Tournament Selection Operator Research Articles

ОЦІНКА ОБЧИСЛЮВАЛЬНОЇ СКЛАДНОСТІ ГЕНЕТИЧНОГО АЛГОРИТМУ

The article is devoted to the estimation of computational complexity of a genetic algorithm as one of the key tools for solving optimisation problems. The theoretical aspects of computational complexity of algorithms and the interrelation of elements of a genetic algorithm are considered. The main types of computational complexity of algorithms are described: time, simple and asymptotic. Five basic rules for calculating the asymptotic complexity are given. A mathematical apparatus for estimating the asymptotic complexity of a genetic algorithm is presented, which takes into account the costs of forming the initial population and performing evolution. Evolution occurs through iterations, during which generations of individuals are subjected to certain operations in order to find an optimal solution (crossing, mutation, chromosome decoding, etc.). GA, as a global search algorithm, is considered to find the optimal path without getting stuck in local minima. To assess the computational complexity of GA, we consider solving the traveling salesman problem (TSP) for 28 cities of Ukraine using a modified TSPLIB library and the DEAP platform created in the Python programming language. A block diagram of the GA is presented, the main elements of which are the tournament selection operator, the ordered crossover operator, and the inversion mutation operator. The influence of the population size and the number of generations on the asymptotic complexity of the genetic algorithm in solving the TSP problem is studied. The study considered changing the size of the GA population from 50 to 500 with a step of 50, while for each such value four sets of the number of generations were modelled: from 50 to 200 with a step of 50. Based on the obtained results, we show a linear dependence of the GA execution time on the size of the considered input data. It is shown that the smallest time complexity of the presented GA for the given TSP problem is 0.33848 seconds with a population size of 50 and a similar number of generations, while the largest value is 3.752734 seconds with a population size of 500 and a number of generations of 200. The obtained results can be used to optimise the performance of a GA in the TSP problem.

Applying Developed Genetic Algorithm Operators to the Knapsack Problems

This study investigated the effect of the previously developed random mixed crossover (RMC), back controlled selection (BCSO), double directions sensitive mutation operators (DDSM), and backward controlled termination criteria (BCTC) on the performance of a genetic algorithm (GA). In the first study, the following three benchmark 0-1, bounded, and unbounded knapsack problems problems were analyzed. In the first stage, the existing operators namely; multi-point crossover operator and tournament selection operator, 1% mutation ratio, and the fitness convergence termination criteria were applied to the benchmark problems. In the second stage of the study, the analysis was conducted by separately applying the previously developed operators, RMC, BCSO, DDSM, and BCTC to the same benchmark problems, and the results obtained from the analysis in this stage were compared with those obtained from the first stage. In the third stage of the study, the previously developed RMC, BCSO and DDSM operators, and BCTC were applied to the same benchmark problems in the same analysis, and the results were compared with those obtained from the first stage. The results of the analysis showed that when the developed operators (crossover, selection and mutation) and termination criteria were collectively used, they were more successful than the existing operators and the developed operators that were separately applied to the benchmark problems.

ГЕНЕТИЧНИЙ АЛГОРИТМ ЯК ЗАСІБ РОЗВ’ЯЗАННЯ ОПТИМІЗАЦІЙНИХ ЗАДАЧ

The article focuses on the peculiarities of using the genetic algorithm (GA) for solving optimization problems. It provides a classification of optimization problems and offers a detailed description of the structural elements of the GA and their role in solving the traveling salesman problem. To assess the impact of GA parameters on its effectiveness, a study on the influence of population size on the length of the traveling salesman's route is conducted. Based on the obtained results, it is shown that population size affects the route length, and the optimal population size for this problem is found to be 150. Using the tournament selection operator, the ordered crossover operator, and the inverse mutation operator, we obtained a salesman's route of 9271.735 km, which, based on the results presented in this paper, is optimal for visiting 29 cities.

Auto-enhanced population diversity and ranking selection-based differential evolutionary algorithm applied to the optimal design of water distribution system

Abstract The differential evolution (DE) algorithm is considered the most powerful evolutionary algorithm (EA) for the optimal design of water distribution systems (WDSs). However, when dealing with large-scale WDS optimization, issues such as premature convergence become a concern. This paper presents an auto-enhanced population diversity and ranking selection-based differential evolutionary (AEPD-RSDE) algorithm for the optimal design of WDSs, which is the first work that incorporates an AEPD strategy to avoid the premature convergence issue and enhance the exploration ability of DE applied to WDS optimization. Besides, the proposed algorithm includes a ranking selection strategy that replaces the tournament selection operator to enhance convergence speed. Three well-known WDSs, i.e., the New York Tunnels (NYT), the Hanoi network (HAN), and the Balerma irrigation network (BIN), were used to validate the proposed algorithm. Results indicate the proposed algorithm is able to find the current best solution, with a success rate of 100% for the NYT and HAN cases and lower average cost solution of €1.921 million for the BIN case relative to other EAs. Instead of solely focusing on ultimate performance comparison, search behavior analyses are conducted between different mutation and selection operators, offering deep insight to guide the development of more advanced EAs.

A multi-strategy genetic algorithm for solving multi-point dynamic aggregation problems with priority relationships of tasks

<abstract><p>The multi-point dynamic aggregation problem (MPDAP) that arises in practical applications is characterized by a group of robots that have to cooperate in executing a set of tasks distributed over multiple locations, in which the demand for each task grows over time. To minimize the completion time of all tasks, one needs to schedule the robots and plan the routes. Hence, the problem is essentially a combinatorial optimization problem. The manuscript presented a new MPDAP in which the priority of the task was considered that is to say, some tasks must be first completed before others begin to be executed. When the tasks were located at different priority levels, some additional constraints were added to express the priorities of tasks. Since route selection of robots depends on the priorities of tasks, these additional constraints caused the presented MPDAP to be more complex than ever. To efficiently solve this problem, an improved optimization algorithm, called the multi-strategy genetic algorithm (MSGA), was developed. First of all, a two-stage hybrid matrix coding scheme was proposed based on the priorities of tasks, then to generate more route combinations, a hybrid crossover operator based on 0-1 matrix operations was proposed. Furthermore, to improve the feasibility of individuals, a repair schedule was designed based on constraints. Meanwhile, a $ q $-tournament selection operator was adopted so that better individuals can be kept into the next generation. Finally, experimental results showed that the proposed algorithm is feasible and effective for solving the MPDAP.</p></abstract>

Genetic algorithm with a new round-robin based tournament selection: Statistical properties analysis.

A round-robin tournament is a contest where each and every player plays with all the other players. In this study, we propose a round-robin based tournament selection operator for the genetic algorithms (GAs). At first, we divide the whole population into two equal and disjoint groups, then each individual of a group competes with all the individuals of other group. Statistical experimental results reveal that the devised selection operator has a relatively better selection pressure along with a minimal loss of population diversity. For the consisting of assigned probability distribution with sampling algorithms, we employ the Pearson's chi-square and the empirical distribution function as goodness of fit tests for the analysis of statistical properties analysis. At the cost of a nominal increase of the complexity as compared to conventional selection approaches, it has improved the sampling accuracy. Finally, for the global performance, we considered the traveling salesman problem to measure the efficiency of the newly developed selection scheme with respect to other competing selection operators and observed an improved performance.

Lightweight Artificial Intelligence Technology for Health Diagnosis of Agriculture Vehicles: Parallel Evolving Artificial Neural Networks by Genetic Algorithm

This paper focuses on developing a computationally economic lightweight artificial intelligence (AI) technology for smartphones. Until date, no commercial system is available on this technology. Thus the developed breakthrough technology can enhance the capability of users on the field for monitoring the agricultural vehicles (AgV)s health by analyzing the acoustic noise using smartphone‘s app. This paper can enable the user of AgVs to optimize their farming by management at edge devices: smartphones. Since smartphones use a small integrated computing unit with computational limited resources, thus lighter the system, more favorable to work on. Artificial neural network (ANN) is one of the most favorite AI techniques, but its lightweight architecture—attributed by the number of inputs and hidden layers and neurons—, is one of the most important issues in the context of smartphones. Under the framework of bi-level optimization, we aim to analyze the tournament selection operator based genetic algorithm with hybrid crossover operators, at level-I, to evolve ANN, at level-II to design the lightweight edge device enabled AI technique. The obtained results and numerical evaluative analysis indicate that the optimized design of the lightweight fault detection system responds well to the soundtracks received via microphones. We present the evaluation of the proposed technology on serial programming, parallel programming (PP), GPU programming, and GPU with PP. The results show that PP is enough efficient for the proposed technology and can save the cost of GPU for large scale implementation of the technology.

A harmonic estimator design with evolutionary operators equipped grey wolf optimizer

Harmonic estimation is a challenging design problem in power networks. Accurate estimation of the inter, power and sub harmonics in networks can be a helpful aspect for designing potential solutions for elimination of these harmonics. Harmonic estimation design problem has been considered as an optimization problem with the amalgamation of least square algorithm in past. In this paper, we first propose an Evolutionary Operators Equipped Grey Wolf Optimizer (E-GWO). In this proposal a sinusoidal function enabled bridging is proposed and along with this tournament selection operator and crossover and mutation operation are incorporated at position updation phase. The variant is first benchmarked on latest CEC-2017 functions and then this design problem is addressed. After a meaningful comparison with the previously published approaches, we arrive at the conclusion that proposed modifications have positive implications on the performance of GWO. Proposed harmonic designs are robust when tested with different operating conditions.

Quality-Oriented Study on Mapping Island Model Genetic Algorithm onto CUDA GPU

Genetic algorithm (GA), a global search method, has widespread applications in various fields. One very promising variant model of GA is the island model GA (IMGA) that introduces the key idea of migration to explore a wider search space. Migration will exchange chromosomes between islands, resulting in better-quality solutions. However, IMGA takes a long time to solve the large-scale NP-hard problems. In order to shorten the computation time, modern graphic process unit (GPU), as highly-parallel architecture, has been widely adopted in order to accelerate the execution of NP-hard algorithms. However, most previous studies on GPUs are focused on performance only, because the found solution qualities of the CPU and the GPU implementation of the same method are exactly the same. Therefore, it is usually previous work that did not report on quality. In this paper, we investigate how to find a better solution within a reasonable time when parallelizing IMGA on GPU, and we take the UA-FLP as a study example. Firstly, we propose an efficient approach of parallel tournament selection operator on GPU to achieve a better solution quality in a shorter amount of time. Secondly, we focus on how to tune three important parameters of IMGA to obtain a better solution efficiently, including the number of islands, the number of generations, and the number of chromosomes. In particular, different parameters have a different impact on solution quality improvement and execution time increment. We address the challenge of how to trade off between solution quality and execution time for these parameters. Finally, experiments and statistics are conducted to help researchers set parameters more efficiently to obtain better solutions when GPUs are used to accelerate IMGA. It has been observed that the order of influence on solution quality is: The number of chromosomes, the number of generations, and the number of islands, which can guide users to obtain better solutions efficiently with moderate increment of execution time. Furthermore, if we give higher priority on reducing execution time on GPU, the quality of the best solution can be improved by about 3%, with an acceleration that is 29 times faster than the CPU counterpart, after applying our suggested parameter settings. However, if we give solution quality a higher priority, i.e., the GPU execution time is close to the CPU’s, the solution quality can be improved up to 8%.

Generalized solution for inverse kinematics problem of a robot using hybrid genetic algorithms

The robot control consists of kinematic control and dynamic control. Control methods of the robot involve forward kinematics and inverse kinematics (IK). In Inverse kinematics the joint angles are found for a given position and orientation of the end effector. Inverse kinematics is a nonlinear problem and has multiple solutions. This computation is required to control the robot arms. A Genetic Algorithm (GA) and Hybrid genetic algorithm (HGA) (Genetic Algorithm in conjunction with Nelder-Mead technique) are proposed for solving the inverse kinematics of a robotic arm. HGA introduces two concepts exploration, exploitation. In an exploration phase, the GA identifies the good areas in entire search space and then exploitation phase is performed inside these areas by using Nelder- mead technique Binary Simulated Crossover and niching strategy for binary tournament selection operator is used. Proposed algorithms can be used on any type of manipulator and the only requirement is the forward kinematic equations, which are easily obtained. As a case study inverse kinematics of a Two Link Elbow Manipulator and PUMA manipulator are solved using GA and HGA in MATLAB. The algorithm is able to find all solutions without any error

Novel genetic algorithm for loading pattern optimization based on core physics heuristics

A genetic algorithm based on novel genetic operators is implemented for the problem of nuclear fuel loading pattern optimization. This is achieved using rank selection or tournament selection and novel crossover operator and fitness function constructions, e.g., improved crossover and mutation operators by considering the chromosomes as permutations (which is a specific feature of the loading pattern problem) and the “stage fitness function” that separates the different objectives of the optimization. Another novel feature of the algorithm is the consideration of the geometric nature of the problem and the desired loading pattern solutions. A new geometric crossover is developed to utilize this geometric knowledge and its implementation exhibits good results. A comprehensive study is performed on the effect of different adaptive mutation strategies on the performances of the algorithm. The new algorithm is implemented and applied to two benchmark problems and used to study the effect of boundary conditions on the symmetry of the obtained best solutions.

Novel Genetic Algorithms for Loading Pattern Optimization Using State-of-the-Art Operators and a Simple Test Case

Novel genetic algorithms (GAs) are developed by using state-of-the-art selection and crossover operators, e.g., rank selection or tournament selection instead of the traditional roulette (fitness proportionate (FP)) selection operator and novel crossover and mutation operators by considering the chromosomes as permutations (which is a specific feature of the loading pattern (LP) problem). The algorithm is applied to a representative model of a modern pressurized water reactor (PWR) core and implemented using a single objective fitness function (FF), i.e., keff. The results obtained for some reference cases using this setup are excellent. They are obtained using a tournament selection operator with a linear ranking (LR) selection probability method and a new geometric crossover operator that allows for geometrical, rather than random, swaps of gene segments between the chromosomes and control over the sizes of the swapped segments. Finally, the effect of boundary conditions (BCs) on the symmetry of the obtained best solutions is studied and the validity of the “symmetric loading patterns” assumption is tested.

A fireworks algorithm using tournament selection operator

A fireworks algorithm using tournament selection operator

An improved clonal selection algorithm using a tournament selection operator and its application to microstrip coupler design

An improved clonal selection algorithm using a tournament selection operator and its application to microstrip coupler design

Optimal capacitor placement in distorted distribution networks with different load models using Penalty Free Genetic Algorithm

Abstract Genetic Algorithm with special constraint handling procedure is proposed for the discrete optimization problem of capacitor placement and sizing in distribution system for cost reduction and power quality improvement. We use gene encoding that enables simple integer representation of possible different number of capacitors of various standard sizes to be placed on a bus. A pair-wise comparison in tournament selection operator is used so that it does not require any penalty parameter tuning, thus avoiding the most difficult aspect of the selection of appropriate penalty parameters. Proposed Penalty Free Genetic Algorithm (PFGA) is tested on 18-bus, 69-bus and 141-bus systems and the obtained results are better than the results from other methods. Simulations with different load models are also performed. It is shown that load models where active and reactive loads are voltage dependent, such as residential, commercial and industrial, constant Z and constant I model lead to completely different solutions. Therefore, careful load modeling should be put in place in order to obtain more realistic picture of the total savings.

A multistage multiobjective substation siting and sizing model based on operator–repair genetic algorithm

The establishment of a multistage multiobjective substation siting and sizing planning model, taking into account various constraints such as load flow constraint, maximum capacity constraint, and maximum power supply radius constraint makes possible substation planning between multiple years to be adjusted to achieve an optimal overall plan. Through multiple optimization objectives, it is possible to prevent the plan from becoming useless because of excessive changes in power supply affiliation during the multistage optimization process. To find the optimal solution for the model, a repair operator is proposed and used with an improved multiobjective genetic algorithm to repair the decision variables for each chromosome corresponding to one stage so as to satisfy the constraints while ensuring that population diversity evolves heuristically to the optimal solution. Moreover, a tournament selection operator based on crowding distance is adopted, which can prevent the algorithm from premature convergence and make populations trend to the Pareto frontier. Experimental results show that the proposed model and algorithm can efficiently solve the issue of rolling planning between multiple target years and achieve a joint optimal planning. © 2014 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.

Sci-Thur AM: Planning - 04: Evaluation of the fluence complexity, solution quality, and run efficiency produced by five fluence parameterizations implemented in PARETO multiobjective radiotherapy treatment planning software.

PARETO (Pareto-Aware Radiotherapy Evolutionary Treatment Optimization) is a novel multiobjective treatment planning system that performs beam orientation and fluence optimization simultaneously using an advanced evolutionary algorithm. In order to reduce the number of parameters involved in this enormous search space, we present several methods for modeling the beam fluence. The parameterizations are compared using innovative tools that evaluate fluence complexity, solution quality, and run efficiency. A PARETO run is performed using the basic weight (BW), linear gradient (LG), cosine transform (CT), beam group (BG), and isodose-projection (IP) methods for applying fluence modulation over the projection of the Planning Target Volume in the beam's-eye-view plane. The solutions of each run are non-dominated with respect to other trial solutions encountered during the run. However, to compare the solution quality of independent runs, each run competes against every other run in a round robin fashion. Score is assigned based on the fraction of solutions that survive when a tournament selection operator is applied to the solutions of the two competitors. To compare fluence complexity, a modulation index, fractal dimension, and image gradient entropy are calculated for the fluence maps of each optimal plan. We have found that the LG method results in superior solution quality for a spine phantom, lung patient, and cauda equina patient. The BG method produces solutions with the highest degree of fluence complexity. Most methods result in comparable run times. The LG method produces superior solution quality using a moderate degree of fluence modulation.

LAMARCKIAN LEARNING IN CLONAL SELECTION ALGORITHM FOR NUMERICAL OPTIMIZATION

In this paper, we introduce Lamarckian learning theory into the Clonal Selection Algorithm and propose a sort of Lamarckian Clonal Selection Algorithm, termed as LCSA. The major aim is to utilize effectively the information of each individual to reinforce the exploitation with the help of Lamarckian local search. Recombination operator and tournament selection operator are incorporated into LCSA to further enhance the ability of global exploration. We compare LCSA with the Clonal Selection Algorithm in solving twenty benchmark problems to evaluate the performance of LCSA. The results demonstrate that the Lamarckian local search makes LCSA more effective and efficient in solving numerical optimization problems.

Multiobjective optimization of an industrial grinding operation using elitist nondominated sorting genetic algorithm

The elitist version of nondominated sorting genetic algorithm (NSGA II) has been adapted to optimize the industrial grinding operation of a lead-zinc ore beneficiation plant. Two objective functions have been identified in this study: (i) throughput of the grinding operation is maximized to maximize productivity and (ii) percent passing of one of the most important size fractions is maximized to ensure smooth flotation operation following the grinding circuit. Simultaneously, it is also ensured that the grinding product meets all other quality requirements, to ensure least possible disturbance in the following flotation circuit, by keeping two other size classes and percent solid of the grinding product and recirculation load of the grinding circuit within the user specified bounds (constraints). Three decision variables used in this study are the solid ore flowrate and two water flowrates at two sumps, primary and secondary, each of them present in each of the two stage classification units. Nondominating (equally competitive) optimal solutions (Pareto sets) have been found out due to conflicting requirements between the two objectives without violating any of the constraints considered for this problem. Constraints are handled using a technique based on tournament selection operator of genetic algorithm which makes the process get rid of arbitrary tuning requirement of penalty parameters appearing in the popular penalty function based approaches for handling constraints. One of the Pareto points, along with some more higher level information, can be used as set points for the previously mentioned two objectives for optimal control of the grinding circuit. Implementation of the proposed technology shows huge industrial benefits.

An efficient constraint handling method for genetic algorithms

Many real-world search and optimization problems involve inequality and/or equality constraints and are thus posed as constrained optimization problems. In trying to solve constrained optimization problems using genetic algorithms (GAs) or classical optimization methods, penalty function methods have been the most popular approach, because of their simplicity and ease of implementation. However, since the penalty function approach is generic and applicable to any type of constraint (linear or nonlinear), their performance is not always satisfactory. Thus, researchers have developed sophisticated penalty functions specific to the problem at hand and the search algorithm used for optimization. However, the most difficult aspect of the penalty function approach is to find appropriate penalty parameters needed to guide the search towards the constrained optimum. In this paper, GA's population-based approach and ability to make pair-wise comparison in tournament selection operator are exploited to devise a penalty function approach that does not require any penalty parameter. Careful comparisons among feasible and infeasible solutions are made so as to provide a search direction towards the feasible region. Once sufficient feasible solutions are found, a niching method (along with a controlled mutation operator) is used to maintain diversity among feasible solutions. This allows a real-parameter GA's crossover operator to continuously find better feasible solutions, gradually leading the search near the true optimum solution. GAs with this constraint handling approach have been tested on nine problems commonly used in the literature, including an engineering design problem. In all cases, the proposed approach has been able to repeatedly find solutions closer to the true optimum solution than that reported earlier.