Crossover Schemes Research Articles

Elite-guided Resampling and Multi-mutation based Differential Evolution with exponential crossover for numerical optimization

In the existing Differential Evolution (DE) research, there are two main crossover schemes: exponential crossover and binomial crossover. Most researchers believe that binomial crossover is skilled in handling numerical optimization problems while exponential crossover has the advantage in handling optimization problems with certain correlation between adjacent variables. However, we discover that DE variants with exponential crossover can achieve performance comparable to advanced ones utilizing binomial crossover in optimization applications, provided that an appropriate crossover rate CR and associated parameter control are established. In this paper, an Elite-guided Resampling and Multi-mutation based DE with exponential crossover (ERM-DE) is raised to fill the blank in this field, and its main highlights are as follows: First, a novel structure with two stages is raised in our ERM-DE algorithm. The first stage is elite-guided global opposition learning based resampling, and the other is novel exponential crossover DE evolution stage. Second, a Novel Parameter Control (NPC) technique involving scale factor F and crossover rate CR is raised. Different from applying the fitness-based parameter control, the adaptation schemes of the parameters F and CR in our ERM-DE algorithm are fitness-independent. In addition, this NPC technique will also be selectively applied to the trial vector generation strategy DE/target-to-pbest/1/exp with or without optional archive. Third, a novel population Diversity Enhancement Mechanism (DEM) is proposed, which can enhance population diversity by recalculating individuals in a stagnant state. Finally, a time stamp mechanism is posed to deal with outdated inferior and historical solutions in the external archive. A Large test suite with 88 benchmark functions from CEC2013, CEC2014, and CEC2017 test suites is used for algorithm validation and the experimental results indicate that our ERM-DE demonstrates competitiveness with several state-of-the-art DE variants.

Differential Evolution with exponential crossover can be also competitive on numerical optimization

Differential Evolution (DE) is a powerful population-based evolutionary algorithm for global optimization, and it is widely used in many scientific and engineering applications. There are two commonly used crossover schemes in the literature: one is binomial crossover and the other is exponential crossover. The majority of DE researchers believe that DE variants employing binomial crossover usually obtain superior performance than the ones employing exponential crossover on numerical optimization and DE variants with exponential crossover are good at tackling optimization problems with linkages among neighboring variables. On the contrary, here in this paper, a new perspective is proposed that DE variant with exponential crossover can obtain competitive performance with the ones employing binomial crossover on numerical optimization regardless of whether there are linkages among the variables or not after discovering the proper crossover rate Cr and its corresponding parameter control, and the main contributions of the paper can be summarized as follows: (1) The first powerful DE variant with exponential crossover, namely the DE-EXP algorithm, which is superior to the recent winner DE variants, e.g. LSHADE, iLSHADE and jSO, in Congress on Evolutionary Computation (CEC) competitions, is developed for numerical optimization; (2) A novel parameter control of crossover rate Cr is developed for exponential crossover and the value of Cr can be automatically generated not only in the initialization stage but also during the evolution. (3) A black-box model illustrating the fitness-value-dependency weakness of the recent winner DE variants in CEC competitions is given and a novel fitness-value-independent adaptation scheme for scale factor F is proposed in the DE-EXP algorithm to overcome the fitness-value-dependency weakness. A larger test suite containing 88 benchmarks is used for the validation of our DE-EXP algorithm, and experiment results show its superiority in comparison with several state-of-the-art DE variants.

Differential evolution-driven traffic light scheduling for vehicle-pedestrian mixed-flow networks

This study addresses the bi-objective traffic light scheduling problem (TLSP), which aims to minimize the network-wise delay time of all vehicles and pedestrians within a predefined finite-time window. In this study, to solve this real-time optimization problem, an efficient discrete differential evolution-driven approach named DDE is proposed. The DDE includes discrete versions of mutation and crossover schemes together with a usual selection operation. Furthermore, an additional operator called greedy local search operation is combined with the search procedure of the DDE to increase the convergence speed. Finally, numerical experiments are conducted on 32 different traffic case studies generated based on the infrastructure of traffic network in Jurong area of Singapore. The optimization results produced by the DDE are compared with the optimal results achieved by the commercial GUROBI solver. The performance of the DDE is also compared with other metaheuristics namely ABC, GA, HS, Jaya, DSCA and DSCA-LS, which are designed in the literature to solve the TLSP. The performance comparison is analyzed using diverse metrics such as statistical values of optimization results, statistical analysis using the Wilcoxon signed-rank test, average relative error percentage, and convergence analysis. The comparison illustrates the significantly better and promising search ability of the DDE as compared to the other metaheuristics.

A new and fast rival genetic algorithm for feature selection

Feature selection is one of the significant steps in classification tasks. It is a pre-processing step to select a small subset of significant features that can contribute the most to the classification process. Presently, many metaheuristic optimization algorithms were successfully applied for feature selection. The genetic algorithm (GA) as a fundamental optimization tool has been widely used in feature selection tasks. However, GA suffers from the hyperparameter setting, high computational complexity, and the randomness of selection operation. Therefore, we propose a new rival genetic algorithm, as well as a fast version of rival genetic algorithm, to enhance the performance of GA in feature selection. The proposed approaches utilize the competition strategy that combines the new selection and crossover schemes, which aim to improve the global search capability. Moreover, a dynamic mutation rate is proposed to enhance the search behaviour of the algorithm in the mutation process. The proposed approaches are validated on 23 benchmark datasets collected from the UCI machine learning repository and Arizona State University. In comparison with other competitors, proposed approach can provide highly competing results and overtake other algorithms in feature selection.

Differential Evolution: A review of more than two decades of research

Since its inception in 1995, Differential Evolution (DE) has emerged as one of the most frequently used algorithms for solving complex optimization problems. Its flexibility and versatility have prompted several customized variants of DE for solving a variety of real life and test problems. The present study, surveys the near 25 years of existence of DE. In this extensive survey, 283 research articles have been covered and the journey of DE is shown through its basic aspects like population generation, mutation schemes, crossover schemes, variation in parameters and hybridized variants along with various successful applications of DE. This study also provides some key bibliometric indicators like highly cited papers having citations more than 500, publication trend since 1996, journal citations etc. The main aim of the present document is to serve as an extended summary of 25 years of existence of DE, intended for dissemination to interested parties. It is expected that the present survey would generate interest among the new users towards the philosophy of DE and would also guide the experience researchers.

Adaptive Multi-crossover Evolutionary Algorithm for Real-world Optimization Problems

Evolutionary algorithms (EAs) have been extensively used since their invention. EAs are considered as a powerful tool to solve numerous optimisation problems in various fields. Their search mechanisms have been actively developed to improve their search efficiency toward global optima solutions. This study aims to investigate the effects of using different types of recombination (crossover) schemes. It introduces an adaptive version of EA called adaptive multi-crossover evolutionary algorithm (AMCEA). The proposed AMCEA offers multiple forms of heuristic crossover operators based on genetic algorithm (GA) and harmony search algorithm (HSA). The proposed technique improves the search attitude by allowing the effective utilisation of exploration and exploitation strategies during the evolution process. The quality of the proposed AMCEA is evaluated on six real-world numerical optimisation problems (IEEE-CEC2011), and results are compared with those obtained with five variants of GA and HSA. Results demonstrate the superiority of the AMCEA over previously improved algorithms in terms of solution quality; it achieves the lowest mean results and lowest best results in 75% and 66% of the total experiment cases, respectively.

Multi-objective unbalanced assignment problem with restriction of jobs to agents via NSGA-II

In this paper, an approach based on genetic algorithm has been proposed for solving multi-objective unbalanced assignment problems with restriction of job(s) to different agents which may arise due to the inability/poor efficiency of performing certain jobs by some agents dealing with an additional constraint on the maximum number of jobs that can be performed by an agent. As the cost and time are considered as the most important factors for managerial decision in economic/industrial establishments, so here the total cost of assignment of jobs to agents and the total time of completion of jobs by the agents are considered as the two prime objectives. This gives rise to an NP-hard 0-1 programming problem and to solve this problem, we have equipped NSGA-II with a newly developed crossover having the capability of repairing infeasible solution and two new mutation schemes. Also, for comparison of the results obtained from this algorithm, some other variants of this algorithm with existing crossover and mutation schemes have been considered. Finally, to illustrate the performance of proposed approach, a set of test problems have been solved and the results have been analysed for different variants of NSGA-II and some potential future research directions has been discussed.

A New Clocking Scheme for Quantum-dot Cellular Automata Based Designs with Single or Regular Cells

Quantum-Dot Cellular Automata (QCA) is one of the newest technologies that play very important role to design Nano scale electronic devices that are likely to meet the requirements of the modern digital systems, as compared to micro fabricated devices in CMOS technology. In this paper, we proposed a new clocking scheme for QCA circuits, in which single phase cells (90°) or regular cells are used. We design combinational circuits with single phase cells. According to the previous clocking schemes there are no such schemes exist where only single phase cells are used for crossing as well as data propagation. In previous coplanar crossover schemes both cells (90° and 45°) are used for circuit design. The main limitation of these schemes is that there is a possibility of cross coupling between the two wires (one of 90° and another is 45°) during fabrication, when placement of any cells are misaligned. In the new scheme only single phase cells are used, so there is no misalignment of cells. Simulation results indicate that our designs with new clocking scheme achieve same results in comparison to the best previous relevant works. Simulation and verification are carried out by QCADesigner.

Ant colony optimization with different crossover schemes for global optimization

Global optimization, especially large scale optimization problems arise as a very interesting field of research, because they appear in many real-world problems. Ant colony optimization is one of o...

The Economic Dispatch of Cogeneration Systems in the Deregulation Market

This paper presents an Improved Genetic Algorithm (IGA) to solve the economic dispatch of cogeneration systems in a deregulated market. Based on bi-lateral trade between cogeneration systems and utility, an objective function is derived for the cogeneration systems to obtain the maximal profit while stratifying the operational constraints. IGA takes advantage of the conventional GA and tabu search. The crossover and mutation schemes of conventional GA are improved by a competition mechanism to avoid the prematurity. Tabu Lists with heuristic rules are also employed in the searching process to enhance performance. The IGA approach is demonstrated by using a real cogeneration system. Results can offer an efficient way for cogeneration systems to promote the competed ability.

Process of 3D wireless decentralized sensor deployment using parsing crossover scheme

A Wireless Sensor Networks (WSN) usually consists of numerous wireless devices deployed in a region of interest, each able to collect and process environmental information and communicate with neighboring devices. It can thus be regarded as a Multi-Agent System for territorial security, where individual agents cooperate with each other to avoid duplication of effort and to exploit other agent’s capacities. The problem of sensor deployment becomes non-trivial when we consider environmental factors, such as terrain elevations. Due to the fact that all sensors are homogeneous, the chromosomes that encode sensor positions are actually interchangeable, and conventional crossover schemes such as uniform crossover would cause some redundancy as well as over-concentration in certain specific geographical area. We propose a Parsing Crossover Scheme that intends to reduce redundancy and ease geographical concentration pattern in an effort to facilitate the search. The proposed parsing crossover method demonstrates better performances than those of uniform crossover under different terrain irregularities.

QoS Routing Optimization Based on Improved Genetic Algorithm

A improved genetic algorithm is proposed to QoS routing optimization. By improving coding schemes, fitness function designs, selection schemes, crossover schemes and variations, the proposed method can effectively reduce computational complexity and improve coding accuracy. Simulations are carried out to compare our algorithm with the traditional genetic algorithms. Experimental results show that our algorithm converges quickly and is reliable. Hence, our method vastly outperforms the traditional algorithms.

OPTIMAL POWER FLOW EVALUATION OF POWER SYSTEM USING GENETIC ALGORITHM

This paper presents an efficient genetic algorithm for solving non-convex optimal power flow (OPF) problems with bus voltage constraints for practical application. In this method, the individual is the binary-coded representation that contains a mixture of continuous and discrete control variables, and crossover and mutation schemes are proposed to deal with continuous/discrete control variables, respectively. The objective of OPF is defined that not only to minimize total generation cost but also to improve the bus voltage profile.. The proposed method is demonstrated for a IEEE 30-bus four generator ystem, and it is compared with conventional method.The experimental results show that the GA OPF method is superior to the conventional.

Depth-control strategies for crossover in tree-based genetic programming

The standard subtree crossover operator in the tree-based genetic programming (GP) has been considered as problematic. In order to improve the standard subtree crossover, controlling depth of crossover points becomes a research topic. However, the existence of many different and inconsistent crossover depth-control schemes and the possibility of many other depth-control schemes make the identification of good depth-control schemes a challenging problem. This paper aims to investigate general heuristics for making good depth-control schemes for crossover in tree-based GP. It analyses the patterns of depth of crossover points in good predecessor programs of five GP systems that use the standard subtree crossover and four approximations of the optimal crossover operator on three problems in different domains. The analysis results show that an effective depth-control scheme is problem-dependent and evolutionary stage-dependent, and that good crossover events have a strong preference for roots and (less strongly) bottoms of parent program trees. The results also show that some ranges of depths between the roots and the bottoms are also preferred, suggesting that unequal-depth-selection-probability strategies are better than equal-depth-selection-probability strategies.

Evaluation of the genetic algorithm parameters on the optimization performance: a case study on pump-and-treat remediation design

In this study, the impacts of different crossover and encoding schemes on the performance of a genetic algorithm (GA) in finding optimal pump-and-treat (P&T) remediation designs are investigated. For this purpose, binary and Gray encodings of the decision variables are tested. Uniform and two-point crossover schemes are evaluated for two different crossover probabilities. Analysis is performed for two P&T system optimization scenarios. Results show that uniform crossover operator with Gray encoding outperforms the other alternatives for the complex problem with higher number of decision variables. On the other hand, when a simpler problem, which had a lower number of decision variables, is solved, the efficiency of GA is independent of the encoding and crossover schemes.

A hierarchically defined fault pattern generator using genetic algorithm

Test generation using fault algorithms is a complex procedure. This paper presents a hierarchical approach for test vector generation, which searches for a compact set of test patterns, in an otherwise large search space. Genetic algorithms (GAs) have been effective in solving many search and optimisation problems. Since test generation is a search process over a large vector space, it is an ideal candidate for GAs. The GA evolves candidate test vectors and sequences, using a fault simulator to compute the fitness of each candidate test. Various GA parameters are studied, including population size, fitness function and mutation rate, as well as selection and crossover schemes. The search for fitter members is possible by modifying a reference table. The main focus in this paper is on the hierarchical expansion of the module into its constituent modules and the fault analysis would be performed only on those submodules which give faulty responses. The variable crossover and mutation rates help in not being trapped in local minima. The different award numbers allows us in focussing on those test sets which give superior detection possibilities with respect to others.

Elitist genetic algorithm for assignment problem with imprecise goal

The objective of this research paper is to solve a generalized assignment problem with imprecise cost(s)/time(s) instead of precise one by elitist genetic algorithm (GA). Here, the impreciseness of cost(s)/time(s) has been represented by interval valued numbers, as interval valued numbers are the best representation than others like random variable representation with a known probability distribution and fuzzy representation. To solve these types of problems, an elitist GA has been developed with interval valued fitness function. In this developed GA, the existing ideas about the order relations of interval valued numbers have been modified from the point of view of two types of decision making viz., optimistic decision making and pessimistic decision making. This modified approach has been used in the selection process for selecting better chromosomes/individuals for the next generation and in finding the best as well as the worst chromosomes/individuals in each generation. Here two new crossover schemes and two new mutation schemes have been introduced. In order to maintain the feasibility with crossover operations, a repair algorithm has been suggested. Extensive comparative computational studies based on different parameters of our developed algorithm on one illustrative example have also been reported.

Scheduling trucks in container terminals using a genetic algorithm

Trucks are the most popular transport equipment in most mega-terminals, and scheduling them to minimize makespan is a challenge that this article addresses and attempts to resolve. Specifically, the problem of scheduling a fleet of trucks to perform a set of transportation jobs with sequence-dependent processing times and different ready times is investigated, and the use of a genetic algorithm (GA) to address the scheduling problem is proposed. The scheduling problem is formulated as a mixed integer program. It is noted that the scheduling problem is NP-hard and the computational effort required to solve even small-scale test problems is prohibitively large. A crossover scheme has been developed for the proposed GA. Computational experiments are carried out to compare the performance of the proposed GA with that of GAs using six popular crossover schemes. Computational results show that the proposed GA performs best, with its solutions on average 4.05% better than the best solutions found by the other six GAs.

Hybrid-coded crossover for binary-coded genetic algorithms in constrained optimization

The success of genetic searches greatly depends on appropriate selections for many search parameters. This situation becomes more critical for optimization problems involving sharp constraint surfaces. When penalty function approaches are used to handle the constraints, the genetic algorithm conducts the search on a design space which has continually changing contours during the evolution. This often leads to incorrect gene extinctions at early stages of the search, and thus prevents the search from attaining the final global solution. This paper aims to devise a hybrid-coded crossover strategy for binary-coded genetic algorithms (BGA) which combines the major content of two-point crossover and the full domain representation characteristics embedded in many crossover schemes of real-coded genetic algorithms. It is found that the unique hybrid-coded crossover scheme can largely prevent the binary-coded genetic searches from falsely converging to sub-optimal solutions. Comparisons between BGA with the hybrid-coded crossover and the traditional two-point crossover are conducted in a number of illustrative problems with varied combinations of constraints.

A bit-masking oriented data structure for evolutionary operators implementation in genetic algorithms

In the present paper a special bit-masking oriented data structure for an improved implementation of crossover and mutation operators in genetic algorithms is shown. The developed data structure performs evolutionary operators in two separate steps: crossover and mutation mask fill and a special boolean based function application. Both phases are optimized to reach a more efficient, fast and flexible genetic reproduction than standard implementations. The method has been powered adding a multi-layered, bit-masking oriented data structure and a boolean operation based control mixer, allowing special blended crossover operators obtained by superposition of the standard ones. Several examples of crossover schemes produced by these extended controls are presented. In addition, a special purpose crossover scheme, capable to process at the same time two distinct groups of design variables with separate crossover schemes is shown, in order to improve efficiency and convergence speed of some discrete/continuous optimization problems. Finally, to highlight further capabilities of the bit-masking approach, a special single-step version of an evolutionary direction operator is also illustrated.