Chaotic Search Method Research Articles

THE DEVELOPMENT OF AN ALGORITHM FOR TEACHER’S CHOOSING THE NATURE SCIENCE EDUCATION MODEL CURRICULUM

The mechanisms of teacher's choice of a model curriculum for integrated courses in the natural sciences are investigated. Heuristic algorithms for such a choice are proposed. Among them, a chaotic-search method based on the general indexing of the corresponding model program effectiveness forecast is offered, in which the teachers were asked to give a general assessment of the program and describe the rationale for the choice. The same teachers were offered to make a choice based on the so-called criterion-evaluation algorithm of choice. Namely, for the model programs, 12 parameters are proposed, which are subject to expert evaluation by teachers in an бordinal scale with ten gradations. We considered the index calculated as the sum of 12 estimates for the relevant parameters. This index allows further ranking of programs in order of preferences. Thus, an appropriate program бьselection algorithm is formed. The proposed criteria contain both subjective and objective components, so they should include information about the possibility of implementing the appropriate program depending on the level of the educational institution teacher and the material and organizational support professional competence. The article analyzed the dependence of the model educational programs choice on the example of integrated science courses and the «Geography». The statistical analysis of the conjugation tables showed inconsistency in the frequency distributions of course selections depending on the selection algorithm. This means that the criterionevaluation algorithm of choice gives different results in the relation to the chaotic-search algorithm. The question arises whether it is possible to trust the criterion-evaluation algorithm. It is noted that the answer to this question can be obtained only after analyzing the implementation of model programs. Along with the criterion-evaluation algorithm, a binary choice algorithm is proposed, where each of the criteria is evaluated on a 10-point scale, then a pairwise analysis is carried out for all criteria and, based on the statistical criterion of signs, a conclusion is made about the advantages of the program. Obviously, such an algorithm for hosting several programs could not work correctly, so it needs to be improved.

Vehicle Routing Problem with Deadline and Stochastic Service Times: Case of the Ice Cream Industry in Santiago City of Chile

The research evaluates the vehicular routing problem for distributing refrigerated products. The mathematical model corresponds to the vehicle routing problem with hard time windows and a stochastic service time (VRPTW-ST) model applied in Santiago de Chile. For model optimization, we used tabu search, chaotic search and general algebraic modeling. The model’s objective function is to minimize the total distance traveled and the number of vehicles using stochastic waiting restrictions at the customers’ facilities. The experiments were implemented in ten scenarios by modifying the number of customers. Experiments were established with several customers that can be solved using the general algebraic modeling technique in order to validate the tabu search and the chaotic search methods. The study considered two algorithms modified with Monte Carlo (tabu search and chaotic search). Additionally, two modified algorithms, TSv2 and CSv2, were proposed to reduce execution time. These algorithms were modified by delaying the Monte Carlo procedure until the first set of sub-optimal routes were found. The results validate the metaheuristic chaotic search to solve the VRPTW-ST. The chaotic search method obtained a superior performance than the tabu search method when solving a real problem in a large city. Finally, the experiments demonstrated a direct relationship between the percentage of customers with stochastic waiting time and the model resolution time.

Non-maximum suppression for object detection based on the chaotic whale optimization algorithm

Non-maximum suppression (NMS) as a post-processing step for object detection is mainly used to remove redundant bounding boxes in the object and plays a vital role in many detectors. Its positioning accuracy mainly depends on the bounding box with the highest score, and this strategy is difficult to eliminate the false positive. In order to solve the problem, this paper regards the post-processing step as a combinatorial optimization problem and combines the chaotic whale optimization algorithm and non-maximum suppression. The chaotic search method is used to generate an initial combinatorial solution, and the whale optimization algorithm is discretized to create an updated combinatorial strategy. Under the guidance of the fitness function, the optimal combination is searched. In addition, the method of difference set area (DSA) is proposed to optimize the final detection result. The experiment uses the current mainstream framework Faster R-CNN as the detector on PASCAL VOC2012, COCO2017 and the Warships datasets. The experimental results show that the proposed method can significantly improve the average precision (AP) of detectors compared with the most advanced methods.

A Novel Artificial Bee Colony Algorithm for Structural Damage Detection

A novel artificial bee colony (ABC) algorithm to detect structural damage via modal and frequency analyses is proposed (named as TCABC algorithm). Compared to the standard ABC algorithm, tabu search method and chaotic search method are adopted in the proposed algorithm to enhance the exploration and exploitation ability. The tabu search method uses a memory function to avoid the solution being trapped in a local minimum, which increases the exploitation ability. Chaotic search method generates more searching points for finding the global minimum, which increases the exploration ability. Additionally, the first roulette wheel selection is replaced by the tournament selection to enhance the global searching ability of the TCABC algorithm. Several explicit test functions and an implicit damage detection function are employed to check the numerical results obtained from ABC and TCABC algorithms. Afterward, the damage detection accuracy of the TCABC algorithm is verified under different circumstances, and several recommendations are given for using the TCABC algorithm to detect structural damages under actual conditions. Finally, an experimental study is applied to examine the performance of TCABC algorithm for damage detection. The results show the following: (1) compared to traditional ABC algorithm, TCABC algorithm performs better; (2) fewer groups lead to faster convergence as demonstrated by both algorithms used in the same damage situation; (3) TCABC algorithm can infer the locations and extents of the damage when the groupings are inaccurate; (4) the accuracy of the field test data profoundly affects the precision of the damage detection results. In other words, stronger noises result in worse identification results; (5) whether or not the noises exist, the more data are measured, the more accurate the results can be achieved; (6) the TCABC algorithm can efficiently detect structural damage in the experimental study.

Improvement and Application of Hybrid Firefly Algorithm

Aiming at the problem of poor global search ability and slow convergence speed when solving optimization problems, this paper proposes improved hybrid firefly algorithm (HFA). HFA improves the position updating method, mutation strategy, chaotic search method and evolution strategy of the population. Specifically, the improved position update formula considers both the effect of high-brightness fireflies on position-updated fireflies, and the effects of the optimal firefly on position-updated fireflies. At the same time, a method of adaptive adjustment parameters in the position update formula is presented, which makes the position update method exhibit strong global search ability and local search ability in the initial stage and the later stage of iteration, respectively. In addition, a combined mutation operator is introduced into HFA, which effectively takes the local search and global search ability of the algorithm into account. Since chaotic search exhibits good ergodicity, an operation of randomly moving all fireflies in the population according to chaotic search is given, which enhances the ability of the algorithm to traverse the whole search space, and further improves the global search ability of the algorithm. To verify the effectiveness of HFA, 28 CEC2017 test problems are selected. The calculation results of 28 CEC2017 test problems show that compared with other algorithms, the accuracy of HFA is obviously better than that of other algorithms. Finally, HFA and other intelligent optimization methods in the literatures are used to optimize the structural parameters of cantilever beams. The optimization results show that the weight of the cantilever beam obtained by HFA is obviously smaller than other algorithms. The calculation results of CEC2017 test problems and practical problem show that the solving quality of HFA is obviously better than other algorithms.

Cluster optimisation in information retrieval using self-exploration-based PSO

Self-exploration capability is an important and necessary factor in all social communities where individual assumes to have their own intelligence. Macro social influencing factors are responsible for decision nature taken by an individual, whereas self-exploration process can be considered as a refinement of that decision by use of the cognitive capability to explore a number of surrounding possibilities. The mathematical model corresponding to the individual self-exploration process can be expressed with the help of the chaotic search method. In this paper, chaotic search-based self-exploration has integrated with social influenced-based particle swarm optimisation (PSO) to represent better computational model so that the complex optimisation problem could solve more efficiently. Two different levels of self-exploration called intrinsic cascade self-exploration and extrinsic cascade self-exploration have applied in association with PSO. This paper has applied the proposed concept to cluster documents data in the area of information retrieval and to achieve the global solutions for high dimensional numerical optimisation problems.

Study on an Improved ACO Algorithm Based on Multi-Strategy in Solving Function Problem

In order to overcome the blindness of chaotic search, improve the convergence speed and global solving ability of the basic ant colony optimization(ACO) algorithm, an improved ACO algorithm based on combining multi-population strategy, adaptive adjustment pheromone strategy, chaotic search method and min-max ant strategy (MPCSMACO)is proposed in this paper. In the proposed MPCSMACO algorithm, the multi-population strategy is introduced to realize the information exchange and cooperation among the various types of ant colony. The chaotic search method with the ergodicity, randomness and regularity by using the logistic mapping is used to overcome too long search time, avoid falling into the local extremum in the initial stage and improve the search accuracy in the late search. The min-max ant strategy is used to avoid the local optimization solution and the stagnation. And the ants with different probability search different area according to the concentration of pheromone, so as to reduce the search number of the blindness of chaotic search method. Several Benchmark functions are selected to testify the performance of the MPCSMACO algorithm. The experiment results show that the MPCSMACO algorithm takes on the better global search ability and convergence performance.

Hybrid particle swarm optimization with chaotic search for solving integer and mixed integer programming problems

A novel chaotic search method is proposed, and a hybrid algorithm combining particle swarm optimization (PSO) with this new method, called CLSPSO, is put forward to solve 14 integer and mixed integer programming problems. The performances of CLSPSO are compared with those of other five hybrid algorithms combining PSO with chaotic search methods. Experimental results indicate that in terms of robustness and final convergence speed, CLSPSO is better than other five algorithms in solving many of these problems. Furthermore, CLSPSO exhibits good performance in solving two high-dimensional problems, and it finds better solutions than the known ones. A performance index (PI) is introduced to fairly compare the above six algorithms, and the obtained values of (PI) in three cases demonstrate that CLSPSO is superior to all the other five algorithms under the same conditions.

Pattern Synthesis of Planar Nonuniform Circular Antenna Arrays Using a Chaotic Adaptive Invasive Weed Optimization Algorithm

A novel invasive weed optimization (IWO) variant called chaotic adaptive invasive weed optimization (CAIWO) is proposed and applied for the optimization of nonuniform circular antenna arrays. A chaotic search method has been combined into the modified IWO with adaptive dispersion, where the seeds produced by a weed are dispersed in the search space with standard deviation specified by the fitness value of the weed. To evaluate the performance of CAIWO, several representative benchmark functions are minimized using various optimization algorithms. Numerical results demonstrate that the proposed approach improves the performance of the algorithm significantly, in terms of both the convergence speed and exploration ability. Moreover, the scheme of CAIWO is employed to find out an optimal set of weights and antenna element separation to obtain a radiation pattern with maximum side-lobe level (SLL) reduction with different numbers of antenna element under two cases with different purposes. The design results obtained by CAIWO have comfortably outperformed the published results obtained by other state-of-the-art metaheuristics in a statistically meaningful way.

An improved monkey algorithm with dynamic adaptation

The paper proposes an improved monkey optimization algorithm with dynamic adaptation. In the algorithm, the chaotic search method instead of random process is employed to generate random numbers in initialization process, climb process and watch-jump process so as to avoid repeating search in the same neighborhood. Moreover, two parameters (the evolutionary speed factor and the aggregation degree) are introduced to describe the evolution state of monkeys. The step length of each monkey in climb process is different and decreases dynamically based on its own evolutionary speed factor, and an increase of the aggregation degree of monkeys achieves the dynamical increase of the eyesight, watch times and somersault distance of monkeys. Then, features of the improved algorithm are analyzed through performing several test functions in numerical experiments. Finally, experimental results show that the algorithm significantly improves the search ability of monkey algorithm and has an advantage of robustness.

A Method for Solving Asymmetric Traveling Salesman Problems Using Block Shift Operation and Chaotic Neurodynamics

An asymmetric traveling salesman problem is one in which the costs for travel between one city and another are not symmetric. In this paper, we propose a method for solving such problems based on chaotic search method. It uses block-city exchange method, block insertion method, and 2-opt exchange as exchanging methods. In the block-city exchange method, we consider several cities as a block, and the whole block is exchanged with other city. In the block insertion method, we consider several cities as a block, and the block is inserted at the specified location. In the proposed method, a switching between two exchange methods is determined by chaotic neurodynamics. In the proposed method, the block-city exchange method uses one of exchange method for any instance. The other exchange method is selected from the 2-opt exchange and block insertion methods according to the standard deviations of the costs city-wise and that of all branches in the instance. The proposed method obtains better or equivalent solutions with the conventional heuristic methods for asymmetric TSPs.