number of representative constraints changes, trust-region techniques may effectively be adopted to obtain global convergence. Numerical results are given to show the efficiency of the proposed algorithm.     

Topology optimization using a reaction–diffusion equation

This paper presents a structural topology optimization method based on a reaction–diffusion equation. In our approach, the design sensitivity for the topology optimization is directly employed as the reaction term of the reaction–diffusion equation. The distribution of material properties in the design domain is interpolated as the density field which is the solution of the reaction–diffusion equation, so free generation of new holes is allowed without the use of the topological gradient method. Our proposed method is intuitive and its implementation is simple compared with optimization methods using the level set method or phase field model. The evolution of the density field is based on the implicit finite element method. As numerical examples, compliance minimization problems of cantilever beams and force maximization problems of magnetic actuators are presented to demonstrate the method’s effectiveness and utility.     

Parametric appraisal and optimization in machining of CFRP composites by using TLBO (teaching–learning based optimization algorithm)

The present paper focuses on machining (turning) aspects of CFRP (epoxy) composites by using single point HSS cutting tool. The optimal setting i.e. the most favourable combination of process parameters (such as spindle speed, feed rate, depth of cut and fibre orientation angle) has been derived in view of multiple and conflicting requirements of machining performance yields viz. material removal rate, surface roughness, SR \((\hbox {R}_{\mathrm{a}})\) (of the turned product) and cutting force. This study initially derives mathematical models (objective functions) by using statistics of nonlinear regression for correlating various process parameters with respect to the output responses. In the next phase, the study utilizes a recently developed advanced optimization algorithm teaching–learning based optimization (TLBO) in order to determine the optimal machining condition for achieving satisfactory machining performances. Application potential of TLBO algorithm has been compared to that of genetic algorithm (GA). It has been observed that exploration of TLBO appears more fruitful in contrast to GA in the context of this case experimental research focused on machining of CFRP composites.     

Free vibration analysis and shape optimization of variable thickness plates and shells—II. Sensitivity analysis and shape optimization

In this paper an automated approach is used to carry out sensitivity analysis and to obtain optimum shapes for plates and shells in which the natural frequencies are maximized. The free vibration analysis is carried out with the nine-noded, degenerated, Huang-Hinton shell element implemented and tested in Part I of this paper. Design variables that specify either the shape or thickness distribution of the structures are considered. Special attention is focused on the sensitivity calculations and problems connected with their accuracy and performance are highlighted when the semi-analytical and finite difference methods are used. Advantages and disadvantages of each method are discussed. The optimal solution is found by the use of a structural optimization algorithm which integrates the finite element module (Part I), sensitivity analysis and a mathematical programming method: sequential quadratic programming (SQP). Optimal forms are then obtained for a set of benchmark examples using the two sensitivity analysis techniques and their results are compared. The results obtained for optimum solutions in the present paper justify the usage of the semi-analytical method for sensitivities calculations for structural shape optimization purposes.     

An algebraic Riccati equation approach to H∞ optimization

This paper considers the general (so-called four block) H^∞ optimal control problem with the assumption that system states are available for feedback. It is shown that infimization of the H^∞ norm of the closed loop transfer function over all linear constant, i.e., nondynamic, stabilizing state feedback laws can be completely characterized via an algebraic Riccati equation. It is further shown that the optimal norm is not improved by allowing feedback to be dynamic. Thus, the general state-feedback H^∞ optimal control problem can be solved by iteratively solving one ARE and the controller can be chosen to be static gain.