Multi-parent Crossover Operator Research Articles

The Influence of Noise on Multi-Parent Crossover for an Island Model Genetic Algorithm

Many optimization problems tackled by evolutionary algorithms are not only computationally expensive, but also complicated with one or more sources of noise. One technique to deal with high computational overhead is parallelization. However, though the existing literature gives good insights about the expected behavior of parallelized evolutionary algorithms, we still lack an understanding of their performance in the presence of noise. This paper considers how parallelization might be leveraged together with multi-parent crossover in order to handle noisy problems. We present a rigorous running time analysis of an island model with weakly connected topology tasked with hill climbing in the presence of general additive noise (i.e., noisy OneMax ). Our proofs yield insights into the relationship between the noise intensity and number of required parents. We translate this into positive and negative results for two kinds of multi-parent crossover operators. We then empirically analyze and extend this framework to investigate the trade-offs between noise impact, optimization time, and limits of computation power to deal with noise.

Gene expression programming with dual strategies and neighborhood search for symbolic regression problems

As an evolutionary algorithm for automatic generation of computer programs, Gene expression programming (GEP) has received a lot of attention because it can generate concise and highly accurate solutions. However, GEP also has some unsatisfactory aspects, such as too many control parameters and a lack of balance between exploration and exploitation. Therefore, a new GEP with dual strategies and neighborhood search (DNSGEP) is proposed in this paper for symbolic regression problems. As the core part, a new multi-parent crossover operator with neighborhood search is proposed to replace the original transposition and recombination operators in GEP, which greatly reduces the excessive control parameters in GEP. To assist the multi-parent crossover operator in selecting parents, selection weight is used to assess the quality of individuals in the population. The multi-parent crossover operator combines selection weight to learn more from the better parents. In order to satisfy the different needs of global search and local search of the algorithm, two different crossover strategies are extended on the basis of the multi-parent crossover operator. Furthermore, a population distribution entropy strategy to GEP is proposed for determining when the algorithm should choose which crossover strategy to use. DNSGEP is compared with GEP and three GEP variants on 14 symbolic regression problems and 6 even parity problems. Experimental results show that DNSGEP has the success rate and accuracy that are fully superior to GEP, GEPADF and OGEP, not inferior to SLGEP.

Optimization of Warehouse Operations with Genetic Algorithms

We present a complete, fully automatic solution based on genetic algorithms for the optimization of discrete product placement and of order picking routes in a warehouse. The solution takes as input the warehouse structure and the list of orders and returns the optimized product placement, which minimizes the sum of the order picking times. The order picking routes are optimized mostly by genetic algorithms with multi-parent crossover operator, but for some cases also permutations and local search methods can be used. The product placement is optimized by another genetic algorithm, where the sum of the lengths of the optimized order picking routes is used as the cost of the given product placement. We present several ideas, which improve and accelerate the optimization, as the proper number of parents in crossover, the caching procedure, multiple restart and order grouping. In the presented experiments, in comparison with the random product placement and random product picking order, the optimization of order picking routes allowed the decrease of the total order picking times to 54%, optimization of product placement with the basic version of the method allowed to reduce that time to 26% and optimization of product placement with the methods with the improvements, as multiple restart and multi-parent crossover to 21%.

An Adaptive Memetic Approach for Heterogeneous Vehicle Routing Problems with two-dimensional loading constraints

Abstract The heterogeneous fleet vehicle routing problem with two-dimensional loading constraints (2L- HFVRP) is a complex variant of the classical vehicle routing problem. 2L-HFVRP seeks for minimal cost set of routes to serve a set of customers using a fleet of vehicles of different capacities, fixed and variable operating costs, different dimensions, and restricted loading constraints. To effectively deal with the 2L-HFVRP, we propose a two-stage method that successively calls the routing stage and the packing stage. For the routing stage, we propose an adaptive memetic approach that integrates new multi-parent crossover operators with multi-local search algorithms in an adaptive manner. A time-varying fitness function is proposed to avoid prematurity and improve search performance. An adaptive quality-and-diversity selection mechanism is devised to control the application of the memetic operators and the local search algorithms. In the packing stage, five heuristics are adopted and hybridised to perform the packing process. Experiments on a set of 36 2L-HFVRP benchmark instances demonstrate that the proposed method provides highly competitive results in comparison with state-of-the-art algorithms. In particular, the proposed method obtains the best results for several instances.

Optimizing non-unit repetitive project resource and scheduling by evolutionary algorithms

Repetitive project scheduling is a frequently encountered and challenging task in project planning. Researchers have developed numerous methods for the scheduling and planning of repetitive construction projects. However, almost all current repetitive scheduling methods are based on identical production units or they neglect the priorities of activities. This work presents a new hybrid evolutionary approach, called the fuzzy clustering artificial bee colony approach (FABC), to optimize resource assignment and scheduling for non-unit repetitive projects (NRP). In FABC, the fuzzy c-means clustering technique applies several multi-parent crossover operators to utilize population information efficiently and to improve convergence efficiency. The scheduling subsystem considers the following: (1) the logical relationships among activities throughout the project; (2) the assignment of multiple resources; and (3) the priorities of activities in groups to calculate project duration. Two numerical case studies are analyzed to demonstrate the use of the FABC-NRP model and its ability to optimize the scheduling of non-unit repetitive construction projects. Experimental results indicate that the proposed method yields the shortest project duration on average and deviation of optimal solution among benchmark algorithms considered herein and those considered previously. The outcomes will help project managers to prepare better schedules of repetitive projects.

A binary-continuous invasive weed optimization algorithm for a vendor selection problem

This paper introduces a novel and practical vendor selection problem of a firm that cooperates with multiple geographically dispersed stores. In this problem, the firm entrusts some of its business process to external vendors, and each store can split the ordered quantity between one or more potential vendors, represented as a multi-sourcing strategies. Moreover, the Cobb–Douglas demand function is utilised to establish a relationship between the market demand and the selling price; representing price-sensitive demand. This paper seeks to choose the best vendors, to allocate the stores to them, and to find the optimal values for inventory-related decisions. The approach is based on the integration of the vendor selection problem and the inventory-related decisions in order to generate additional opportunities for system-wide operational efficiency and cost-effectiveness. The aim is to minimise total cost of the firm consisting of costs associated with the vendor selection and inventory-related decisions. A novel meta-heuristic called the binary-continuous invasive weed optimization (BCIWO) algorithm that is capable of solving both binary and continuous optimization problems is developed to solve the complicated NP-hard problem. As there is no benchmark available in the literature, an efficient genetic algorithm enhanced by a multi-parent crossover operator is designed to solve the problem in order to validate the results obtained using BCIWO. The algorithms are tuned using the response surface methodology, based on which their performances are analyzed statistically. Finally, the applicability of the proposed approach and the solution methodologies are demonstrated.

A simulation-based quantitative analysis on the topological heritability of Dandelion-encoded meta-heuristics for tree optimization problems

The solutions to many optimization paradigms arising from different application domains can be modeled as a tree graph, in such a way that nodes represent the variables to be optimized and edges evince topological relationships between such variables. In these problems the goal is to infer an optimal tree graph interconnecting all nodes under a measure of topological fitness, for which a wide portfolio of exact and approximative solvers have hitherto been reported in the related literature. In this context a research line of interest in the last few years has been focused on the derivation of solution encoding strategies suited to deal with the topological constraints imposed by tree graph configurations, particularly when the encoded solution undergoes typical operators from Evolutionary Computation. Almost all contributions within this research area focus on the use of standard crossover and mutation operators from Genetic Algorithms onto the graph topology beneath encoded individuals. However, the pace at which new evolutionary operators have emerged from the community has grown much sharply during the last decade. This manuscript elaborates on the topological heritability of the so-called Dandelion tree encoding approach under non-conventional operators. This experimental application-agnostic-based study gravitates on the topological transmission of Dandelion-encoded solutions under a certain class of multi-parent crossover operators that lie at the core of the family of \((\mu +1)\) evolution strategies and in particular, the so-called Harmony Search algorithm. Metrics to define topological heritability and respect will be defined and evaluated over a number of convergence scenarios for the population of the algorithm, from which insightful conclusions will be drawn in terms of the preserved structural properties of the newly produced solutions with respect to the initial Dandelion-encoded population.

Soft time-windows for a bi-objective vendor selection problem under a multi-sourcing strategy: Binary-continuous differential evolution

This paper introduces a novel and practical integration of the inventory control and vendor selection problems for a manufacturing system that provides multiple products for several stores located in different places. The replenishment policy of each store is the economic order quantity under a multi-sourcing strategy in which the demand rate decreases as the selling price increases. In this strategy, the ordered quantity of each store for each product can be replenished by a set of selected vendors among all. In addition, the selected vendors can deliver the required products within a certain time window based on a soft time-window mechanism. The aim is to minimize the total system cost and delivery schedule violations, simultaneously. A trade-off between the two objectives is generated using the min–max approach to obtain near fair non-dominated solutions. As the problem is known to be NP-hard, a novel meta-heuristic algorithm called binary-continuous differential evolution (BCDE) is developed to make the original differential evolution capable of solving both binary and continuous optimization problems. Moreover, an improved genetic algorithm with a multi-parent crossover operator is designed to solve the problem. While the applicability of the proposed approach and the solution methodologies are demonstrated, the solution algorithms are tuned and their performances are analyzed and compared statistically. Finally, sensitivity analyses on the size of the soft time-window and the bandwidth factor of the BCDE algorithm are conducted.

Using Fuzzy Clustering Chaotic-based Differential Evolution to solve multiple resources leveling in the multiple projects scheduling problem

Project scheduling is an important part of construction project planning. Resource leveling is the process used within project scheduling to reduce fluctuations in resource usage over the period of project implementation. These fluctuations frequently create the untenable requirement of regularly hiring and firing temporary staff resources to meet short-term project needs. Construction project decision makers currently rely on experience-based methods to manage fluctuations. However, these methods lack consistency and may result in unnecessary wastage of resources or costly schedule overruns. This research introduces a novel optimization model called the Fuzzy Clustering Chaotic-based Differential Evolution for solving multiple resources leveling in the multiple projects scheduling problem (FCDE-MRLMP). The novel Fuzzy Clustering Chaotic-based Differential Evolution (FCDE) algorithm integrates fuzzy c-means clustering and chaotic techniques into the original Differential Evolution (DE) algorithm to handle complex optimization problems. The chaotic technique prevents the optimization algorithm from converging prematurely. The fuzzy c-means clustering technique acts as several multi-parent crossover operators in order to utilize population information efficiently and enhance convergence efficiency. Experiments run indicate that the proposed model obtains optimal results more reliably and efficiently than the benchmark algorithms considered. The proposed optimization model is a promising alternative approach to assist project managers to handle resource-leveling project scheduling problems effectively.

Enhanced social emotional optimisation algorithm with elite multi-parent crossover

Social emotional optimisation algorithm SEOA has been successfully applied in a variety of real-world applications. However, it may suffer from slow convergence rate when solving complex optimisation problems. In order to improve the performance of SEOA on complex optimisation problems, in this paper, an enhanced social emotional optimisation algorithm with elite multi-parent crossover MCSEOA is proposed. In MCSEOA, it employs the elite multi-parent crossover operator to exploit the neighbourhood solutions of the current population. The numerical experiments are conducted on 13 classical test functions. Comparison results demonstrate that MCSEOA can significantly improve the performance of the traditional SEOA.

A novel attribute reduction algorithm based on rough set and improved artificial fish swarm algorithm

Attribute Reduction (AR) is an important preprocessing step for data mining. AR based on rough set is an efficient method. Its reduction performance has been verified to be better or comparable with other methods in large amount of works, but existing reduction algorithms have some problems such as slow convergent speed and probably converging to a local optimum. A novel attribute reduction algorithm based on Artificial Fish Swarm Algorithm (AFSA) and rough set is proposed. For AFSA has a slow convergence rate in the later phase of iterations, normal distribution function, Cauchy distribution function, multi-parent crossover operator, mutation operator and modified minimal generation gap model are adopted to improve AFSA. The attribute reduction algorithm based on improved AFSA and rough set takes full advantages of the improved AFSA and rough set,which are faster, more efficient, simpler, and easier to be implemented. Datasets in the UC Irvine (UCI) Machine Learning Repository are selected to verify the aforementioned new method. The results show that above algorithm can search the attribute reduction set effectively, and it has low time complexity and the excellent global search ability.

A multi-parent genetic algorithm for the quadratic assignment problem

Instead of using traditional (two-parent) crossover operator, multi-parent crossover operator is used in genetic algorithms to improve solution quality for many numerical optimization problems. However, very few literatures are available on multi-parent crossover operator for combinatorial optimization problems, especially, quadratic assignment problem (QAP). This paper proposes a multi-parent extension of the sequential constructive crossover (MPSCX), which is a generalization of the traditional sequential constructive crossover (SCX), for the QAP. Then a multi-parent genetic algorithm (MPGA) using MPSCX is developed. Experimental results on ten QAPLIB instances show that our MPGA significantly improves GA using SCX by up to 1.75 % in average assignment cost with maximum of 2.79 % away from the best known solution value. Finally, the efficiency of our MPGA is compared against MPGA using an existing multi-parent crossover for the problem. Experimental results show that our MPGA is better.

An efficient hybrid differential evolution based serial method for multimode resource-constrained project scheduling

The Multimode Resource-Constrained (MRC) problem aims at finding the start times and execution modes for the activities of a project that minimizes project duration under current precedence constraints and resource limitations. This study integrates the fuzzy c-means clustering technique and the chaotic technique into the Differential Evolution to develop the Fuzzy Clustering Chaotic-based Differential Evolution (FCDE) algorithm, an efficient hybrid approach to solving MRC and other related problems. Within the FCDE, the chaos prevents the optimization algorithm from premature convergence and the fuzzy c-means clustering acts as several multi-parent crossover operators for utilizing population information efficiently and enhance convergence efficiency. Further, this study applies a serial method to reflect individual-user priorities into the active schedule and the project duration calculations. Experiments run indicate that the proposed FCDE-MRC obtains optimal results more reliably and efficiently than the benchmark algorithms considered. The FCDE-MRC is a promising alternative methodology to handling resource-constrained problems.

Hybridizing Artificial Bee Colony Algorithm with Multi-Parent Crossover Operator

Artificial Bee Colony algorithm (ABC) is a new optimization algorithms used to solve several optimization problems. The algorithm is a swarm-based that simulates the intelligent behavior of honey bee swarm in searching for food sources. Several variations of ABC have been three existing solution vectors, the new solution vectors will replace the worst three vectors in the food source proposed to enhance its performance. This paper proposes a new variation of ABC that uses multi-parent crossover named multi parent crossover operator artificial bee colony (MPCO-ABC). In the proposed technique the crossover operator is used to generate three new parents based on memory (FSM). The proposed algorithm has been tested using a set of benchmark functions. The experimental results of the MPCO-ABC are compared with the original ABC, GABC. The results prove the efficiency of MPCO-ABC over ABC. Another comparison of MPCO-ABC results made with the other variants of ABC that use crossover and/or mutation operator. The MPCO-ABC almost always shows superiority on all test functions.

CLPS-GA: A case library and Pareto solution-based hybrid genetic algorithm for energy-aware cloud service scheduling

Since the appearance of cloud computing, computing capacity has been charged as a service through the network. The optimal scheduling of computing resources (OSCR) over the network is a core part for a cloud service center. With the coming of virtualization, the OSCR problem has become more complex than ever. Previous work, either on model building or scheduling algorithms, can no longer offer us a satisfactory resolution. In this paper, a more comprehensive and accurate model for OSCR is formulated. In this model, the cloud computing environment is considered to be highly heterogeneous with processors of uncertain loading information. Along with makespan, the energy consumption is considered as one of the optimization objectives from both economic and ecological perspectives. To provide more attentive services, the model seeks to find Pareto solutions for this bi-objective optimization problem. On the basis of classic multi-objective genetic algorithm, a case library and Pareto solution based hybrid Genetic Algorithm (CLPS-GA) is proposed to solve the model. The major components of CLPS-GA include a multi-parent crossover operator (MPCO), a two-stage algorithm structure, and a case library. Experimental results have verified the effectiveness of CLPS-GA in terms of convergence, stability, and solution diversity.

Particle Swarm Assisted Genetic Algorithm for the Optimal Design of Flexbeam Sections

This paper considers the optimum design of flexbeam cross-sections for a full-scale bearingless helicopter rotor, using an efficient hybrid optimization algorithm based on particle swarm optimization, and an improved genetic algorithm, with an effective constraint handling scheme for constrained nonlinear optimization. The basic operators of the genetic algorithm, of crossover and mutation, are revisited, and a new rank-based multi-parent crossover operator is utilized. The rank-based crossover operator simultaneously enhances both the local, and the global exploration. The benchmark results demonstrate remarkable improvements, in terms of efficiency and robustness, as compared to other state-of-the-art algorithms. The developed algorithm is adopted for two baseline flexbeam section designs, and optimum cross-section configurations are obtained with less function evaluations, and less computation time.

Using a fuzzy clustering chaotic-based differential evolution with serial method to solve resource-constrained project scheduling problems

Abstract The resource-constrained problem seeks to find the optimal sequence that minimizes project duration under current precedence constraints and resource limitations. This study integrates the fuzzy c-means clustering technique and the chaotic technique into the Differential Evolution (DE) algorithm to develop the Fuzzy Clustering Chaotic-based Differential Evolution (FCDE) algorithm, an innovative approach to solving complex optimization problems. Within the FCDE, the chaotic technique prevents the optimization algorithm from premature convergence and the fuzzy c-means clustering technique acts as several multi-parent crossover operators in order to utilize population information efficiently and enhance convergence efficiency. Further, this study applies a serial method to reflect individual-user priorities into the active schedule and the project duration calculations. The FCDE and serial method are then integrated into a novel optimization model called the Fuzzy Clustering Chaotic-based Differential Evolution for Solving Resource Constrained Project Scheduling Problem (FCDE-RCPSP). Experiments run indicate that the proposed FCDE-RCPSP obtains optimal results more reliably and efficiently than the benchmark algorithms considered. The FCDE-RCPSP is a promising alternative approach to handling resource-constrained project scheduling problems.

A memetic algorithm for the Minimum Sum Coloring Problem

Given an undirected graph G, the Minimum Sum Coloring Problem (MSCP) is to find a legal assignment of colors (represented by natural numbers) to each vertex of G such that the total sum of the colors assigned to the vertices is minimized. This paper presents a memetic algorithm for MSCP based on a tabu search procedure with two neighborhoods and a multi-parent crossover operator. Experiments on a set of 77 well-known DIMACS and COLOR 2002–2004 benchmark instances show that the proposed algorithm achieves highly competitive results in comparison with five state-of-the-art algorithms. In particular, the proposed algorithm can improve the best known results for 15 instances.

A FITNESS-BASED MULTI-PARENT CROSSOVER OPERATOR WITH PROBABILISTIC SELECTION

Several multi-parent crossover operators have been proposed to increase the performance of genetic algorithms. In these cases, the operators allow several parents to simultaneously take part in creating offspring. However, the operators need to find a balance between the two conflicting goals of exploitation and exploration. Strong exploitation allows fast convergence to succeed but can lead to premature convergence while strong exploration can lead to better solution quality but slower convergence. This paper proposes a new fitness based scanning multi-parent crossover operator for genetic algorithms. The new operator seeks out the optimal setting for the two goals in order to achieve the highest benefits from both. The operator uses a probabilistic selection with an incremental threshold value to allow strong exploration in the early stages of the algorithms and strong exploitation in their later stages. Experiments conducted on some test functions show that the operator can give better solution quality and more convergence consistency when compared with some other well-known multi-parent crossover operators.

A Multilevel Memetic Approach for Improving Graph k-Partitions

Graph partitioning is one of the most studied NP-complete problems. Given a graph <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">G</i> =( <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">V</i> , <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">E</i> ) , the task is to partition the vertex set <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">V</i> into <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</i> disjoint subsets of about the same size, such that the number of edges with endpoints in different subsets is minimized. In this paper, we present a highly effective multilevel memetic algorithm, which integrates a new multiparent crossover operator and a powerful perturbation-based tabu search algorithm. The proposed crossover operator tends to preserve the backbone with respect to a certain number of parent individuals, i.e., the grouping of vertices which is common to all parent individuals. Extensive experimental studies on numerous benchmark instances from the graph partitioning archive show that the proposed approach, within a time limit ranging from several minutes to several hours, performs far better than any of the existing graph partitioning algorithms in terms of solution quality.