一种改进的禁忌搜索算法及其在连续全局优化中的应用

禁忌搜索算法是一种元启发式的全局优化算法,是局部搜索算法的一种推广,已被成功地应用于许多组合优化问题中。本文针对有界闭区域上的连续函数全局优化问题,提出了一种改进的禁忌搜索算法,并进行了理论分析和数值实验。数值实验表明,对于连续函数全局优化问题的求解该算法是可行有效的,并且结构简单,迭代次数较少,是一种较好的全局启发式优化算法。     

Continuous ant colony system and tabu search algorithms hybridized for global minimization of continuous multi-minima functions

A new hybrid optimization method, combining Continuous Ant Colony System (CACS) and Tabu Search (TS) is proposed for minimization of continuous multi-minima functions. The new algorithm incorporates the concepts of promising list, tabu list and tabu balls from TS into the framework of CACS. This enables the resultant algorithm to avoid bad regions and to be guided toward the areas more likely to contain the global minimum. New strategies are proposed to dynamically tune the radius of the tabu balls during the execution and also to handle the variable correlations. The promising list is also used to update the pheromone distribution over the search space. The parameters of the new method are tuned based on the results obtained for a set of standard test functions. The results of the proposed scheme are also compared with those of some recent ant based and non-ant based meta-heuristics, showing improvements in terms of accuracy and efficiency.     

Tabu Search directed by direct search methods for nonlinear global optimization

In recent years, there has been a great deal of interest in metaheuristics in the optimization community. Tabu Search (TS) represents a popular class of metaheuristics. However, compared with other metaheuristics like genetic algorithm and simulated annealing, contributions of TS that deals with continuous problems are still very limited. In this paper, we introduce a continuous TS called Directed Tabu Search (DTS) method. In the DTS method, direct-search-based strategies are used to direct a tabu search. These strategies are based on the well-known Nelder–Mead method and a new pattern search procedure called adaptive pattern search. Moreover, we introduce a new tabu list conception with anti-cycling rules called Tabu Regions and Semi-Tabu Regions. In addition, Diversification and Intensification Search schemes are employed. Numerical results show that the proposed method is promising and produces high quality solutions.     

A hybrid method combining continuous tabu search and Nelder–Mead simplex algorithms for the global optimization of multiminima functions

Tabu search (TS) is a metaheuristic, which proved efficient to solve various combinatorial optimization problems. However, few works deal with its application to the global minimization of functions depending on continuous variables. To perform this task, we propose an hybrid method combining tabu search and simplex search (SS). TS allows to cover widely the solution space, to stimulate the search towards solutions far from the current solution, and to avoid the risk of trapping into a local minimum. SS is used to accelerate the convergence towards a minimum. The Nelder–Mead simplex algorithm is a classical very powerful local descent algorithm, making no use of the objective function derivatives. A “simplex” is a geometrical figure consisting, in n-dimensions, of (n+1) points. If any point of a simplex is taken as the origin, the n other points define vector directions that span the n-dimension vector space. Through a sequence of elementary geometric transformations (reflection, contraction and extension), the initial simplex moves, expands or contracts. To select the appropriate transformation, the method only uses the values of the function to be optimized at the vertices of the simplex considered. After each transformation, the current worst vertex is replaced by a better one. Our algorithm called continuous tabu simplex search (CTSS) implemented in two different forms (CTSS_single, CTSS_multiple) is made up of two steps: first, an adaptation of TS to continuous optimization problems, allowing to localize a “promising area”; then, intensification within this promising area, involving SS. The efficiency of CTSS is extensively tested by using analytical test functions of which global and local minima are known. A comparison is proposed with several variants of tabu search, genetic algorithms and simulated annealing. CTSS is applied to the design of a eddy current sensor aimed at non-destructive control.     

A Continuous Genetic Algorithm Designed for the Global Optimization of Multimodal Functions

Genetic algorithms are stochastic search approaches based on randomized operators, such as selection, crossover and mutation, inspired by the natural reproduction and evolution of the living creatures. However, few published works deal with their application to the global optimization of functions depending on continuous variables.A new algorithm called Continuous Genetic Algorithm (CGA) is proposed for the global optimization of multiminima functions. In order to cover a wide domain of possible solutions, our algorithm first takes care over the choice of the initial population. Then it locates the most promising area of the solution space, and continues the search through an intensification inside this area. The selection, the crossover and the mutation are performed by using the decimal code. The efficiency of CGA is tested in detail through a set of benchmark multimodal functions, of which global and local minima are known. CGA is compared to Tabu Search and Simulated Annealing, as alternative algorithms.     

A new solution algorithm for improving performance of ant colony optimization

This study proposes an improved solution algorithm using ant colony optimization (ACO) for finding global optimum for any given test functions. The procedure of the ACO algorithms simulates the decision-making processes of ant colonies as they forage for food and is similar to other artificial intelligent techniques such as Tabu search, Simulated Annealing and Genetic Algorithms. ACO algorithms can be used as a tool for optimizing continuous and discrete mathematical functions. The proposed algorithm is based on each ant searches only around the best solution of the previous iteration with β. The proposed algorithm is called as ACORSES, an abbreviation of ACO Reduced SEarch Space. β is proposed for improving ACO’s solution performance to reach global optimum fairly quickly. The ACORSES is tested on fourteen mathematical test functions taken from literature and encouraging results were obtained. The performance of ACORSES is compared with other optimization methods. The results showed that the ACORSES performs better than other optimization algorithms, available in literature in terms of minimum values of objective functions and number of iterations.     

A hybrid shuffled complex evolution approach based on differential evolution for unconstrained optimization

Numerous optimization methods have been proposed for the solution of the unconstrained optimization problems, such as mathematical programming methods, stochastic global optimization approaches, and metaheuristics. In this paper, a metaheuristic algorithm called Modified Shuffled Complex Evolution (MSCE) is proposed, where an adaptation of the Downhill Simplex search strategy combined with the differential evolution method is proposed. The efficiency of the new method is analyzed in terms of the mean performance and computational time, in comparison with the genetic algorithm using floating-point representation (GAF) and the classical shuffled complex evolution (SCE-UA) algorithm using six benchmark optimization functions. Simulation results and the comparisons with SCE-UA and GAF indicate that the MSCE improves the search performance on the five benchmark functions of six tested functions.     

DC-GRASP: directing the search on continuous-GRASP

Several papers in the scientific literature use metaheuristics to solve continuous global optimization. To perform this task, some metaheuristics originally proposed for solving combinatorial optimization problems, such as Greedy Randomized Adaptive Search Procedure (GRASP), Tabu Search and Simulated Annealing, among others, have been adapted to solve continuous global optimization problems. Proposed by Hirsch et al., the Continuous-GRASP (C-GRASP) is one example of this group of metaheuristics. The C-GRASP is an adaptation of GRASP proposed to solve continuous global optimization problems under box constraints. It is simple to implement, derivative-free and widely applicable method. However, according to Hedar, due to its random construction, C-GRASP may fail to detect promising search directions especially in the vicinity of minima, which may result in a slow convergence. To minimize this problem, in this paper we propose a set of methods to direct the search on C-GRASP, called Directed Continuous-GRASP (DC-GRASP). The proposal is to combine the ability of C-GRASP to diversify the search over the space with some efficient local search strategies to accelerate its convergence. We compare the DC-GRASP with the C-GRASP and other metaheuristics from literature on a set of standard test problems whose global minima are known. Computational results show the effectiveness and efficiency of the proposed methods, as well as their ability to accelerate the convergence of the C-GRASP.     

Hybridizing local search algorithms for global optimization

In this paper, we combine two types of local search algorithms for global optimization of continuous functions. In the literature, most of the hybrid algorithms are produced by combination of a global optimization algorithm with a local search algorithm and the local search is used to improve the solution quality, not to explore the search space to find independently the global optimum. The focus of this research is on some simple and efficient hybrid algorithms by combining the Nelder–Mead simplex (NM) variants and the bidirectional random optimization (BRO) methods for optimization of continuous functions. The NM explores the whole search space to find some promising areas and then the BRO local search is entered to exploit optimal solution as accurately as possible. Also a new strategy for shrinkage stage borrowed from differential evolution (DE) is incorporated in the NM variants. To examine the efficiency of proposed algorithms, those are evaluated by 25 benchmark functions designed for the special session on real-parameter optimization of CEC2005. A comparison study between the hybrid algorithms and some DE algorithms and non-parametric analysis of obtained results demonstrate that the proposed algorithms outperform most of other algorithms and their difference in most cases is statistically considerable. In a later part of the comparative experiments, a comparison of the proposed algorithms with some other evolutionary algorithms reported in the CEC2005 confirms a better performance of our proposed algorithms.     

A modified quasisecant method for global optimization

This paper presents an algorithm for global optimization problem whose objective functions is Lipschitz continuous but not necessarily differentiable. The proposed algorithm consists of local and global search procedures which are based on and inspired by quasisecant method, respectively. The aim of the global search procedure is to identify “promising” basins in the search space. Once a promising basin is identified, the search procedure skips from an exhausted area to the obtained basin, and the local search procedure is then applied at this basin. It proves that the proposed algorithm converges to the global minimum solution if the local ones are finite and isolated. The proposed method is tested by academic benchmarks, numerical performance and comparison show that it is efficient and robust. Finally, The method is applied to solve the sensor localization problem.     

The continuous reactive tabu search: Blending combinatorial optimization and stochastic search for global optimization

A novel algorithm for the global optimization of functions (C-RTS) is presented, in which a combinatorial optimization method cooperates with a stochastic local minimizer. The combinatorial optimization component, based on the Reactive Tabu Search recently proposed by the authors, locates the most promising boxes, in which starting points for the local minimizer are generated. In order to cover a wide spectrum of possible applications without user intervention, the method is designed with adaptive mechanisms: the box size is adapted to the local structure of the function to be optimized, the search parameters are adapted to obtain a proper balance of diversification and intensification. The algorithm is compared with some existing algorithms, and the experimental results are presented for a variety of benchmark tasks.     

A novel metaheuristics approach for continuous global optimization

This paper proposes a novel metaheuristics approach to find the global optimum of continuous global optimization problems with box constraints. This approach combines the characteristics of modern metaheuristics such as scatter search (SS), genetic algorithms (GAs), and tabu search (TS) and named as hybrid scatter genetic tabu (HSGT) search. The development of the HSGT search, parameter settings, experimentation, and efficiency of the HSGT search are discussed. The HSGT has been tested against a simulated annealing algorithm, a GA under the name GENOCOP, and a modified version of a hybrid scatter genetic (HSG) search by using 19 well known test functions. Applications to Neural Network training are also examined. From the computational results, the HSGT search proved to be quite effective in identifying the global optimum solution which makes the HSGT search a promising approach to solve the general nonlinear optimization problem.     

A niche hybrid genetic algorithm for global optimization of continuous multimodal functions

A niche hybrid genetic algorithm (NHGA) is proposed in this paper to solve continuous multimodal optimization problems more efficiently, accurately and reliably. It provides a new architecture of hybrid algorithms, which organically merges the niche techniques and Nelder–Mead's simplex method into GAs. In the new architecture, the simplex search is first performed in the potential niches, which likely contain a global optimum, to locate the promising zones within search space, quickly and reliably. Then another simplex search is used to quickly discover the global optimum in the located promising zones. The proposed method not only makes the exploration capabilities of GAs stronger through niche techniques, but also has more powerful exploitation capabilities by using simplex search. So it effectively alleviates premature convergence and improves weak exploitation capacities of GAs. A set of benchmark functions is used to demonstrate the validity of NHGA and the role of every component of NHGA. Numerical experiments show that the NHGA may, efficiently and reliably, obtain a more accurate global optimum for the complex and high-dimension multimodal optimization problems. It also demonstrates that the new hybrid architecture is potential and can be used to generate more potential hybrid algorithms.     

A tabu search algorithm for solving economic lot scheduling problem

The economic lot scheduling problem has driven considerable amount of research. The problem is NP-hard and recent research is focused on finding heuristic solutions rather than searching for optimal solutions. This paper introduces a heuristic method using a tabu search algorithm to solve the economic lot scheduling problem. Diversification and intensification schemes are employed to improve the efficiency of the proposed Tabu search algorithm. Experimental design is conducted to determine the best operating parameters for the Tabu search. Results show that the tabu search algorithm proposed in this paper outperforms two well known benchmark algorithms.     

A Comparison of Global Optimization Methods for the Design of a High-speed Civil Transport

The conceptual design of aircraft often entails a large number of nonlinear constraints that result in a nonconvex feasible design space and multiple local optima. The design of the high-speed civil transport (HSCT) is used as an example of a highly complex conceptual design with 26 design variables and 68 constraints. This paper compares three global optimization techniques on the HSCT problem and two test problems containing thousands of local optima and noise: multistart local optimizations using either sequential quadratic programming (SQP) as implemented in the design optimization tools (DOT) program or Snyman's dynamic search method, and a modified form of Jones' DIRECT global optimization algorithm. SQP is a local optimizer, while Snyman's algorithm is capable of moving through shallow local minima. The modified DIRECT algorithm is a global search method based on Lipschitzian optimization that locates small promising regions of design space and then uses a local optimizer to converge to the optimum. DOT and the dynamic search algorithms proved to be superior for finding a single optimum masked by noise of trigonometric form. The modified DIRECT algorithm was found to be better for locating the global optimum of functions with many widely separated true local optima.     

On a continuous approach for the maximum weighted clique problem

This paper is focused on computational study of continuous approach for the maximum weighted clique problem. The problem is formulated as a continuous optimization problem with a nonconvex quadratic constraint given by the difference of two convex functions (d.c. function). The proposed approach consists of two main ingredients: a local search algorithm, which provides us with crucial points; and a procedure which is based on global optimality condition and which allows us to escape from such points. The efficiency of the proposed algorithm is illustrated by computational results.     

Desarrollo de un algoritmo de optimización global en colonias de hormigas con selección de región factible para espacios continuos

This study introduces a new algorithm for the ant colony optimization (ACO) method, which has been proposed to solve global optimization problems with continuous decision variables. This algorithm, namely ACO-FRS, involves a strategy for the selection of feasible regions during optimization search and it performs the exploration of the search space using a similar approach to that used by the ants during the search of food. Four variants of this algorithm have been tested in several benchmark problems and the results of this study have been compared with those reported in literature for other ACO-type methods for continuous spaces. Overall, the results show that the incorporation of the selection of feasible regions allows the performing of a global search to explore those regions with low level of pheromone, thus increasing the feasibility of ACO for finding the global optimal solution.     

A local linear embedding module for evolutionary computation optimization

A Local Linear Embedding (LLE) module enhances the performance of two Evolutionary Computation (EC) algorithms employed as search tools in global optimization problems. The LLE employs the stochastic sampling of the data space inherent in Evolutionary Computation in order to reconstruct an approximate mapping from the data space back into the parameter space. This allows to map the target data vector directly into the parameter space in order to obtain a rough estimate of the global optimum, which is then added to the EC generation. This process is iterated and considerably improves the EC convergence. Thirteen standard test functions and two real-world optimization problems serve to benchmark the performance of the method. In most of our tests, optimization aided by the LLE mapping outperforms standard implementations of a genetic algorithm and a particle swarm optimization. The number and ranges of functions we tested suggest that the proposed algorithm can be considered as a valid alternative to traditional EC tools in more general applications. The performance improvement in the early stage of the convergence also suggests that this hybrid implementation could be successful as an initial global search to select candidates for subsequent local optimization.     

Lamination Design Optimization for Continuous Fiber Reinforced Composites of Variable Thicknesses北大核心CSCD

由于具备高的比强度、比刚度,利用连续纤维增强复合材料代替传统金属材料以实现结构轻量化正受到设计者们的广泛关注。然而,结构的复杂性给复合材料的铺层设计与优化带来了很大的挑战。针对航空用复合材料铺层设计约束多的问题,通过逐步构建设计变量准确表达结构的铺层信息。基于经典遗传算法框架,结合各设计变量特点,定义了铺层优化算法中的遗传算子,通过引入“修复”策略保证了每一代解都能满足设计约束,分布在可行域区间内。最后利用精英保留策略提高了算法的局部寻优能力,可以降低复杂复合材料结构铺层设计的计算成本。通过解决经典benchmark问题并与已有优化结果的比较,验证了前述铺层优化算法的全局、局部寻优能力,为工程实际中的复合材料铺层设计优化提供了理论支撑。     

A modified DNA genetic algorithm for parameter estimation of the 2-Chlorophenol oxidation in supercritical water

Based on the mechanism of biological DNA genetic information and evolution, a modified DNA genetic algorithm (MDNA-GA) is proposed to estimate the kinetic parameters of the 2-Chlorophenol oxidation in supercritical water. In this approach, DNA encoding method, choose crossover operator and frame-shift mutation operator inspired by the biological DNA are developed for improving the global searching ability. Besides, an adaptive mutation probability which can be adjusted automatically according to the diversity of population is also adopted. A local search method is used to explore the search space to accelerate the convergence towards global optimum. The performance of MDNA-GA in typical benchmark functions and kinetic parameter estimation is studied and compared with RNA-GA. The experimental results demonstrate that the proposed algorithm can overcome premature convergence and yield the global optimum with high efficiency.