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.     

Accelerated parallel texture optimization

Texture optimization is a texture synthesis method that can efficiently reproduce various features of exemplar textures. However, its slow synthesis speed limits its usage in many interactive or real time applications. In this paper, we propose a parallel texture optimization algorithm to run on GPUs. In our algorithm, k-coherence search and principle component analysis （PCA） are used for hardware acceleration, and two acceleration techniques are further developed to speed up our GPU-based texture optimization. With a reasonable precomputation cost, the online synthesis speed of our algorithm is 4000＋ times faster than that of the original texture optimization algorithm and thus our algorithm is capable of interactive applications. The advantages of the new scheme are demonstrated by applying it to interactive editing of flow-guided synthesis.     

Parameter optimization of modern machining processes using teaching–learning-based optimization algorithm

Modern machining processes are now-a-days widely used by manufacturing industries in order to produce high quality precise and very complex products. These modern machining processes involve large number of input parameters which may affect the cost and quality of the products. Selection of optimum machining parameters in such processes is very important to satisfy all the conflicting objectives of the process. In this research work, a newly developed advanced algorithm named ‘teaching–learning-based optimization (TLBO) algorithm’ is applied for the process parameter optimization of selected modern machining processes. This algorithm is inspired by the teaching–learning process and it works on the effect of influence of a teacher on the output of learners in a class. The important modern machining processes identified for the process parameters optimization in this work are ultrasonic machining (USM), abrasive jet machining (AJM), and wire electrical discharge machining (WEDM) process. The examples considered for these processes were attempted previously by various researchers using different optimization techniques such as genetic algorithm (GA), simulated annealing (SA), artificial bee colony algorithm (ABC), particle swarm optimization (PSO), harmony search (HS), shuffled frog leaping (SFL) etc. However, comparison between the results obtained by the proposed algorithm and those obtained by different optimization algorithms shows the better performance of the proposed algorithm.     

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).     

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 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.     

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.     

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.     

Topology optimization of neural networks based on a coupled genetic algorithm and particle swarm optimization techniques (c-GA–PSO-NN)

In this short paper, a coupled genetic algorithm and particle swarm optimization technique was used to supervise neural networks where the applied operators and connections of layers were tracked by genetic algorithm and numeric values of biases and weights of layers were examined by particle swarm optimization to modify the optimal network topology. The method was applied for a previously studied case, and results were analyzed. The convergence to the optimal topology was highly fast and efficient, and the obtained weights and biases revealed great reliability in reproduction of data. The optimal topology of neural networks was obtained only after seven iterations, and an average square of the correlation (R ²) of 0.9989 was obtained for the studied cases. The proposed method can be used for fast and reliable topology optimization of neural networks.

     

Distributed regularized online optimization using forward–backward splitting

This paper considers the problem of distributed online regularized optimization over a network that consists of multiple interacting nodes. Each node is endowed with a sequence of loss functions that are time-varying and a regularization function that is fixed over time. A distributed forward–backward splitting algorithm is proposed for solving this problem and both fixed and adaptive learning rates are adopted. For both cases, we show that the regret upper bounds scale as O( √T ), where T is the time horizon. In particular, those rates match the centralized counterpart. Finally, we show the effectiveness of the proposed algorithms over an online distributed regularized linear regression problem.