CHAOTIC ANNEALING NEURAL NETWORK FOR GLOBAL OPTIMIZATION OF CONSTRAINED NONLINEAR PROGRAMMING

Chaotic neural networks have global searching ability.But their applications are generally confined to combinatorial optimization to date.By introducing chaotic noise annealing process into conventional Hopfield network,this paper proposes a new chaotic annealing neural network (CANN) for global optimization of continuous constrained non linear programming.It is easy to implement,conceptually simple,and generally applicable.Numerical experiments on severe test functions manifest that CANN is efficient and reliable to search for global optimum and outperforms the existing genetic algorithm GAMAS for the same purpose.

Multi-objective global optimization approach predicted quasi-layered ternary TiOS crystals with promising photocatalytic properties

Titanium dioxide(TiO_(2))has attracted considerable research attentions for its promising applications in solar cells and photocatalytic devices.However,the intrinsic challenge lies in the relatively low energy conversion efficiency of TiO_(2),primarily attributed to the substantial band gaps(exceeding 3.0 eV)associated with its rutile and anatase phases.Leveraging multi-objective global optimization,we have identified two quasi-layered ternary Ti-O-S crystals,composed of titanium,oxygen,and sulfur.The calculations of formation energy,phonon dispersions,and thermal stability confirm the chemical,dynamical and thermal stability of these newly discovered phases.Employing the state-of-art hybrid density functional approach and many-body perturbation theory(quasiparticle GW approach and Bethe-Salpeter equation),we calculate the optical properties of both the TiOS phases.Significantly,both phases show favorable photocatalytic characteristics,featuring band gaps suitable for visible optical absorption and appropriate band alignments with water for effective charge carrier separation.Therefore,ternary compound TiOS holds the potential for achieving high-efficiency photochemical conversion,showing our multi-objective global optimization provides a new approach for novel environmental and energy materials design with multicomponent compounds.

Dark Forest Algorithm:A Novel Metaheuristic Algorithm for Global Optimization Problems

Metaheuristic algorithms,as effective methods for solving optimization problems,have recently attracted considerable attention in science and engineering fields.They are popular and have broad applications owing to their high efficiency and low complexity.These algorithms are generally based on the behaviors observed in nature,physical sciences,or humans.This study proposes a novel metaheuristic algorithm called dark forest algorithm(DFA),which can yield improved optimization results for global optimization problems.In DFA,the population is divided into four groups:highest civilization,advanced civilization,normal civilization,and low civilization.Each civilization has a unique way of iteration.To verify DFA’s capability,the performance of DFA on 35 well-known benchmark functions is compared with that of six other metaheuristic algorithms,including artificial bee colony algorithm,firefly algorithm,grey wolf optimizer,harmony search algorithm,grasshopper optimization algorithm,and whale optimization algorithm.The results show that DFA provides solutions with improved efficiency for problems with low dimensions and outperforms most other algorithms when solving high dimensional problems.DFAis applied to five engineering projects to demonstrate its applicability.The results show that the performance of DFA is competitive to that of current well-known metaheuristic algorithms.Finally,potential upgrading routes for DFA are proposed as possible future developments.

Global Solutions to Nonconvex Problems by Evolution of Hamilton-Jacobi PDEs

Computing tasks may often be posed as optimization problems.The objective functions for real-world scenarios are often nonconvex and/or nondifferentiable.State-of-the-art methods for solving these problems typically only guarantee convergence to local minima.This work presents Hamilton-Jacobi-based Moreau adaptive descent(HJ-MAD),a zero-order algorithm with guaranteed convergence to global minima,assuming continuity of the objective function.The core idea is to compute gradients of the Moreau envelope of the objective(which is"piece-wise convex")with adaptive smoothing parameters.Gradients of the Moreau envelope(i.e.,proximal operators)are approximated via the Hopf-Lax formula for the viscous Hamilton-Jacobi equation.Our numerical examples illustrate global convergence.

Adaptive State-Dependent Diffusion for Derivative-Free Optimization

This paper develops and analyzes a stochastic derivative-free optimization strategy.A key feature is the state-dependent adaptive variance.We prove global convergence in probability with algebraic rate and give the quantitative results in numerical examples.A striking fact is that convergence is achieved without explicit information of the gradient and even without comparing different objective function values as in established methods such as the simplex method and simulated annealing.It can otherwise be compared to annealing with state-dependent temperature.

Application of Evolution Sequential Number Theoretic Optimization in Global Optimization

Synthesis of chemical processes is of non-convex and multi-modal. Deterministic strategies often fail to find global optimum within reasonable time scales. Stochastic methodologies generally approach global solution in probability. In recogniting the state of art status in the discipline, a new approach for global optimization of processes, based on sequential number theoretic optimization (SNTO), is proposed. In this approach, subspaces and feasible points are derived from uniformly scattered points, and iterations over passing the corner of local optimum are enhanced via parallel strategy. The efficiency of the approach proposed is verified by results obtained from various case studies.

A New Hybrid Method for Constrained Global Optimization

By combining properly the simulated annealing algorithm and the nonlinear programming neural network, a new hybrid method for comtrained global optimization is proposed in this paper. To maintain the applicability of the simulated annealing algorithm used in the hybrid method as general as possible, the nonlinear programming neural network is employed at each iteration to find only a feasible solution to the original constrained problem rather than a local optimal solution. Such a feasible solution is obtained by solving an auxiliary optimization problem with a new objective function. The computational results for two numerical examples indicate that the proposed hybrid method for constrained global optimization is not only highly reliable but also much more effcient than the simulated annealing algorithm using the penalty function method to deal with the constraints.

Hybridizing grey wolf optimization with differential evolution for global optimization and test scheduling for 3D stacked SoC

A new meta-heuristic method is proposed to enhance current meta-heuristic methods for global optimization and test scheduling for three-dimensional （3D） stacked system-on-chip （SoC） by hybridizing grey wolf optimization with differential evo- lution （HGWO）. Because basic grey wolf optimization （GWO） is easy to fall into stagnation when it carries out the operation of at- tacking prey, and differential evolution （DE） is integrated into GWO to update the previous best position of grey wolf Alpha, Beta and Delta, in order to force GWO to jump out of the stagnation with DE＇s strong searching ability. The proposed algorithm can accele- rate the convergence speed of GWO and improve its performance. Twenty-three well-known benchmark functions and an NP hard problem of test scheduling for 3D SoC are employed to verify the performance of the proposed algorithm. Experimental results show the superior performance of the proposed algorithm for exploiting the optimum and it has advantages in terms of exploration.

A New Chaotic Parameters Disturbance Annealing Neural Network for Solving Global Optimization Problems

Since there were few chaotic neural networks applicable to the global optimization, in this paper, we propose a new neural network model ? chaotic parameters disturbance annealing (CPDA) network, which is superior to other existing neural networks, genetic algorithms, and simulated annealing algorithms in global optimization. In the present CPDA network, we add some chaotic parameters in the energy function, which make the Hopfield neural network escape from the attraction of a local minimal solution and with the parameter annealing, our model will converge to the global optimal solutions quickly and steadily. The converge ability and other characters are also analyzed in this paper. The benchmark examples show the present CPDA neural network's merits in nonlinear global optimization.

Metamodel-based Global Optimization Using Fuzzy Clustering for Design Space Reduction

High fidelity analysis are utilized in modern engineering design optimization problems which involve expensive black-box models.For computation-intensive engineering design problems,efficient global optimization methods must be developed to relieve the computational burden.A new metamodel-based global optimization method using fuzzy clustering for design space reduction(MGO-FCR) is presented.The uniformly distributed initial sample points are generated by Latin hypercube design to construct the radial basis function metamodel,whose accuracy is improved with increasing number of sample points gradually.Fuzzy c-mean method and Gath-Geva clustering method are applied to divide the design space into several small interesting cluster spaces for low and high dimensional problems respectively.Modeling efficiency and accuracy are directly related to the design space,so unconcerned spaces are eliminated by the proposed reduction principle and two pseudo reduction algorithms.The reduction principle is developed to determine whether the current design space should be reduced and which space is eliminated.The first pseudo reduction algorithm improves the speed of clustering,while the second pseudo reduction algorithm ensures the design space to be reduced.Through several numerical benchmark functions,comparative studies with adaptive response surface method,approximated unimodal region elimination method and mode-pursuing sampling are carried out.The optimization results reveal that this method captures the real global optimum for all the numerical benchmark functions.And the number of function evaluations show that the efficiency of this method is favorable especially for high dimensional problems.Based on this global design optimization method,a design optimization of a lifting surface in high speed flow is carried out and this method saves about 10 h compared with genetic algorithms.This method possesses favorable performance on efficiency,robustness and capability of global convergence and gives a new optimization strategy for engineering design optimization problems involving expensive black box models.

Seeker optimization algorithm:a novel stochastic search algorithm for global numerical optimization

A novel heuristic search algorithm called seeker op- timization algorithm （SOA） is proposed for the real-parameter optimization. The proposed SOA is based on simulating the act of human searching. In the SOA, search direction is based on empir- ical gradients by evaluating the response to the position changes, while step length is based on uncertainty reasoning by using a simple fuzzy rule. The effectiveness of the SOA is evaluated by using a challenging set of typically complex functions in compari- son to differential evolution （DE） and three modified particle swarm optimization （PSO） algorithms. The simulation results show that the performance of the SOA is superior or comparable to that of the other algorithms.

Global Optimization Method Using SLE and Adaptive RBF Based on Fuzzy Clustering

High fidelity analysis models,which are beneficial to improving the design quality,have been more and more widely utilized in the modern engineering design optimization problems.However,the high fidelity analysis models are so computationally expensive that the time required in design optimization is usually unacceptable.In order to improve the efficiency of optimization involving high fidelity analysis models,the optimization efficiency can be upgraded through applying surrogates to approximate the computationally expensive models,which can greately reduce the computation time.An efficient heuristic global optimization method using adaptive radial basis function（RBF） based on fuzzy clustering（ARFC） is proposed.In this method,a novel algorithm of maximin Latin hypercube design using successive local enumeration（SLE） is employed to obtain sample points with good performance in both space-filling and projective uniformity properties,which does a great deal of good to metamodels accuracy.RBF method is adopted for constructing the metamodels,and with the increasing the number of sample points the approximation accuracy of RBF is gradually enhanced.The fuzzy c-means clustering method is applied to identify the reduced attractive regions in the original design space.The numerical benchmark examples are used for validating the performance of ARFC.The results demonstrates that for most application examples the global optima are effectively obtained and comparison with adaptive response surface method（ARSM） proves that the proposed method can intuitively capture promising design regions and can efficiently identify the global or near-global design optimum.This method improves the efficiency and global convergence of the optimization problems,and gives a new optimization strategy for engineering design optimization problems involving computationally expensive models.

A Parameter-Free Filled Function for Unconstrained Global Optimization

The filled function method is an approach for finding a global minimum of multi-dimensional functions. With more and more relevant research, it becomes a promising way used in unconstrained global optimization. Some filled functions with one or two parameters have already been suggested. However, there is no certain criterion to choose a parameter appropriately. In this paper, a parameter-free filled function was proposed. The definition of the original filled function and assumptions of the objective function given by Ge were improved according to the presented parameter-free filled function. The algorithm and numerical results of test functions were reported. Conclusions were drawn in the end. Key words global optimization - filled function method - local minimizer MSC 2000 90C30

A New Subdivision Algorithm for the Bernstein Polynomial Approach to Global Optimization

In this paper, an improved algorithm is proposed for unconstrained global optimization to tackle non-convex nonlinear multivariate polynomial programming problems. The proposed algorithm is based on the Bernstein polynomial approach. Novel features of the proposed algorithm are that it uses a new rule for the selection of the subdivision point, modified rules for the selection of the subdivision direction, and a new acceleration device to avoid some unnecessary subdivisions. The performance of the proposed algorithm is numerically tested on a collection of 16 test problems. The results of the tests show the proposed algorithm to be superior to the existing Bernstein algorithm in terms of the chosen performance metrics.

A composite particle swarm algorithm for global optimization of multimodal functions

During the last decade, many variants of the original particle swarm optimization （PSO） algorithm have been proposed for global numerical optimization, hut they usually face many challenges such as low solution quality and slow convergence speed on multimodal function optimization. A composite particle swarm optimization （CPSO） for solving these difficulties is presented, in which a novel learning strategy plus an assisted search mechanism framework is used. Instead of simple learning strategy of the original PSO, the proposed CPSO combines one particle＇s historical best information and the global best information into one learning exemplar to guide the particle movement. The proposed learning strategy can reserve the original search information and lead to faster convergence speed. The proposed assisted search mechanism is designed to look for the global optimum. Search direction of particles can be greatly changed by this mechanism so that the algorithm has a large chance to escape from local optima. In order to make the assisted search mechanism more efficient and the algorithm more reliable, the executive probability of the assisted search mechanism is adjusted by the feedback of the improvement degree of optimal value after each iteration. According to the result of numerical experiments on multimodal benchmark functions such as Schwefel, Rastrigin, Ackley and Griewank both with and without coordinate rotation, the proposed CPSO offers faster convergence speed, higher quality solution and stronger robustness than other variants of PSO.

GLOBAL OPTIMIZATION OF PUMP CONFIGURATION PROBLEM USING EXTENDED CROWDING GENETIC ALGORITHM

An extended crowding genetic algorithm (ECGA) is introduced for solvingoptimal pump configuration problem, which was presented by T. Westerlund in 1994. This problem hasbeen found to be non-convex, and the objective function contained several local optima and globaloptimality could not be ensured by all the traditional MINLP optimization method. The concepts ofspecies conserving and composite encoding are introduced to crowding genetic algorithm (CGA) formaintain the diversity of population more effectively and coping with the continuous and/or discretevariables in MINLP problem. The solution of three-levels pump configuration got from DICOPT++software (OA algorithm) is also given. By comparing with the solutions obtained from DICOPT++, ECPmethod, and MIN-MIN method, the ECGA algorithm proved to be very effective in finding the globaloptimal solution of multi-levels pump configuration via using the problem-specific information.

A new hybrid algorithm for global optimization and slope stability evaluation

A new hybrid optimization algorithm was presented by integrating the gravitational search algorithm （GSA） with the sequential quadratic programming （SQP）, namely GSA-SQP, for solving global optimization problems and minimization of factor of safety in slope stability analysis. The new algorithm combines the global exploration ability of the GSA to converge rapidly to a near optimum solution. In addition, it uses the accurate local exploitation ability of the SQP to accelerate the search process and find an accurate solution. A set of five well-known benchmark optimization problems was used to validate the performance of the GSA-SQP as a global optimization algorithm and facilitate comparison with the classical GSA. In addition, the effectiveness of the proposed method for slope stability analysis was investigated using three ease studies of slope stability problems from the literature. The factor of safety of earth slopes was evaluated using the Morgenstern-Price method. The numerical experiments demonstrate that the hybrid algorithm converges faster to a significantly more accurate final solution for a variety of benchmark test functions and slope stability problems.

Chaos-enhanced moth-flame optimization algorithm for global optimization

Moth-flame optimization(MFO)is a novel metaheuristic algorithm inspired by the characteristics of a moth’s navigation method in nature called transverse orientation.Like other metaheuristic algorithms,it is easy to fall into local optimum and leads to slow convergence speed.The chaotic map is one of the best methods to improve exploration and exploitation of the metaheuristic algorithms.In the present study,we propose a chaos-enhanced MFO(CMFO)by incorporating chaos maps into the MFO algorithm to enhance its performance.The chaotic map is utilized to initialize the moths’population,handle the boundary overstepping,and tune the distance parameter.The CMFO is benchmarked on three groups of benchmark functions to find out the most efficient one.The performance of the CMFO is also verified by using two real engineering problems.The statistical results clearly demonstrate that the appropriate chaotic map(singer map)embedded in the appropriate component of MFO can significantly improve the performance of MFO.

Multi-swingby optimization of mission to Saturn using global optimization algorithms

Based on the trajectory design of a mission to Saturn, this paper discusses four different trajectories in various swingby cases. We assume a single impulse to be applied in each case when the spacecraft approaches a celestial body. Some optimal trajectories ofEJS, EMS, EVEJS and EVVEJS flying sequences are obtained using five global optimization algorithms： DE, PSO, DP, the hybrid algorithm PSODE and another hybrid algorithm, DPDE. DE is proved to be supe- rior to other non-hybrid algorithms in the trajectory optimi- zation problem. The hybrid algorithm of PSO and DE can improve the optimization performance of DE, which is vali- dated by the mission to Saturn with given swingby sequences. Finally, the optimization results of four different swingby sequences are compared with those of the ACT of ESA.

A New F-C Function for Box Constrained Global Optimization

To solve the global optimization problems which have several local minimizers,a new F-C function is proposes by combining a lled function and a cross function.The properties of the F-C function are discussed and the corresponding algorithm is given in this paper.F-C function has the same local minimizers with the objective function.Therefore,the F-C function method only needs to minimize the objective function once in the rst iteration.Numerical experiments are performed and the results show that the proposed method is very effective.