An Efficient Bi-objective Genetic Algorithm for the Single Batch-Processing Machine Scheduling Problem with Sequence Dependent Family Setup Time and Non-identical Job Sizes

This paper considers the problem of minimizing make-span and maximum tardiness simultaneously for scheduling jobs under non-identical job sizes, dynamic job arrivals, incompatible job families,and sequence-dependentfamily setup time on the single batch- processor, where split size of jobs is allowed between batches. At first, a new Mixed Integer Linear Programming (MILP) model is proposed for this problem; then, it is solved by -constraint method.Since this problem is NP-hard, a bi-objective genetic algorithm (BOGA) is offered for real-sized problems. The efficiency of the proposed BOGA is evaluated to be comparedwith many test problemsby -constraint method based on performance measures. The results show that the proposed BOGAis found to be more efficient and faster than the -constraint method in generating Pareto fronts in most cases

A Variable Neighborhood MOEA/D for Multiobjective Test Task Scheduling Problem

Test task scheduling problem (TTSP) is a typical combinational optimization scheduling problem. This paper proposes a variable neighborhood MOEA/D (VNM) to solve the multiobjective TTSP. Two minimization objectives, the maximal completion time (makespan) and the mean workload, are considered together. In order to make solutions obtained more close to the real Pareto Front, variable neighborhood strategy is adopted. Variable neighborhood approach is proposed to render the crossover span reasonable. Additionally, because the search space of the TTSP is so large that many duplicate solutions and local optima will exist, the Starting Mutation is applied to prevent solutions from becoming trapped in local optima. It is proved that the solutions got by VNM can converge to the global optimum by using Markov Chain and Transition Matrix, respectively. The experiments of comparisons of VNM, MOEA/D, and CNSGA (chaotic nondominated sorting genetic algorithm) indicate that VNM performs better than the MOEA/D and the CNSGA in solving the TTSP. The results demonstrate that proposed algorithm VNM is an efficient approach to solve the multiobjective TTSP

New technique to quantify chaotic dynamics based on differences between semi-implicit integration schemes

Many novel chaotic systems have recently been identified and numerically studied. Parametric chaotic sets are a valuable tool for determining and classifying oscillation regimes observed in nonlinear systems. Thus, efficient algorithms for the construction of parametric chaotic sets are of interest. This paper discusses the performance of algorithms used for plotting parametric chaotic sets, considering the chaotic Rossler, Newton-Leipnik and Marioka-Shimizu systems as examples. In this study, we compared four different approaches: calculation of largest Lyapunov exponents, statistical analysis of bifurcation diagrams, recurrence plots estimation and introduced the new analysis method based on differences between a couple of numerical models obtained by semi-implicit methods. The proposed technique allows one to distinguish the chaotic and periodic motion in nonlinear systems and does not require any additional procedures such as solutions normalization or the choice of initial divergence value which is certainly its advantage. We evaluated the performance of the algorithms with the two-stage approach. At the first stage, the required simulation time was estimated using the perceptual hash calculation. At the second stage, we examined the performance of the algorithms for plotting parametric chaotic sets with various resolutions. We explicitly demonstrated that the proposed algorithm has the best performance among all considered methods. Its implementation in the simulation and analysis software can speed up the calculations when obtaining high-resolution multi-parametric chaotic sets for complex nonlinear systems

Fractional Order Load-Frequency Control of Interconnected Power Systems Using Chaotic Multi-objective Optimization

This is the author accepted manuscript. The final version is available from Elsevier via the DOI in this record.Fractional order proportional-integral-derivative (FOPID) controllers are designed for load frequency control (LFC) of two interconnected power systems. Conflicting time domain design objectives are considered in a multi objective optimization (MOO) based design framework to design the gains and the fractional differ-integral orders of the FOPID controllers in the two areas. Here, we explore the effect of augmenting two different chaotic maps along with the uniform random number generator (RNG) in the popular MOO algorithm - the Non-dominated Sorting Genetic Algorithm-II (NSGA-II). Different measures of quality for MOO e.g. hypervolume indicator, moment of inertia based diversity metric, total Pareto spread, spacing metric are adopted to select the best set of controller parameters from multiple runs of all the NSGA-II variants (i.e. nominal and chaotic versions). The chaotic versions of the NSGA-II algorithm are compared with the standard NSGA-II in terms of solution quality and computational time. In addition, the Pareto optimal fronts showing the trade-off between the two conflicting time domain design objectives are compared to show the advantage of using the FOPID controller over that with simple PID controller. The nature of fast/slow and high/low noise amplification effects of the FOPID structure or the four quadrant operation in the two inter-connected areas of the power system is also explored. A fuzzy logic based method has been adopted next to select the best compromise solution from the best Pareto fronts corresponding to each MOO comparison criteria. The time domain system responses are shown for the fuzzy best compromise solutions under nominal operating conditions. Comparative analysis on the merits and de-merits of each controller structure is reported then. A robustness analysis is also done for the PID and the FOPID controllers

The Effects of Using Chaotic Map on Improving the Performance of Multiobjective Evolutionary Algorithms

Chaotic maps play an important role in improving evolutionary algorithms (EAs) for avoiding the local optima and speeding up the convergence. However, different chaotic maps in different phases have different effects on EAs. This paper focuses on exploring the effects of chaotic maps and giving comprehensive guidance for improving multiobjective evolutionary algorithms (MOEAs) by series of experiments. NSGA-II algorithm, a representative of MOEAs using the nondominated sorting and elitist strategy, is taken as the framework to study the effect of chaotic maps. Ten chaotic maps are applied in MOEAs in three phases, that is, initial population, crossover, and mutation operator. Multiobjective problems (MOPs) adopted are ZDT series problems to show the generality. Since the scale of some sequences generated by chaotic maps is changed to fit for MOPs, the correctness of scaling transformation of chaotic sequences is proved by measuring the largest Lyapunov exponent. The convergence metric γ and diversity metric Δ are chosen to evaluate the performance of new algorithms with chaos. The results of experiments demonstrate that chaotic maps can improve the performance of MOEAs, especially in solving problems with convex and piecewise Pareto front. In addition, cat map has the best performance in solving problems with local optima

A New Real-Time Path Planning Method Based on the Belief Space

A new approach of real-time path planning based on belief space is proposed, which solves the problems of modeling the real-time detecting environment and optimizing in local path planning with the fusing factors. Initially, a double-safe-edges free space is defined for describing the sensor detecting characters, so as to transform the complex environment into some free areas, which can help the robots to reach any positions effectively and safely. Then, based on the uncertainty functions and the transferable belief model (TBM), the basic belief assignment (BBA) spaces of each factor are presented and fused in the path optimizing process. So an innovative approach for getting the optimized path has been realized with the fusing the BBA and the decision making by the probability distributing. Simulation results indicate that the new method is beneficial in terms of real-time local path planning

Neizrazita strategija optimizacije potrošnje energije za paralelno hibridno električno vozilo korištenjem kaotičnog nedominirajućeg genetskog algoritma sortiranja

This paper presented a parallel hybrid electric vehicle (HEV) equipped with a hybrid energy storage system. To handle complex energy flow in the powertrain system of this HEV, a fuzzy-based energy management strategy was established. A chaotic multi-objective genetic algorithm, which optimizes the parameters of fuzzy membership functions, was also proposed to improve fuel economy and HC, CO, and NOx emissions. The main target of this algorithm is to escape from local optima and obtain high quality trade-off solutions. Chaotic initialization operator, chaotic crossover and mutation operators, chaotic disturbance operator, and chaotic local search operator were integrated into non-dominated sorting genetic algorithm II (NSGA-II) to form this new algorithm named chaotic NSGA-II (C-NSGA-II). Simulation results and comparisons demonstrated that chaotic operators can enhance searching ability for optimal solutions. In conclusion, C-NSGA-II is suitable for solving HEV energy management optimization problem.Ovaj rad prikazuje paralelno hibridno električno vozilo (HEV) opremljeno hibridnim spremnikom energije. Kako bi se omogućila funkcionalnost pogonskog sklopa ovakvog HEV-a korištena je strategija raspolaganja energijom zasnovana na neizrazitoj logici. Također, prikazan je više kriterijski genetski algoritam kaosa za optimiranje parametara neizrazite funkcije povezanih s ekonomskim pokazateljem te pokazateljima emisije HC-a, CO-a i NOx-a. Osnovni cilj algoritma je omogućiti izlazak iz lokalnih optimuma i uspostavljanjem kompromisa omogućiti dosezanje boljih rješenja. Kaotični inicijalizacijski operator, kaotično križanje i operator mutacije, kaotični operator poremećaja i kaotični operator lokalnog pretraživanje uključeni su u nedominirajući genetski algoritam sortiranja II (NSGA-II) u svrhu formulacije novog problema nazvanog kaotični NSGA-II (C-NSGA-II). Simulacijski rezultati i usporedbe prikazuju kako kaotični operator može povećati uspješnost traženja optimalnog rješenja. Zaključno, C-NSGA-II je primjeren za rješavanje problema raspolaganja energijom u HEV-u

Sistemática para alocação, sequenciamento e balanceamento de lotes em múltiplas linhas de produção

Diante dos desafios impostos pelo sistema econômico, características dos mercados e exigências dos clientes, as empresas são forçadas a operar com lotes de produção cada vez menores, dificultando a gestão de operações e a otimização dos sistemas produtivos. Desse modo, intensifica-se nos meios corporativos e acadêmicos a busca por abordagens que possibilitem a criação de diferenciais competitivos de mercado, sendo esta a justificativa prática deste trabalho, que propõe uma sistemática integrada para alocação, sequenciamento e balanceamento de lotes em um horizonte de programação em múltiplas linhas de produção em um sistema multiproduto com operadores polivalentes. A sistemática proposta foi dividida em três fases. A primeira fase utiliza um algoritmo genético multiobjetivo com o intuito de determinar a linha de produção em que cada lote será produzido. A segunda fase é responsável pelo sequenciamento dos lotes produtivos e se apoia em uma alteração da regra Apparent Tardiness Cost (ATC). Na terceira fase utilizou-se o método Ranked Positional Weight (RPW) para balancear a distribuição das tarefas entre os operadores polivalentes de cada linha de produção, respeitando a precedência das tarefas. A sistemática foi aplicada em dados reais do segmento têxtil, aprimorando os indicadores produtivos e de entrega e conferindo maior flexibilidade ao processo frente à demanda sazonal.Faced with the challenges imposed by the economic system, characteristic of the markets and requirements of the customers, the companies are forced to operate with smaller production batches, making it difficult to manage operations and optimization of the production systems. In this way, the search for improvements that allow the creation of competitive differentials of market is intensified in the corporate and academic circles. This is the practical justification for this work, which proposes an integrated systematics for the allocation, sequencing and balancing of batches in a horizon of programming in multiple production lines in a multiproduct system with multipurpose operators. The systematic proposal was divided into three phases. The first phase uses a multiobjective genetic algorithm with intention to determine the production line in which each batch will be produced. The second phase is responsible for the sequencing of productive batches and is based on a change in the rule Apparent Tardiness Cost (ATC). In the third phase the method Ranked Positional Weight (RPW) was used to balance the distribution of the tasks between the multipurpose operators of each line of production, respecting the precedence of the tasks. The systematics was applied in real data of the textile segment, improving the productive and delivery indicators and giving greater flexibility of the process against the seasonal demand