A dynamic programming-based particle swarm optimization algorithm for an inventory management problem under uncertainty
This article presents a dynamic programming-based particle swarm optimization (DP-based PSO) algorithm for solving an inventory management problem for large-scale construction projects under a fuzzy random environment. By taking into account the purchasing behaviour and strategy under rules of international bidding, a multi-objective fuzzy random dynamic programming model is constructed. To deal with the uncertainties, a hybrid crisp approach is used to transform fuzzy random parameters into fuzzy variables that are subsequently defuzzified by using an expected value operator with optimistic–pessimistic index. The iterative nature of the authors’ model motivates them to develop a DP-based PSO algorithm. More specifically, their approach treats the state variables as hidden parameters. This in turn eliminates many redundant feasibility checks during initialization and particle updates at each iteration. Results and sensitivity analysis are presented to highlight the performance of the authors’ optimization method, which is very effective as compared to the standard PSO algorithm.
- # Dynamic Particle Swarm Optimization Algorithm
- # Dynamic Particle Swarm Optimization
- # Fuzzy Random Environment
- # Expected Value Operator
- # Dynamic Particle Swarm
- # Inventory Management Problem
- # Dynamic Optimization Algorithm
- # Programming-based Optimization
- # Particle Swarm Optimization Algorithm
- # Hidden Parameters
13
- 10.1016/j.ijpe.2011.04.033
- Jun 25, 2011
- International Journal of Production Economics
23
- 10.1061/(asce)0733-9364(2006)132:6(615)
- Jun 1, 2006
- Journal of Construction Engineering and Management
135
- 10.1016/j.ejor.2007.10.044
- Feb 1, 2009
- European Journal of Operational Research
25
- 10.3844/ajassp.2009.1.12
- Jan 1, 2009
- American Journal of Applied Sciences
34
- 10.1016/s0377-2217(97)00219-1
- Oct 1, 1998
- European Journal of Operational Research
15
- 10.1080/0305215x.2010.497186
- May 1, 2011
- Engineering Optimization
79
- 10.1016/j.ins.2008.03.003
- Mar 18, 2008
- Information Sciences
25
- 10.1016/j.ejor.2008.12.008
- Jan 1, 2010
- European Journal of Operational Research
1888
- 10.1007/978-1-4684-5287-7
- Jan 1, 1988
1414
- 10.1007/s00158-009-0460-7
- Dec 12, 2009
- Structural and Multidisciplinary Optimization
- Research Article
32
- 10.1016/j.omega.2018.04.010
- May 8, 2018
- Omega
Capacitated disassembly scheduling and pricing of returned products with price-dependent yield
- Research Article
23
- 10.1080/0305215x.2014.928815
- Jun 30, 2014
- Engineering Optimization
This article puts forward a cloud theory-based particle swarm optimization (CTPSO) algorithm for solving a variant of the vehicle routing problem, namely a multiple decision maker vehicle routing problem with fuzzy random time windows (MDVRPFRTW). A new mathematical model is developed for the proposed problem in which fuzzy random theory is used to describe the time windows and bi-level programming is applied to describe the relationship between the multiple decision makers. To solve the problem, a cloud theory-based particle swarm optimization (CTPSO) is proposed. More specifically, this approach makes improvements in initialization, inertia weight and particle updates to overcome the shortcomings of the basic particle swarm optimization (PSO). Parameter tests and results analysis are presented to highlight the performance of the optimization method, and comparison of the algorithm with the basic PSO and the genetic algorithm demonstrates its efficiency.
- Research Article
16
- 10.1061/(asce)co.1943-7862.0001329
- May 29, 2017
- Journal of Construction Engineering and Management
Abstract The supply of construction materials is one of the most important in construction engineering, playing an increasingly important role on the efficient operation of the construction supply c...
- Research Article
20
- 10.1111/risa.13509
- May 29, 2020
- Risk Analysis
The risk of medical waste pollution and huge demand of daily medical waste disposal pose great difficulties to medical waste management. Establishing medical waste disposal centers (MWDCs) is considered one of the ways to reduce the environmental and public risk of medical waste pollution. However, how to serve the medical waste disposal demand in optimal MWDCs' locations is a key challenge due to the complexity of the whole system and relationships among stakeholders. This article develops a soft-path solution for reducing risks as well as mitigating the related costs by optimizing the MWDC location-allocation problem. A risk mitigation-oriented bilevel equilibrium optimization model is developed for modeling the Stackelberg game behavior between the local government and the medical institutions. The objectives of the local government are minimizing the total risk of loss, the subsidy costs, and the investment cost of building the MWDCs, while minimizing the disposal and transportation costs are the objectives at the medical institution level. Fuzzy random variables are introduced by combining insufficient historical data with expert knowledge via consulting surveys to describe the coexisting uncertainties in the data. To solve the model, a hybrid approach combined with the interactive fuzzy programming technique and an Entropy-Boltzmann selection-based genetic algorithm are designed and tested. The Chengdu Medical Waste Disposal Centers Planning Project is used as a practical application. The results show that it is possible to achieve a balanced market with higher economic efficiency and significantly reduced risk through an appropriate principle of interactive actions between the bilevel stakeholders.
- Research Article
19
- 10.1061/(asce)me.1943-5479.0000243
- Aug 1, 2013
- Journal of Management in Engineering
Abstract Risk control in project management has been receiving increasing attention in recent years. This paper proposes an approach based on a risk-assessment program and demonstrates how this can be extended to enhance the multimode resource-constrained project-scheduling problem (MRCPSP) to realize risk control and effective scheduling. The main contribution of this paper is to provide a means to control scheduling and material-purchasing risks by using a bilevel decision framework to identify risk and conduct a focused evaluation. Specifically, this paper establishes a hybrid uncertain multiobjective bilevel programming model and introduces an expected-value operator to deal with the hybrid uncertainty. A multiswarm differential-updating particle swarm optimization is developed to support the model calculations. Worthiness and efficiency of the proposed approach is validated using a case study. This approach can help improve scheduling strategies and ensure realistic project-planning.
- Research Article
28
- 10.1109/tem.2017.2686489
- Aug 1, 2017
- IEEE Transactions on Engineering Management
Large construction and infrastructure projects are a billion-dollar business, but few studies have addressed the integrated operations in this unique domain of the construction supply chain (CSC). The comparison between the CSC and a conventional supply chain enables us to examine its framework and establish a quantitative optimization model for the CSC. To introduce the integrated operations concept into the CSC, many uncertainties need to be first dealt with, for which a multiobjective uncertain optimization model is developed. As the optimization of the owner and fabricator's costs and the service level are the main objectives, a hybrid genetic algorithm with fuzzy-random method is developed to solve the optimization model. An integrated multiobjective purchasing and production planning model is then constructed and applied to a hydropower construction project in Southwest China. The results illustrate that efficient integrated operations are critical for the CSC performance. The optimization results also indicate that considering of uncertain rush orders and delay times can be vital for optimum CSC performance. With this proposed method, construction managers can quickly respond to changing uncertain demand. This paper has highlighted that project managers need to collaborate with other stakeholders to ensure optimal CSC performance.
- Research Article
13
- 10.1016/j.autcon.2023.104847
- Mar 23, 2023
- Automation in Construction
Mathematical relations between supplier capacities, the resulting material supply shortages, together with the impact of material delays on construction projects are not well defined. In response to this, this paper presents a novel multi-objective mixed integer linear programming model that considers the selection of suitable suppliers, inventory management practices, order quantities and the possibility of splitting a material order as integrated decisions to be optimised. The trade-off between the overall procurement cost and the weighted lateness, a measure of material delay impacts, is optimised. Material prices, supplier capacities, and resulting delays are treated as fuzzy scenario-based parameters. The proposed model is tested on a numerical example and computation experiments validate the model performance. An extensive sensitivity analysis is carried out and results suggest that by considering high variations in uncertain supplier capacities, the model would generate lower procurement cost and show less significant delay impacts. Whereas greater variations in uncertain material prices cause the total procurement cost to grow 55%; greater variations in uncertain delay durations also drastically increase the weighted lateness by over 70%. This highlights the importance of having high quality estimates for uncertain parameters. Additionally, the analysis also indicates that a minimum overall satisfaction level of 0.9338 can be achieved depending on the model user's strategies, and the proposed scenario-adjusted problem outperforms problems modelled under deterministic market conditions. The major contribution of this paper lies in the development of a fuzzy scenario-based model to solve the supplier selection and material purchasing problem in construction supply chains.
- Research Article
7
- 10.1108/ecam-12-2016-0263
- Aug 16, 2018
- Engineering, Construction and Architectural Management
PurposeThe goal of making buy-in decisions is to purchase materials at the right time with the required quantity and a minimum material cost (MC). To help achieve this goal, the purpose of this paper is to find a way of optimizing the buy-in decision with the consideration of flexible starting date of non-critical activities which makes daily demand adjustable.Design/methodology/approachFirst, a specific algorithm is developed to calculate a series of demand combinations modeling daily material demand for all the possible start dates. Second, future material prices are predicted by applying artificial neural network. Third, the demand combinations and predicted prices are used to generate an optimal buy-in decision.FindingsBy comparing MC in situation when non-critical activities always start at the earliest date to that in situations when the starting date is flexible, it is found that making material buy-in decision with the consideration of the flexibility usually helps reduce MC.Originality/valueIn this paper, a material buy-in decision-making method that accounts non-critical activities’ flexible starting date is proposed. A ternary cycle algorithm is developed to calculate demand combinations. The results that making material buy-in decision considering non-critical activities’ flexible starting date can reduce MC in most times indicates that contractors may consider non-critical activities’ flexibility a part of the buy-in decision-making process, so as to achieve an MC decrease and profit increase.
- Research Article
1
- 10.1155/2018/9376080
- Jan 1, 2018
- Mathematical Problems in Engineering
There is a growing concern that business enterprises focus primarily on their economic activities and ignore the impact of these activities on the environment and the society. This paper investigates a novel sustainable inventory-allocation planning model with carbon emissions and defective item disposal over multiple periods under a fuzzy random environment. In this paper, a carbon credit price and a carbon cap are proposed to demonstrate the effect of carbon emissions’ costs on the inventory-allocation network costs. The percentage of poor quality products from manufacturers that need to be rejected is assumed to be fuzzy random. Because of the complexity of the model, dynamic programming-based particle swarm optimization with multiple social learning structures, a DP-based GLNPSO, and a fuzzy random simulation are proposed to solve the model. A case is then given to demonstrate the efficiency and effectiveness of the proposed model and the DP-based GLNPSO algorithm. The results found that total costs across the inventory-allocation network varied with changes in the carbon cap and that carbon emissions’ reductions could be utilized to gain greater profits.
- Research Article
3
- 10.1080/0305215x.2014.881807
- Feb 19, 2014
- Engineering Optimization
In this article, a novel self-regulating and self-evolving particle swarm optimizer (SSPSO) is proposed. Learning from the idea of direction reversal, self-regulating behaviour is a modified position update rule for particles, according to which the algorithm improves the best position to accelerate convergence in situations where the traditional update rule does not work. Borrowing the idea of mutation from evolutionary computation, self-evolving behaviour acts on the current best particle in the swarm to prevent the algorithm from prematurely converging. The performance of SSPSO and four other improved particle swarm optimizers is numerically evaluated by unimodal, multimodal and rotated multimodal benchmark functions. The effectiveness of SSPSO in solving real-world problems is shown by the magnetic optimization of a Halbach-based permanent magnet machine. The results show that SSPSO has good convergence performance and high reliability, and is well matched to actual problems.
- Conference Article
1
- 10.1109/mic.2013.6758157
- Aug 1, 2013
In order to solve the problem of minimizing cost of power generation calculation in voltage stability constrained optimal power flow optimal of power system, dynamic double-population particle swarm optimization algorithm is used on the basis of the traditional particle swarm optimization algorithm, In this algorithm the particles not only depends on successful experience to move but also get experience from failure cases. And the particles are constantly changing in the process of iteration, which overcomes the local convergence of traditional PSO. The dynamic double-population particle swarm optimization algorithm is applied to the voltage stability constrained optimal power flow calculation to minimizing the generation cost problem, which was tested in a standard IEEE30 system, in order to prove the effectiveness of dynamic double-population particle swarm optimization algorithm, it is compared with genetic algorithm (GA) and results show that, dynamic double-population particle swarm optimization algorithm is better than genetic algorithm in computing power cost minimization problem.
- Research Article
- 10.4028/www.scientific.net/amr.860-863.2211
- Dec 13, 2013
- Advanced Materials Research
This paper proposes a new application of dynamic particle swarm optimization (PSO) algorithm for parameter identification of vector controlled asynchronous propulsion motor (APM) in electric propulsion ship. The dynamic PSO modifies the inertia weight, learning coefficients and two independent random sequences which affect the convergence capability and solution quality, in order to improve the performance of the standard PSO algorithm. The standard PSO and dynamic PSO algorithms use measurements of the mt-axis currents, voltages of APM as the inputs to parameter identification system. The experimental results obtained compare the identified parameters with the actual parameters. There is also a comparison of the solution quality between standard PSO and dynamic PSO algorithms. The results demonstrate that the dynamic PSO algorithm is better than standard PSO algorithm for APM parameter identification. Dynamic PSO algorithm can improve the performance of ship propulsion motor under abrupt load variation.
- Conference Article
13
- 10.1109/isie.2013.6563616
- May 1, 2013
This paper proposes a novel application of a dynamic particle swarm optimization (PSO) algorithm for determining a maximum power point (MPP) of a solar photovoltaic (PV) panel. Solar PV cells have a non-linear V-I characteristic with a distinct MPP which depends on environmental factors such as temperature and irradiation. In order to continuously harvest maximum power from the solar PV panel, it always has to be operated at its MPP. The proposed dynamic PSO algorithm is one of the PSO algorithm variants, which modifies the acceleration coefficients of the cognitive and social components in the velocity update equation of the PSO algorithm as linear time-varying parameters to improve the global search capability of particles in the early stage of the optimization process and direct the global optima at the end stage. The obtained simulation results are compared with MPPs achieved using other algorithms such as the standard PSO, and Perturbation and Observation (P&O) algorithms under various atmospheric conditions. The results show that the dynamic PSO algorithm is better than the standard PSO and P&O algorithms for determining and tracking MPPs of solar PV panels.
- Conference Article
- 10.1109/cibim.2011.5949226
- Apr 1, 2011
Biometric models are typically designed a priori using limited number of samples acquired from complex environments that change in time during operations. Therefore, these models are often poor representatives of the biometric trait to be recognized. To circumvent this problem, ensemble of classifiers can be used to integrate solutions obtained from multiple diverse classifiers. In this paper, two dynamic particle swarm optimization (DPSO) algorithms are compared for the evolution of classifier ensembles during supervised incremental learning of newly-acquired data samples in video-based face recognition. Using the properties of these population-based optimization algorithms, an incremental DPSO learning strategy for adaptive classification systems (ACSs) is employed to evolve a pool of fuzzy ARTMAP classifiers while an heterogeneous ensemble is selected through a greedy search process that seeks to maximize both performance and diversity. The performance of dynamic niching PSO (DNPSO) and speciation PSO (SPSO) algorithms is assessed in terms of classification rate, resource requirements and diversity for different incremental learning scenarios of new data blocks extracted from real-world video streams. Simulation results indicate that both DPSO algorithms can efficiently create accurate ensembles while reducing computational complexity. In addition, directly selecting representative subswarm particles to form diversified classifier ensembles significantly reduces the computational complexity.
- Research Article
19
- 10.1177/1687814018824930
- Mar 1, 2019
- Advances in Mechanical Engineering
A dynamic adaptive particle swarm optimization and genetic algorithm is presented to solve constrained engineering optimization problems. A dynamic adaptive inertia factor is introduced in the basic particle swarm optimization algorithm to balance the convergence rate and global optima search ability by adaptively adjusting searching velocity during search process. Genetic algorithm–related operators including a selection operator with time-varying selection probability, crossover operator, and n-point random mutation operator are incorporated in the particle swarm optimization algorithm to further exploit optimal solutions generated by the particle swarm optimization algorithm. These operators are used to diversify the swarm and prevent premature convergence. Tests on nine constrained mechanical engineering design optimization problems with different kinds of objective functions, constraints, and design variables in nature demonstrate the superiority of the dynamic adaptive particle swarm optimization and genetic algorithm against several other meta-heuristic algorithms in terms of solution quality, robustness, and convergence rate in most cases.
- Research Article
67
- 10.1007/s11042-020-08699-8
- Mar 13, 2020
- Multimedia Tools and Applications
Image segmentation has considered an important step in image processing. Fuzzy c-means (FCM) is one of the commonly used clustering algorithms because of its simplicity and effectiveness. However, FCM has the disadvantages of sensitivity to initial values, falling easily into local optimal solution and sensitivity to noise. To tackle these disadvantages, many optimization-based fuzzy clustering methods have been proposed in the literature survey. Particle swarm optimization (PSO) has good global optimization capability and a hybrid of FCM and PSO have improved accuracy over tradition FCM clustering. In this paper, a new image segmentation method based on Dynamic Particle swarm optimization (DPSO) and FCM algorithm along with the noise reduction mechanism is proposed. DPSO has the advantages to change the inertia weight and learning parameters dynamically. It adopts the inertia weight according to the fitness value and learning parameters along with time. The proposed method combines DPSO with FCM, using the advantages of global optimization searching and parallel computing of DPSO to find a superior result of the FCM algorithm. Moreover, a noise reduction mechanism based on the surrounding pixels is used for enhancing the anti-noise ability. The synthetic image and Magnetic Resonance Imaging (MRI) have been used for testing the proposed method by introducing different types of noises and the results show that the proposed algorithm has better performance and less sensitive to noise.
- Book Chapter
3
- 10.1007/978-981-32-9775-3_81
- Dec 4, 2019
This paper proposes a modified optimal PIDD2 controller for flexible-link manipulator. The single flexible link is modeled mathematically in which the flexible link and base rotation are modeled as stiff systems using Lagrange’s method. The system obtained as a result will have one degree of freedom. In the proposed work, the comparison of two types of controller, i.e., PID and PIDD2, is done for controlling the position and trajectory of the single-link manipulator. The main objective is to control the trajectory with minimum tip oscillation. The tuning of the controllers is done using the Ziegler–Nichols (Z-N) method and Dynamic Particle Swarm Optimization (DPSO) algorithm. The dynamic particle swarm optimization algorithm is an improved version of the particle swarm optimization algorithm which identifies and eliminates the dilemma of stagnation and local optima. The findings show that the PIDD2 controller with dynamically tuned parameters is better in controlling the position and trajectory of the single-link manipulator. All the simulations were performed on MATLAB–SIMULINK.
- Research Article
2
- 10.25236/ajcis.2021.040109
- Jan 1, 2021
- Academic Journal of Computing & Information Science
The octane number of hydrogenated gasoline is difficult to be obtained in real time in the modeling of finished gasoline blending formula. Considering the problems of XGBOOST algorithm, gradient lifting tree algorithm and random forest regression algorithm network, a dynamic harmonious search hybrid particle swarm optimization (DSHPHO) algorithm was proposed to predict the octane number of finished gasoline. In this algorithm, the improved HS algorithm is embedded into the PSO algorithm, and all the particles are considered as harmonious memory (HM). Search by harmony search (HS) algorithm of randomness and evolution mechanism to improve the diversity of particle swarm, makes more ergodic particle swarm at the beginning of the search, reduce sensitivity to the initial value of the algorithm and keep randomly generated in the whole evolution process of the possibility of new particles, fundamentally solves the particle swarm optimization algorithm in dimension increase diversity is less defects. The algorithm has faster convergence speed and better global search ability. Finally, based on this method and industrial historical data, the octane number prediction model of hydrogenated gasoline components is established. The simulation results show that the dynamic harmonious search hybrid particle swarm optimization algorithm has better prediction performance than the traditional particle swarm optimization algorithm, and can be used to predict the octane number.
- Research Article
1
- 10.4304/jcp.8.8.2011-2017
- Jan 8, 2013
- Journal of Computers
For improving the equalization performance of higher-order QAM signals, orthogonal Wavelet transform dynamic Weighted Multi-Modulus blind equalization Algorithm based on the Dynamic Particle Swarm Optimization(DPSO-WWMMA) is proposed. In this proposed algorithm, dynamic particle swarm optimization algorithm and orthogonal wavelet transform are introduced into dynamic Weighted Multi-Modulus blind equalization Algorithm(WMMA). Accordingly, the equalizer weight vector can be optimized by Dynamic Particle Swarm Optimization(DPSO) algorithm, the autocorrelation of the input signals can be reduced via using orthogonal wavelet transform, and the WMMA is used to choose appropriate error model to match QAM constellations. The theoretical analyses and computer simulations in underwater acoustic channels indicate that the proposed algorithm can obtain the fastest convergence rate and the smallest steady mean square error in equalizing high-order QAM signals. So, the proposed algorithm has important reference value in the underwater acoustic communications.
- Research Article
9
- 10.17148/iarjset.2016.3115
- Jan 20, 2016
- IARJSET
1 Abstract: This paper proposes a dynamic particle swarm optimization (PSO) algorithm for optimal generation rescheduling of a power system including renewable energy sources such as the solar and wind energy sources. The algorithm is to minimize total operating costs of this hybrid power system. The proposed dynamic PSO algorithm is one of the standard PSO algorithm variants, which modifies the acceleration coefficients of the cognitive and social components in the velocity update equation of the PSO algorithm as linear time-varying parameters. The acceleration coefficients are varied during the evolution process of the PSO algorithm to improve the global search capability of particles in the early stage of the optimization process and direct the global optima at the end stage. The dynamic PSO algorithm based optimal generation rescheduling of the power system with and without solar and wind powers is considered on the standard IEEE 30-bus 6-generator 41-transmission line test power system. The numerical results demonstrate the capabilities of the proposed algorithm to generate optimal solutions of the power system considering the renewable energy resources. The comparison with the standard PSO algorithm demonstrates the superiority of the proposed algorithm and confirms its potential to reschedule an optimal generation of the power system including the solar and wind energy sources.
- Research Article
- 10.3724/sp.j.1087.2008.00104
- Jul 10, 2008
- Journal of Computer Applications
Dynamic Double-population Particle Swarm Optimization (DDPSO) algorithm was presented to solve the problem that the standard PSO algorithm easily fell into a locally optimized point, where the population was divided into two sub-populations varying with their own evolutionary learning strategies and exchanging between them. The algorithm had been applied to power system Unit Commitment (UC). The DDPSO particle consisted of a two-dimensional real number matrix representing the generation schedule. According to the proposed coding manner, the DDPSO algorithm could directly solve UC. Simulation results show that the proposed method performs better in term of precision and convergence property.
- Book Chapter
1
- 10.1007/978-981-10-1837-4_97
- Aug 24, 2016
This paper investigates a novel inventory and distribution planning model with non-conforming items disposal (NIDPNCID) under fuzzy random environment to minimize the whole process cost. In this process, a certain fraction or a random number of produced items are defective. These non-conforming items are rejected in order to improve the consumer satisfaction. To solve the problem, a dynamic programming-based particle swarm optimization (DP-based PSO) algorithm with fuzzy random simulation is proposed, which can be easy to implement. In more specific terms, DP-based PSO can reduce the dimensions of a particle by using the state equation, which significantly reduced the solution space.
- Conference Article
5
- 10.1109/wcica.2012.6358140
- Jul 1, 2012
For the difficulty of tuning the PID controller parameter to control a complex chaotic system, in order to overcome the shortage of basic particle swarm optimization, this paper improves the inertia weight and introduces the uncontrolled chaotic system into the PSO algorithm, proposes the improved dynamic chaos particle swarm optimization algorithm. This paper applies the algorithm to the chaos PID controller parameter optimization and takes a simulation study on the PID control method for the chaotic ship steering control, the results show that the controller parameter optimized by the proposed method can quickly stabilize the chaotic system to fixed point, and the control effectiveness is demonstrated.
- Research Article
8
- 10.1117/1.oe.52.10.107103
- Oct 4, 2013
- Optical Engineering
An innovative method based on dynamic particle swarm optimization (DPSO) algorithm is presented to demodulate the strain profile along a fiber Bragg grating (FBG) from its reflection spectrum, which is calculated by using the modified transfer matrix method. To improve the optimization performances of algorithm itself, the inertia weight of the DPSO algorithm is adjusted dynamically according to the distance between the individual particle and the global optimal particle in the current population. Then the numerical simulation and experimental verification of the reconstruction of nonuniform strain profiles are comprehensively carried out. Both the simulation examples and experimental results verify the feasibility and validity of the present method.
- Book Chapter
- 10.1007/978-3-642-18387-4_55
- Jan 1, 2011
Risk prediction about investor portfolio holdings can provide powerful test of asset pricing theories. In this paper, we present dynamic Particle Swarm Optimization (PSO) algorithm to Markowitz portfolio selection problem, and improved the algorithm in pseudo code as well as implement in computer program. Furthermore in order to prevent blindness in operation and selection of investment, we tried to make risk least and seek revenue most in investment and so do in the program. As used in practice, it showed great application value.
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