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This paper establishes a novel technique, which is called the G-double-Laplace transform. This technique is an extension of the generalized Laplace transform. We study its properties with examples and various theorems related to the G-double-Laplace transform that have been addressed and proven. Finally, we apply the G-double-Laplace transform decomposition method to solve the nonlinear sine-Gordon and coupled sine-Gordon equations. This method is a combination of the G-double-Laplace transform and decomposition method. In addition, some examples are examined to establish the accuracy and effectiveness of this technique.

With the increasing penetration of renewable energy resources, such as wind and photovoltaic (PV) production, in future microgrids, challenges arise due to the potential interruption of these resources caused by changing weather conditions. In this paper, we propose a mixed-integer quadratic programming (MIQP) based bi-level model for the optimal operation of microgrids under worst-case (WC) scenarios of renewable energy resource outages. The upper-level problem formulates the minimization of energy loss and load shedding in a demand-side management (DSM) program, as well as optimal charging and discharging of electric vehicles (EVs) and energy storage systems (ESSs). The lower-level problem models the maximization of renewable energy curtailment to account for the worst-case realization of renewable resource outages. A decomposition and re-formulation method is adopted to solve the proposed bi-level optimization model, which includes binary variables in both levels. The proposed model and algorithm are implemented in the Julia programming language and solved with the Gurobi commercial solver. The model is analyzed using a 33-node microgrid under different cases to evaluate its performance, showcasing optimal microgrid operation results under worst-case renewable resource interruptions.

In this paper, we analyze the identification of the amount of pollutant discharged problem by each source in a heat system when the dynamics of the state are governed by a parameterized unknown operator. In this way, we introduce the notion of average sentinel. The decomposition method is used to solve the equation of this problem, the gradient method is used to calculate the averaged control, and the combination of the two methods is used to estimate the pollution terms. Numerical example is given to confirm this result.

The purpose of this paper is to apply multistage stochastic programming to the transmission line expansion planning problem, especially when uncertain demand scenarios exist. Since the problem of transmission line expansion planning requires an intensive computational load, dual decomposition is used to decompose the problem into smaller problems. Following this, progressive hedging and proximal bundle methods are used to restore the decomposed solutions to the original problems. Mixed-integer linear programming is involved in the problem to decide where new transmission lines should be constructed or reinforced. However, integer variables in multistage stochastic programming (MSSP) are intractable since integer variables are not restored. Therefore, the branch-and-bound algorithm is applied to multistage stochastic programming methods to force convergence of integer variables.In addition, this paper suggests combining progressive hedging and dual decomposition in stochastic integer programming by sharing penalty parameters. The simulation results tested on the IEEE 30-bus system verify that our combined model sped up the computation and achieved higher accuracy by achieving the minimised cost.

Abstract Background Recent improvements in life expectancy in many countries stem from reduced mortality from cardiovascular disease and cancer above the age of 60. This is the combined result of decreased incidence and improved survival among those with disease. The latter has led to a higher proportion in the population of people with a past history of disease. This is a group with higher mortality than the general population. How growing shares of persons with past history of disease and improved survival with disease have affected changes in life expectancy of the total population is the objective of this paper. Methods Using register data for the total Swedish population, we stratified the population based on whether individuals have been diagnosed with myocardial infarction, stroke, hip fracture, colon cancer, or breast cancer. Using a novel decomposition approach, we decomposed the changes in life expectancy at age 60 between 1994 and 2016 into contributions from improved survival with disease and from changes in proportion of people with past history of disease. Results Improvements in survival from disease resulted in gains of life expectancy for the total population. However, while the contributions to life expectancy improvements from myocardial infarction, stroke and breast cancer were substantial, the contributions from the other diseases were minor. These gains were counteracted, to various degrees, by the increasing proportion of people with raised mortality due to a past history of disease. For instance, the impact on life expectancy by improved survival from breast cancer was almost halved by the increasing share of females with a past history of breast cancer. Conclusion Rising numbers of survivors of different diseases can slow the increase in life expectancy. This dynamic may represent the costs associated with successful treatment of diseases, and thus, a potential “failure of success.” This dynamic should be considered when assessing mortality and life expectancy trends. As populations are aging and disease survival continues to improve, this issue is likely to become even more important in the future.

In this paper, a new practical formulas of Adomian polynomials has been adapted to resolve nonlinear and non-autonomous ordinary differential equations by the Adomian decomposition method, a simple computational for this new polynomials has been suggested, Therefore new conditions of convergence have been generalized.

The civil aviation industry is moving into the more-electric environment where the civil aircraft uses electricity to meet the multiple energy demands of the associated aircraft subsystems. The civil aircraft's turbofan engine, which is the largest energy supply system of civil aircraft, will thus utilize more fuel resource to provide increased electric energy besides of its conventional responsibility of maintaining the fundamental thrust requirements by aircraft. This will introduce new challenge for the energy optimization analysis of aircraft turbofan engine: it was nearly a simple optimal setting of engine's component parameters for keeping required thrust, but under the more-electric environment it will become an optimization problem in order to minimize the fuel consumption while obeying the multiple constraints by thermodynamic limits of turbofan engine and by varying electric power demands associated with the flight profile of aircraft. We present a complete modeling in this paper for the energy optimization analysis of turbofan engine for more-electric civil aircraft and formulate it as a nonlinear programming form. We propose an algorithm based on Benders decomposition method to solve this problem; the numerical results demonstrate the economic effectiveness of the proposed modeling and algorithm.

There are many challengeable multiobjective optimization problems in different areas, whose optimization objectives are usually diversionary. Decomposition methods and evolution mechanisms enable multiobjective evolutionary algorithms based on decomposition (MOEA/D) to tackle these complex optimization problems efficiently. Therefore, MOEA/D has found wide applications in various fields and been attracting increasingly significant attention from both academia and industry since it was first proposed by Zhang and Li in 2007. Many efforts that are dedicated to improving and extending MOEA/D have been summarized shortly by some papers in their introductions, and there exists only one article that reviewed MOEA/D comprehensively in 2017. However, a number of MOEA/D variants with novel methods solving versatile problems in different fields have been emerging since then. This article is motivated by a more systematic survey of MOEA/D from its original ideas to edge-cutting works, including its basic framework and a comprehensive overview of the improvements on key components (decomposition method, weight vector generation method, and evolutionary operator) and the extensions to both many-objective and constrained multiobjective optimizations. The findings of this survey are categorized in seven aspects with corresponding references. In addition, different from introducing briefly the future research directions of MOEA/D in conclusion of the survey in 2017, we present a more detailed outlook that explores not only the novel challenges but also the future research directions, including three aspects in theory and application researches, its challenges in many-objective optimization, and some issues applying MOEA/D to the cutting-edge areas. It is expected that our work will help researchers to start their MOEA/D-based investigations.

Belief reliability is a new proposed reliability metric considering both aleatory and epistemic uncertainty. In belief reliability theory, system reliability analysis is a key component. Traditional system belief reliability theory for systems with random and uncertain components is based on a complex belief reliability formula, which is not understandable and efficient enough in engineering practise. In this paper, we put forward a novel system belief reliability analysis method, called decomposition method to cope with the problem. An algorithm of this method is proposed according to the properties of the cut sets of systems and the complexity of the algorithm is analyzed and compared with that of the reliability formula method. Finally, the effectiveness and efficiency of this method is further illustrated with a comparative case study.

When dealing with complex multiobjective problems, particle swarm optimization algorithm is easy to fall into local optimum and lead to uneven distribution. Therefore, this paper presents a hybrid multiobjective particle swarm optimization algorithm based on R2 indicator (R2HMOPSO) for solving multiobjective optimization problem. The proposed algorithm uses the sigmoid function mapping method to adjust the inertia weight and learning factors in order to tradeoffs the exploration and exploitation process effectively. In addition, simulation binary crossover operator is designed to reinitialize the particles to improve the search capability of the algorithm and to prevent particles from falling into local optimum and premature convergence. R2 indicator is incorporated into the R2HMOPSO algorithm so as to deal with the solutions of uneven distribution on the true Pareto front. Besides, polynomial mutation is used to maintain diversity in the external archive. The improved algorithm is evaluated on standard benchmarks. By comparing it with four state-of-the-art multiobjective optimization algorithms, the simulation results show that R2HMOPSO algorithm is competitive and effective in terms of convergence and distribution.

The dynamic response of a homogeneous elastic simply-supported beam subjected to a load system moving with a uniform velocity is studied in detail in this paper. Analytical expressions for the dynamic responses of the beam and the load-moving system are obtained by means of a new technique using decomposition method whereby the generalized displacement of the beam is written as an infinite series. The method is versatile and simple so that its application to other related problems is possible. Comparisons between different cases of load-moving systems are made clear. Interaction, load, mass, velocity effects on the beam as well as on the load-moving system are investigated. It is concluded that the inertia effect of the load-moving system cannot be neglected when the traveling velocity and its mass ratio to that of the beam are large.

In many companies, the designers use simulation models to approximate the performance of a production system. Despite the fact that the simulation models are very useful in the detailed planning phase of a production system, the costs for a simulation program are usually high. This is recommended in the cases when the designer seeks for an optimal configuration of the system, and, as a consequence, it is necessary to make a great number of simulation runs. To get rid of this inconvenient, the study proposes the use of analytical instruments in order to estimate the performance of manufacturing system. The aim of this paper is to apply such an analytical approach for a manufacturing line by developing the algorithms for calculating the production rate. Using the Markov chains, the decomposition method as well as the C++ program represents the analytical instruments for a practical implementation. The analytical models results are verified using discrete event simulation with DELMIA Quest software. The main contribution of the article consists in a dynamic adaptation of the production rate by optimizing the buffers according to the effective demand or estimated demand of the market.

The paper deals with the modelling and modal analysis of the hexagonal type nuclear fuel assembly. This very complicated mechanical system is created from the many beam type components shaped into spacer grids. The cyclic and central symmetry of the fuel rod package and load-bearing skeleton is advantageous for the fuel assembly decomposition into six identical revolved fuel rod segments, centre tube and skeleton linked by several spacer grids in horizontal planes. The derived mathematical model is used for the modal analysis of the Russian TVSA-T fuel assembly and validated in terms of experimentally determined natural frequencies, modes and static deformations caused by lateral force and torsional couple of forces. The presented model is the first necessary step for modelling of the nuclear fuel assembly vibration caused by different sources of excitation during the nuclear reactor VVER type operation.

Decomposition-based multi-objective evolutionary algorithms provide a good framework for static multi-objective optimization. Nevertheless, there are few studies on their use in dynamic optimization. To solve dynamic multi-objective optimization problems, this paper integrates the framework into dynamic multi-objective optimization and proposes a memory-enhanced dynamic multi-objective evolutionary algorithm based on L p decomposition (denoted by dMOEA/D- L p ). Specifically, dMOEA/D- L p decomposes a dynamic multi-objective optimization problem into a number of dynamic scalar optimization subproblems and coevolves them simultaneously, where the L p decomposition method is adopted for decomposition. Meanwhile, a subproblem-based bunchy memory scheme that stores good solutions from old environments and reuses them as necessary is designed to respond to environmental change. Experimental results verify the effectiveness of the L p decomposition method in dynamic multi-objective optimization. Moreover, the proposed dMOEA/D- L p achieves better performance than other popular memory-enhanced dynamic multi-objective optimization algorithms.

In this paper, we will study the numerical solution of fuzzy initial value problems using two methods, namely, the least square method and the Adomain decomposition method. Also, comparison between the obtained results is made, as well as with the crisp solution, when the a-level equals one. Â

In this paper we study changes in the size and the composition of the labour force in five OECD countries from 1983 through 2000. We apply a recent decomposition method to quantify the components of the change over time in the crude labour force rate and the mean age of the labour force. Our results show that the change in the crude labour force rate was dominated by the change in age-specific labour force participation rates. For the mean age of the labour force we find that for males the change in the age composition of the population predominately explains the overall change while the results for females are less clear-cut.