Vector Evaluated Genetic Algorithm Research Articles

Hybrid Enhanced Evolutionary Algorithm with Differential Evolution for Distributed No-Wait Flow-Shop Scheduling Problem

Abstract: The distributed no-wait flow-shop scheduling problem (DNWFSP) holds significant importance in real-world production environments. However, existing algorithms for solving the DNWFSP have limitations such as unsatisfactory solutions. Therefore, this paper proposes a hybrid enhanced multi-objective evolutionary algorithm (HEMOEA) with differential evolution (HEMOEA-DE) to solve DNWFSP with the criteria of minimizing makespan and total processing time. The algorithm incorporates a mathematical model for the DNWFSP. Effective encoding and decoding methods are employed, and DE is utilized as an efficient genetic operator for chromosome recombination. The HEMOEA-DE algorithm combines the Pareto dominating, dominated relationship-based fitness function and vector-evaluated genetic algorithm algorithms within HEMOEA to approach the Pareto Front quickly. To evaluate the performance of the proposed method, experiments were conducted on the E. Taillard benchmark problem. The outcomes were compared with those of other well-known algorithms. Regarding convergence and performance on the DNWFSP, the HEMOEA-DE algorithm outperformed other HEMOEA algorithms.

Estimating Soil Hydraulic Parameters during Ponding Infiltration Using a Hybrid Algorithm

Accurate inversion of soil hydraulic parameters based on the van Genuchten–Mualem model has received much attention in soil science research. Herein, a hybrid algorithm method using particle swarm optimization and vector-evaluated genetic algorithm was used to invert the parameters θs, α, n, and Ks, with the objective functions of infiltration rate, cumulative infiltration, and soil water content. Then, numerical experiments were conducted on four typical soils at three initial water content levels (20, 40, and 60% effective saturation) to verify the accuracy of the inverse method. The results showed that the inversed soil water retention and conductivity curves were approximately the same as the real curves, with the root mean square errors of 0.00101–0.00192 cm3·cm−3, 0.00800–0.02519 cm3·cm−3, respectively, and both the Nash-Sutcliffe coefficients were approximately 1.0. Additionally, laboratory experiments were also performed to compare with the inversed parameters for verification, within small root mean squared errors and approximately 1.0 Nash–Sutcliffe coefficients. Furthermore, the method can also achieve acceptably accurate parameter inversion even with substantial measurement errors included in the cumulative infiltration, initial water content, and final water content. Thus, the method is effective and robust and found to be practical in field experiments.

Optimal computing budget allocation for the vector evaluated genetic algorithm in multi-objective simulation optimization

Motivated by the vector evaluation genetic algorithm (VEGA), this research develops simulation budget allocation rules for the VEGA in solving simulation optimization problems. We formulate the selection problem of the VEGA using the optimal computing budget allocation approach, and derive the asymptotically optimal allocation rule and an easily implementable approximated allocation rule. The efficiency of the propose simulation budget allocation rules is demonstrated via comparing with some existing allocation rules. Furthermore, the proposed allocation rule is integrated with the VEGA to solve the multi-objective simulation optimization problems. The numerical experiments on the benchmarking test problems indicate that the proposed allocation rule can improve the search efficiency of the VEGA in stochastic environment by reducing the average distance towards the true Pareto front and improving the purity of the estimated Pareto front.

Inverse Modeling of Soil Hydraulic Parameters Based on a Hybrid of Vector-Evaluated Genetic Algorithm and Particle Swarm Optimization

The accurate estimation of soil hydraulic parameters (θs, α, n, and Ks) of the van Genuchten–Mualem model has attracted considerable attention. In this study, we proposed a new two-step inversion method, which first estimated the hydraulic parameter θs using objective function by the final water content, and subsequently estimated the soil hydraulic parameters α, n, and Ks, using a vector-evaluated genetic algorithm and particle swarm optimization (VEGA-PSO) method based on objective functions by cumulative infiltration and infiltration rate. The parameters were inversely estimated for four types of soils (sand, loam, silt, and clay) under an in silico experiment simulating the tension disc infiltration at three initial water content levels. The results indicated that the method is excellent and robust. Because the objective function had multilocal minima in a tiny range near the true values, inverse estimation of the hydraulic parameters was difficult; however, the estimated soil water retention curves and hydraulic conductivity curves were nearly identical to the true curves. In addition, the proposed method was able to estimate the hydraulic parameters accurately despite substantial measurement errors in initial water content, final water content, and cumulative infiltration, proving that the method was feasible and practical for field application.

Fuzzy optimal portfolio selection based on multi-objective Mean-Variance-Skewness model by using NSGA-II algorithm

Constructing an optimal portfolio is a critical decision for investors. The classic portfolio models generally consider mean and variance of return criteria, which are mostly intended single objective and have been analyzed and studied under conditions of certainty. But, in the real world problem of portfolio selection, is a multi-objective problem and in addition to the criteria of mean and variance of return, other criteria such as liquidity risk should also be considered. On the other hand, in practice, we are faced with a vague inaccurate data and portfolio selection problem must be studied under conditions of fuzzy uncertainty. In this paper, we have developed a new fuzzy multi-objective programming model based on mean-variance-skewness model for optimal portfolio selection under fuzzy uncertainty. The objective functions include maximizing the expected return, maximizing skewness or the chance to gain expected returns and minimizing liquidity risk. Rates of return, rates of turnover, and the maximum number of types of stocks included in the portfolio have been considered as triangular fuzzy numbers. To solve this problem an elitist non-dominated sorting genetic algorithm (NSGA-II) has been developed. Vector evaluated genetic algorithm (VEGA) and non-dominated sorting genetic algorithm (NSGA) were used to compare and evaluate the performance of the proposed solving method. Finally, the results obtained from the algorithms output are compared and analyzed, which indicates a higher efficiency of the proposed solving method compared to other methods.

Investigating the Effect of Imbalance Between Convergence and Diversity in Evolutionary Multi-objective Algorithms

There are two main tasks involved in addressing a multiobjective optimization problem (MOP) by evolutionary multiobjective (EMO) algorithms: 1) make the population converge close to the Pareto-optimal front and 2) maintain adequate population diversity. However, most state-of-the-art EMO algorithms are designed based on the “convergence first and diversity second” principle. It has been observed that although these EMO algorithms have been successful in optimizing many real-world MOPs, they fail to solve certain problems that feature a severe imbalance between diversity preservation and achieving convergence. This paper characterizes an imbalanced MOP by clearly defining properties and indicating the reasons for the existing EMO algorithms’ difficulties in solving them. We then present 14 imbalanced problems, with and without constraints. Computational results using four existing EMO algorithms—elitist non-dominated sorting genetic algorithm (NSGA-II), multiobjective evolutionary algorithm based on decomposition (MOEA/D), strength Pareto evolutionary algorithm 2 (SPEA2), and S metric selection EMO algorithm (SMS-EMOA) and a proposed generalized vector-evaluated genetic algorithm are then presented. It is seen that these EMO algorithms cannot solve these imbalanced problems, but they are able to solve the problems when augmented by multiobjective to multiobjective (M2M), an approach that decomposes the population into several interacting subpopulations. These results and the successful application of the EMO methods with the M2M approach even on standard so-called balanced problems indicate the usefulness of using the M2M approach.

Multi-objective optimization of collation delay and makespan in mail-order pharmacy automated distribution system

In this research, the collation delay (CD) and makespan minimization problem in a mail-order pharmacy automated distribution (MOPAD) system are studied. The MOPAD systems, which are integrated with pharmaceutical auto-dispenser machines, auto-packer machines, and conveyor, are utilized to fulfill the increasing prescription demand in recent years. The motivation of this research is derived from the practical deadlock problem in a MOPAD system of the central fill pharmacies (CFP). Most of the customer orders consist of multiple medications, which need to be collated together before being packaged and shipped. The CD is defined as the fulfillment completion time difference between the first and last medications within the same order, which is a critical factor of the MOPAD systems throughput. When CD is minimized, the makespan often increases. Therefore, alternative scheduling solutions are often needed to balance the CD and makespan in the MOPAD system. This paper presents the trade-off solutions between minimizing CD and the makespan. Three multi-objective genetic algorithms with a three-tuples chromosome design, including Vector Evaluated Genetic Algorithm (VEGA), Multi-Objective Genetic Algorithm (MOGA), and non-dominated sorted genetic algorithm-II (NSGA-II), are implemented and compared under various system settings. Compared to the current implemented longest processing time (LPT) heuristic, three multi-objective genetic algorithms save the CD by 95.67 %, but only increase the makespan by 5.62 % on average. The results also show that the NSGA-II provided the best frontier.

Solving land-use suitability analysis and planning problem by a hybrid meta-heuristic algorithm

The aim of Land-use Suitability Analysis and Planning Problem (LSAPP) is to identify the most suitable parcels of land for future land-uses considering several conflicting criteria. LSAPP can be modeled using a variant of a well-known combinatorial optimization problem called Quadratic Assignment Problem (QAP). In this paper, a multi-objective mathematical model is developed for LSAPP based on QAP modeling. The large-size instances of the proposed multi-objective mathematical model are difficult to solve in a reasonable CPU time using exact algorithms. So, an efficient three-phase hybrid solution procedure is proposed. In the first phase, the compensatory objectives are integrated using Analytic Hierarchy Process (AHP) and Decision-Making Trial and Evaluation Laboratory. Then, based on the aforementioned suitability objective function and other spatial objectives and constraints, a multi-objective LSAPP is constructed. Finally, a hybrid multiple objective meta-heuristic algorithm is proposed to solve the LSAPP. The core of the proposed algorithm is based on Scatter Search while Tabu Search and Variable Neighborhood Search are also utilized. The proposed algorithm is equipped with the concepts of Pareto optimality and Veto Threshold, which improve its efficacy. The proposed algorithm is applied on a real LSAPP case study, in ‘Persian Gulf Knowledge Village’, wherein its performance is compared with a well-known evolutionary computation algorithm called Vector Evaluated Genetic Algorithm (VEGA) using comprehensive statistical analysis. A survey on time complexity of the proposed algorithm is also accomplished. The results show that MOSVNS is significantly superior to VEGA both in single and in multi-objective modes. Furthermore, analysis of time complexity of the proposed algorithm shows that it is of polynomial time and can be applied to significantly larger problems with multiple compensatory and non-compensatory objectives.

MPI-based parallel synchronous vector evaluated particle swarm optimization for multi-objective design optimization of composite structures

This paper presents a decentralized/peer-to-peer architecture-based parallel version of the vector evaluated particle swarm optimization (VEPSO) algorithm for multi-objective design optimization of laminated composite plates using message passing interface (MPI). The design optimization of laminated composite plates being a combinatorially explosive constrained non-linear optimization problem (CNOP), with many design variables and a vast solution space, warrants the use of non-parametric and heuristic optimization algorithms like PSO. Optimization requires minimizing both the weight and cost of these composite plates, simultaneously, which renders the problem multi-objective. Hence VEPSO, a multi-objective variant of the PSO algorithm, is used. Despite the use of such a heuristic, the application problem, being computationally intensive, suffers from long execution times due to sequential computation. Hence, a parallel version of the PSO algorithm for the problem has been developed to run on several nodes of an IBM P720 cluster. The proposed parallel algorithm, using MPI's collective communication directives, establishes a peer-to-peer relationship between the constituent parallel processes, deviating from the more common master-slave approach, in achieving reduction of computation time by factor of up to 10. Finally we show the effectiveness of the proposed parallel algorithm by comparing it with a serial implementation of VEPSO and a parallel implementation of the vector evaluated genetic algorithm (VEGA) for the same design problem.

Multiobjective process planning and scheduling using improved vector evaluated genetic algorithm with archive

AbstractMultiobjective process planning and scheduling (PPS) is a most important practical but very intractable combinatorial optimization problem in manufacturing systems. Many researchers have used multiobjective evolutionary algorithms (moEAs) to solve such problems; however, these approaches could not achieve satisfactory results in both efficacy (quality, i.e., convergence and distribution) and efficiency (speed). As classical moEAs, nondominated sorting genetic algorithm II (NSGA‐II) and SPEA2 can get good efficacy but need much CPU time. Vector evaluated genetic algorithm (VEGA) also cannot be applied owing to its poor efficacy. This paper proposes an improved VEGA with archive (iVEGA‐A) to deal with multiobjective PPS problems, with consideration being given to the minimization of both makespan and machine workload variation. The proposed method tactfully combines the mechanism of VEGA with a preference for the edge region of the Pareto front and the characteristics of generalized Pareto‐based scale‐independent fitness function (gp‐siff) with the tendency to converge toward the central area of the Pareto front. These two mechanisms not only preserve the convergence rate but also guarantee better distribution performance. Moreover, some problem‐dependent crossover, mutation, and local search methods are used to improve the performance of the algorithm. Complete numerical comparisons show that the iVEGA‐A is obviously better than VEGA in efficacy, and the convergence performance is also better than NSGA‐II and SPEA2, while the distribution performance is comparable to and the efficiency is obviously better than theirs. © 2012 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.

Efficient Satellite Scheduling Based on Improved Vector Evaluated Genetic Algorithm

Satellite scheduling is a typical multi-peak, many-valley, nonlinear multi-objective optimization problem. How to effectively implement the satellite scheduling is a crucial research in space areas.This paper mainly discusses the performance of VEGA (Vector Evaluated Genetic Algorithm) based on the study of basic principles of VEGA algorithm, algorithm realization and test function, and then improves VEGA algorithm through introducing vector coding, new crossover and mutation operators, new methods to assign fitness and hold good individuals. As a result, the diversity and convergence of improved VEGA algorithm of improved VEGA algorithm have been significantly enhanced and will be applied to Earth-Mars orbit optimization. At the same time, this paper analyzes the results of the improved VEGA, whose results of performance analysis and evaluation show that although VEGA has a profound impact upon multi-objective evolutionary research, multi-objective evolutionary algorithm on the basis of Pareto seems to be a more effective method to get the non-dominated solutions from the perspective of diversity and convergence of experimental result. Finally, based on Visual C + + integrated development environment, we have implemented improved vector evaluation algorithm in the satellite scheduling.

Hybrid Sampling Strategy-based Multiobjective Evolutionary Algorithm

Recently more research works are focused on multiobjective evolutionary algorithm (MOEA) duo to its ability of global and local search for solving multiobjective optimization problem (MOOP) and ability to provide more practical solutions to decision maker; however, most of existing MOEAs cannot achieve satisfactory results in both quality and computational speed. This paper proposes a hybrid sampling strategy-based multiobjective evolutionary algorithm (HSS-MOEA) to deal with such problem. HSS-MOEA tactfully combines the sampling strategy of vector evaluated genetic algorithm (VEGA) and the sampling strategy according to a new Pareto dominating and dominated relationship-based fitness function (PDDR-FF). The sampling strategy of VEGA prefers the edge area of the Pareto front and PDDR-FF-based sampling strategy has the tendency converging toward the central area of the Pareto front. The hybrid sampling strategies preserve both the convergence rate and the distribution performance. Numerical comparisons show that HSS-MOEA could get the better convergence performance, slightly better or equivalent distribution performance, and obviously better efficiency than existing MOEAs.

Multi-objective evolutionary algorithms for model neuron parameter value selection matching biological behavior under different simulation scenarios

In our previous work, we systematically explored a 12dimensional parameter space of a 2-compartment model of the AB (anterior burster) neuron, which is one of the two cells that form the pacemaker kernel in the pyloric network in the lobster stomatogastric ganglion (STG). Our computational exploration started with a hand-tuned AB model [1] and systematically varied maximal conductances of membrane currents, one at a time with all the other conductances kept constant at their hand-tuned values, to determine ranges and variation steps that produced physiologically realistic behavior. Every parameter set representing an individual model neuron in this gridbased parameter space was simulated and classified as functional if it produced biologically realistic bursting activity. Specifically, we looked at the period, burst duration, spike and slow wave amplitude, number of spikes per burst, spike frequency, and after-hyperpolarization potential, which all had to be within limits determined in physiological experiments. Furthermore, in order to be classified as good, the models had to exhibit proper responses to STG deafferentation (i.e., neuromodulator deprivation) as well as current injections both in the presence and in the absence of neuromodulation. After applying all the criteria, not only have we determined that many different parameter sets performed successfully under all tested conditions, but we have also found several very interesting relationships between parameters, which may indicate the existence of co-regulations in the investigated system [2]. However, the question has always remained: are the ranges determined by varying just one maximum conductance at a time suitable and representative of the solution space of the real AB neuron? Perhaps, if two or more conductances were varied at the same time, the ranges would have been different. Unfortunately, the answer to this question cannot be found by simply extending the ranges of parameter values to some arbitrary limits and simulating all the resulting combinations; this would be unrealistic computationally. Therefore, we utilize an approach alternative to the strict grid determination of the parameter search space, based on an application of Multi-Objective Evolutionary Algorithms (MOEA) to generate a population of neuron models meeting the above selection criteria. In MOEA, the algorithm searches for pseudo-optimal solutions by trying to optimize several, sometimes conflicting, objectives at the same time. In this case, all the selection criteria were implemented as separate objectives in the end-VEGA (elitist non-dominated Vector-Evaluated Genetic Algorithm), previously proposed by the authors [3]. The ranges of variation from the hand-tuned values were set between -100% and +400%. This allowed for an extensive and ample exploration of the parameter space. The results from the simulation of the spontaneous activity alone [4], as well as all the remaining scenarios, on the one hand confirmed our observations about the possible existence of coregulations between some currents, but on the other hand, some of the relationships seen before seem to have disappeared over the extended ranges of values. This may indicate that from Eighteenth Annual Computational Neuroscience Meeting: CNS*2009 Berlin, Germany. 18–23 July 2009

An evolutionary approach to the design of controllable cellular automata structure for random number generation

Cellular automata (CA) has been used in pseudorandom number generation for over a decade. Recent studies show that two-dimensional (2-D) CA pseudorandom number generators (PRNGs) may generate better random sequences than conventional one-dimensional (1-D) CA PRNGs, but they are more complex to implement in hardware than 1-D CA PRNGs. In this paper, we propose a new class of 1-D CA - controllable cellular automata (CCA)-without much deviation from the structural simplicity of conventional 1-D CA. We first give a general definition of CCA and then introduce two types of CCA: CCA0 and CCA2. Our initial study shows that these two CCA PRNGs have better randomness quality than conventional 1-D CA PRNGs, but that their randomness is affected by their structures. To find good CCA0/CCA2 structures for pseudorandom number generation, we evolve them using evolutionary multiobjective optimization techniques. Three different algorithms are presented. One makes use of an aggregation function; the other two are based on the vector-evaluated genetic algorithm. Evolution results show that these three algorithms all perform well. Applying a set of randomness tests on the evolved CCA PRNGs, we demonstrate that their randomness is better than that of 1-D CA PRNGs and can be comparable to that of 2-D CA PRNGs.

Using genetic algorithms to solve a multiple objective groundwater pollution containment problem

The genetic algorithm (GA), a new search technique, is applied to a multiple objective groundwater pollution containment problem. This problem involves finding the set of optimal solutions on the trade‐off curve between the reliability and cost of a hydraulic containment system. The decision variables are how many wells to install, where to install them, and how much to pump from each. The GA is an optimization technique patterned after the biological processes of natural selection and evolution. A GA operates on a population of decision variable sets. Through the application of three specialized genetic operators: selection, crossover, and mutation, a GA population “evolves” toward an optimal solution. In the paper, simple GAs and GAs that can solve multiple objective problems are described. Two variations of a multiple objective GA are formulated: a vector‐evaluated GA (VEGA) and a Pareto GA. For the zero‐fixed cost situation, the Pareto GA is shown to be superior to the VEGA and is shown to produce a trade‐off curve similar to that obtained via another optimization technique, mixed integer chance constrained programming (MICCP). The effect on the VEGA and Pareto GA of parameter variation is shown. The Pareto GA is shown to be capable of incorporating the fixed costs associated with installing a system of wells. Results for several levels of fixed cost are presented. A comparison of computer resources required by the GAs and the MICCP method is given. Future research plans are discussed, including the incorporation of the objective of pump‐out time into the model and the development of parallelized GAs.