Linear Programming Method Research Articles

基于线性规划与熵权TOPSIS法的农林牧渔结构最优化模型研究——以山东省为例

基于线性规划与熵权TOPSIS法的农林牧渔结构最优化模型研究——以山东省为例

Multitask Linear Genetic Programming with Shared Individuals and its Application to Dynamic Job Shop Scheduling

Multitask genetic programming methods have been applied to various domains, such as classification, regression, and combinatorial optimization problems. Most existing multitask genetic programming methods are designed based on tree-based structures, which are not good at reusing building blocks since each sub-tree passes its outputs to only one parent. It may limit the design and performance of knowledge sharing in multitask optimization. Different from tree-based genetic programming, building blocks in linear genetic programming can be easily reused by more than one parent. Besides, existing multitask genetic programming methods always allocate each individual to a specific task and have to duplicate genetic materials from task to task in knowledge transfer, which is inefficient and often produces redundancy. Contrarily, it is natural for a linear genetic programming individual to produce multiple distinct outputs, which enables each linear genetic programming individual to solve multiple tasks simultaneously. With this in mind, we propose a new multitask linear genetic programming method that transfers knowledge via multi-output individuals (i.e., shared individuals among tasks). By integrating different solutions into one multi-output individual, the proposed method efficiently reuses common knowledge among tasks and maintains distinct behaviors for each task. The empirical results show that the proposed method has a significantly better test performance than state-of-the-art multitask genetic programming methods. Further analyses verify that the new knowledge transfer mechanism can adjust the transfer rate automatically and thus improves its effectiveness.

A penalty method for linear programming

A logarithmic penalty method for linear optimization problem with a new approximate function is analyzed. The function addressed makes it possible to offer a displacement-step without major difficulties. We consider some numerical results which show the superiority of this approach versus line search methods.

A steepest feasible direction method for linear programming. Derivation and embedding in the simplex method

A feasible direction method for linear programming has been proposed. The method is embedded in the framework of the simplex method, even though it works with non-edge feasible directions. The direction used is the steepest in the space of all variables or an approximation thereof, and it is found by solving a strictly convex quadratic program in the space of the nonbasic variables. Further, this program guarantees the feasibility of the direction even in the case of degeneracy. To remain within the simplex framework, the direction is represented by an auxiliary, or external, nonbasic column, which is a nonnegative linear combination of original nonbasic columns. We have made an experimental evaluation of the suggested method on both nondegenerate and highly degenerate problem instances. The overall results are very promising for continued research along this line, especially concerning various computational strategies that can be applied when the method is implemented.

Biomathematical Modeling in Evaluation Scheme for Large Scale Innovation Competition

This paper discusses the research on the allocation plan between experts and works in large-scale innovation competitions, establishes 0-1 planning model, Z-score evaluation model, PCA evaluation model, fuzzy evaluation model, "range" model, and difference perception evaluation model. It mainly uses linear programming algorithm and PCCs correlation coefficient to obtain the optimal plan for the allocation of experts and works. We use the method of linear programming to establish a 0-1 planning model with the goal function of maximizing the coverage rate of review experts to participating teams and the number of cross reviews, and sets the constraint condition that each work can be reviewed by 5 different review experts, each expert can review 120 different works, all variables are non-negative integers. An optimal solution is obtained, and the average distance between the review experts and works is calculated as 1439.29893, at this time, the comparability of the review plan is strong. Through analysing the relationship between the original scores of experts and awards for works, the three evaluation models are redesigned: Z-score evaluation scheme, PCA evaluation scheme, fuzzy evaluation scheme. The correlation coefficients between the three plans and the original plan are calculated as 0.94, 0.86, and 0.89 respectively. Therefore, it can be seen that the Z-score evaluation scheme is better than the other two schemes. We have designed a new standard score calculation formula to better reflect the level of an article in the overall work, to calculate the ranking of scores, and analyzed it with the actual ranking of award-winning papers agreed upon by multiple experts. The correlation is 96.32%, indicating that the new standard score formula is reliable. By calculating and analysing the average score and range of two stages of reviews, it is found that the average score and range of the first stage are significantly higher than those of the second stage. The reason may be that the experts in the second stage require stricter standards, and their evaluations are more uniform, which can more accurately evaluate works and eliminate differences in scores among different experts. Therefore, it is more reasonable to adopt two stages for review. For those works with excessively large range outside the low range, this paper establishes a "range" model so that these works can be processed programmatically. Through this model, it is concluded that works with large range values have a connection with awards. Based on the method of differential decisionmaking, we established a complete innovation competition evaluation model - difference perception evaluation model. This model innovatively integrates the characteristics of multiple reviews and the differences between expert judges, can quickly output the final results, and calculates MSE as 0.24 and R² as 0.99 by evaluating and testing the model. The results show that the model can effectively improve the quality and efficiency of the review. At the same time, it makes a preliminary comparison and analysis of current review methods and provides suggestions and ideas for future review methods and processes

СРАВНЕНИЕ МЕТОДОВ РЕШЕНИЯ ТРАНСПОРТНОЙ ЗАДАЧИ

Mathematical programming is a mathematical discipline that studies various extremal problems and develops algorithms for solving them. Among the problems are those of mathematical integer programming. Integer programming is indispensable for solving mathematical programming problems in which some or all of the variables take on integer values. The problems include the transport problem. The paper considers the transport problem and three linear programming methods for solving it: the method of potentials, the method of differential rents and the simplex method. The paper analyzes and assesses the effectiveness of the three algorithms for optimizing transport problems. Several linear optimization algorithms have been studied and presented. The paper contains the basic concepts, formulas, and algorithms of the methods used. The method of potentials, the method of differential rents and the simplex method are considered. The results of solving the problem using these methods are presented and compared. All calculations were performed using Excel.

OPTIMIZATION OF THE PROCESS OF SELECTION OF TECHNOLOGIES AND EQUIPMENT FOR PURIFICATION OF WASTEWATER OF ELECTROPLATE PRODUCTION

More and more attention is being paid to energy and resource efficiency issues, which is why for existing technological processes the solution of optimization problems comes to the fore in order to optimize material costs. No less important is the assessment of the human resource, as well a minimizing the possibility of errors at the stage of making a decision on the implementation / design of new processes. It is the environmental sphere that is associated with a high degree of investment risks and requires a careful approach to justifying the introduction of environmental technologies. As part of the work done, the concept of automated decision making was proposed and an economic and mathematical model was developed for solving the optimization problem for choosing a technology or equipment for wastewater treatment systems of an enterprise using the example of electrochemical enterprises (electroplating production) at the stage of justifying investments. As the main tool for processing input data, it is proposed to use software systems based on the use of partial-integer linear programming methods. As input parameters of the system, the initial concentrations of pollutants, volume flow and the required cleaning efficiency are selected. The main technologies for the treatment and neutralization of wastewater from galvanic production, which are currently used or included in the list of the best available technologies, are presented, and a model is proposed that allows the choice of methods and instrumentation for multi-stage treatment processes to achieve the required quality of discharged water with minimal integral costs for the creation and operation of the designed system. The proposed mathematical model can be used both as a training tool for training specialists in water treatment, and for management personnel in the process of selecting and justifying environmental protection measures or at the stage of supervision of equipment suppliers.

Statistical Assessment of the Product Innovation Impact on Employment and Wages in Ukrainian Industry

Innovation activity of industrial enterprises is one of the most important prerequisites for the socio-economic development of the country. Innovations contribute to the growth of labor productivity, value added and profit, and, consequently, to an increase in the level of wages. Studies of patterns of the product innovation impact (measured as an indicator of the share of innovative products in industrial sales) on employment and wages in the industrial sector of the economy has, therefore, significant theoretical and practical importance. The purpose of the article is a statistical assessment of the relationships between product innovation and employment, as well as between product innovation and wages in Ukrainian industry. Analytical confirmation of a significant decrease in the level of product innovation and employment in Ukrainian industry over the past decades is provided. Using correlation-regression analysis methods, it was empirically proven that there is a high positive correlation between the innovativeness of products and the share of industry in the employment structure of the Ukrainian economy. A regression model was built, allowing to determine how the employment in Ukrainian industry will change with changing the product innovativeness by 1 pp. Almon’s method was used to build a distribution-lag model (with a lag of three years) reflecting a high positive dependence of the index of average monthly salary of a full-time employee in the Ukrainian industry on the growth of the product innovation index. On the basis of proven regularities, a deterministic econometric model for optimization of the technological structure of realized industrial products and innovative products in the context of manufacturing industry was developed and tested at the level of Ukraine; the model was used in estimations by linear programming technique. The optimization criterion is a product innovation increase. The results of modeling lay a theoretical basis for strategic macroeconomic planning and socio-economic forecasting, as they allow for choosing a target optimization function at which wages in the manufacturing industry of Ukraine will reach the desired value.
 Innovative activity of industrial enterprises is one of the most important prerequisites for the socio-economic development of the country. Innovations contribute to the growth of labor productivity, added value and profit, and as a result, to an increase in the level of wages. Accordingly, the study of patterns of impact of product innovation (expressed as an indicator of the share of innovative products in the volume of industrial products sold) on employment and wages in the industrial sector of the economy has significant scientific and applied importance. The purpose of the article is a statistical assessment of the relationships between product innovation and employment, as well as between product innovation and wages in Ukrainian industry. Analytical confirmation of a significant decrease in the level of product innovation and employment in Ukrainian industry over the past decades. With the help of correlation-regression analysis methods, it has been empirically proven that there is a high direct relationship between the innovativeness of products and the share of industry in the structure of employment in the Ukrainian economy. A regression model has been built, with the help of which it is possible to determine how employment in Ukrainian industry will change when the innovativeness of products changes by 1 p.p. Using Almon’s method, a distribution-lag model (with a lag of three years) was built, which reflects the high direct dependence of the index of the average monthly salary of a full-time employee of the Ukrainian industry on the growth of the index of product innovation. On the basis of proven regularities, a deterministic economic-mathematical model for optimization of the technological structure of realized industrial products and innovative products in the context of production of the processing industry was developed and tested at the level of Ukraine, which was solved by the method of linear programming. The optimization criterion is the increase in product innovation. The results of modeling form a scientific basis for strategic macroeconomic planning and forecasting of socio-economic development, as they allow choosing such a target optimization function at which wages in the processing industry of Ukraine will reach the desired value.

OPTIMALISASI PRODUKSI ASESORIS SEPEDA MOTOR DI CV BOUDY MOTOR MENGGUNAKAN METODE SIMPLEKS PROGRAM LINEAR DENGAN SOFTWARE POM-QM

CV Boudy Motor is one of the automotive businesses engaged in manufacturing, production of variations of motorcycle accessories. Demand, inventory and production processes constitute a package system in the productivity of industrial profits. This study aims to determine optimal production and profit using the simplex linear program method with POM-QM software. The calculation results, the optimal production for footstep products is 1,000 pcs and a variation ruler is 2,600 pcs. The total overall profit obtained by CV Boudy Motor from footstep products and variation rulers for per day is Rp. 6,900,000 and for per month with 26 days of active period is Rp. 179,000,000 assuming the profit is in accordance with the goal function and fixed constraint function.

PepPre: Promote Peptide Identification Using Accurate and Comprehensive Precursors.

Accurate and comprehensive peptide precursor ions are crucial to tandem mass-spectrometry-based peptide identification. An identification engine can derive great advantages from the search space reduction enabled by credible and detailed precursors. Furthermore, by considering multiple precursors per spectrum, both the number of identifications and the spectrum explainability can be substantially improved. Here, we introduce PepPre, which detects precursors by decomposing peaks into multiple isotope clusters using linear programming methods. The detected precursors are scored and ranked, and the high-scoring ones are used for subsequent peptide identification. PepPre is evaluated both on regular and cross-linked peptide data sets and compared with 11 methods. The experimental results show that PepPre achieves a remarkable increase of 203% in PSM and 68% in peptide identifications compared to instrument software for regular peptides and 99% in PSM and 27% in peptide pair identifications for cross-linked peptides, surpassing the performance of all other evaluated methods. In addition to the increased identification numbers, further credibility evaluations evidence the reliability of the identified results. Moreover, by widening the isolation window of data acquisition from 2 to 8 Th, with PepPre, an engine is able to identify at least 64% more PSMs, thereby demonstrating the potential advantages of wide-window data acquisition. PepPre is open-source and available at http://peppre.ctarn.io.

Economic, energy and environmental analysis and evaluation of hybrid CCHP system considering different buildings: A two-level optimization model

Combined cooling, heating and power (CCHP) integrated energy systems can realize the gradient utilization of energy and the coordination and complementarity of multiple energy sources, which is the primary choice for solving the energy crisis and alleviating the environmental pressure. However, most current design and operational optimizations for CCHP are performed under rule-based operational strategies. This paper constructs a two-level alternating optimization framework for the planning-operation of the CCHP system with an embedded scheduling strategy. The upper-level solves for the optimal capacity configuration of the system to optimize energy, economic and environmental performance, and the lower-level solves for the operating capacity of the equipment system to optimize the operation and maintenance cost. In order to obtain the optimal configuration scheme and scheduling strategy for the system, a novel multi-objective weIghted meaN oF vectOrs (MOINFO)-mixed integer linear programming (MILP) method is proposed. The optimization results suggest that the hybrid CCHP for three buildings (market, office, and restaurant) under the two-level optimization model can achieve better economic, energy, and environmental performance than the rule-based single-level optimization model. Generally, for the market, office and restaurant, the two-Level model achieves maximum economic, energy and environmental performance improvements of 29.12%, 29.88%, and 42.13%; 38.32%, 19.56%, and 34.68%; and 47.37%, 30.93%, and 45.47%, respectively.

Integrated Multi-Vendor Single-Buyer Inventory System Model in Textile Waste Processing Industry

PT. Superbtex Nonwoven Division is one of the industries implementing a green manufacturing system in Bandung by using textile solid waste as raw material and processing it into value-added finished products. However, the solid waste generated by consumers and garment factories is very large and cannot be accommodated in its entirety by PT. Superbtex Nonwoven Division. Another problem arises in terms of inventory both for vendors and buyers; delivering waste from vendors to buyers in small quantities and frequently can lower inventory costs for buyers, but concurrently raise transportation expenses for vendors, and vice versa. Therefore this research was conducted to solve the problem of an integrated multi vendor-single buyer inventory system that considers independent transportation, sorting, and disposal to find the minimum total system cost by finding the optimal value of order lot size, delivery frequency, and proportion of order lot size. that each vendor needs to send to the buyer. Problem-solving is done using the Mixed Integer Non Linear Programming (MINLP) method with the LINGO 18.0 solver. The results obtained from this study stated that the sorting costs at vendor 1 (S1), the sorting costs at the buyer (Sb), the transportation variable costs (Fy), the delivery truck capacity (X), and the demand rate (D) have a significant effect to changes in total system cost (TC). So that the five parameters need to be estimated carefully to determine the optimal system cost.

Evaluating one engine inoperative conditions in subscale electric vertical take-off and landing aircraft: An in-depth tethered hover test analysis

The direction of propeller rotation in a distributed electric-powered vertical take-off and landing (eVTOL) aircraft significantly influences control forces and induced drag during both helicopter and fixed-wing modes. This study proposes a strategy to determine the most effective rotational direction for each propeller. This approach effectively mitigates one-engine-inoperative (OEI) conditions during helicopter mode for a subscale eVTOL referred to as the optionally piloted personal air vehicle (OPPAV). Moreover, the study developed an optimal control law using the linear programming method, which minimizes the maximum power required for individual motors under OEI conditions. The lowest maximum power was achieved under OEI conditions when both the front and rear propellers in each pod rotated in the same direction. Furthermore, to validate this proposed control law, a tethered hover test was performed using the subscale OPPAV under OEI conditions. Our findings demonstrate that determining the rotational direction of propellers using the newly proposed reconfiguration control method significantly enhances the safety of eVTOL aircraft operating under OEI conditions.

Evaluation of Optimal Cost Structure in Agriculture in Raigad District using Linear Programming Model

Agriculture bears a larger impact on India’s economy, especially on the livelihoods of rural areas. While cultivating the crops, farmers have to keep in mind about the costs incurred in the whole process. This research studies about the costs invested in agriculture by farmers in order to optimize the costs using a mathematical model- linear programming. In particular Raigad district was taken for this research and a survey of 25 farms was conducted. This study resulted in minimum costs can be invested, if linear programming is applied, as compared to their traditional method. The analysis shows a significant difference in the costs invested in traditional method and linear programming method.

Optimasi Kapasitasi Produksi Untuk Memperoleh Keuntungan Maksimum dengan Linear Programming Metode Simpleks

This research is a progress report of the project entitled "Optimization of Production Capacitation to Obtain Maximum Profit with Linear Programming Simplex Method (Study on Alltho Beverage UMKM)". This project aims to help the owner of Alltho Micro, Small, and Medium Enterprises (MSMEs) in optimizing the production and profit of their products. In this study, the linear programming method with the simplex method technique was used to find the optimal solution that maximizes the profits of Alltho UMKM. Data on the maximum capacity of raw materials and product selling prices are determining factors in the calculation. The three main products analyzed were Red Velvet Choco Royal, Choco Royal Oreo, and Greentea Choco Royal. The results showed that using the linear programming simplex method, the optimal production quantities of each product were 10.29 Red Velvet Choco Royal drinks and 11.76 Greentea Choco Royal drinks, while the production of Choco Royal Oreo should be temporarily stopped. These results indicate that Alltho MSMEs can achieve maximum profits of around IDR 227,942 by producing these products according to the recommended quantities. This research provides an important contribution to decision-making in MSME production management, helps improve efficiency in resource utilization, and provides an overview of the importance of applying mathematical techniques in optimizing MSME businesses in a competitive era.

The OPTIMALISASI PENDAPATAN AGROINDUSTRI TAHU DAN TEMPE KABO JAYA DI KECAMATAN SANGATTA UTARA KABUPATEN KUTAI TIMUR

This study aims to determine the optimal revenue and income optimization model for UD Bintang Lima Tahu dan Tempe Kabo Jaya in North Sangatta District. This research was conducted from March to May 2022. The data collected method used was interview and direct observation with the owners of UD Bintang Lima Tahu dan Tempe Kabo Jaya as the population as well as respondents. The analytical tool used LINDO Software with the Linear Programming method. The results showed that the revenue optimization model of UD Bintang Lima Tahu dan Tempe Kabo Jaya was by maximizing raw materials, production machine hours and labor hours. In actual conditions, the total production is 3.423 units of tofu/day and 498 units of tempeh/day. Under optimal conditions, it can produce as much as 3.900 tofu/day and 500 tempeh/day. The total income of UD Bintang Lima Tahu dan Tempe Kabo Jaya is Rp 187.260.000,-/month. Total production is 117.000 units of tofu/month and 15.000 units of tempeh/month with an income of Rp 1.555,- from each sale of 1 tofu and an income of Rp 355.- from every sale of 1 tempeh.

Robust coordinated optimization of the thickening-dewatering process under uncertain feeding conditions

The thickening-dewatering process is extensively used in mineral processing process, but there is usually strong uncertainty in the feeding condition of the thickener. In this work, we present a scenario tree-based mixed-integer linear programming (MILP) method for addressing the coordinated optimization of the thickening-dewatering process under uncertain feeding conditions. First, we developed a prediction model using partial least squares (PLS) to estimate the underflow concentration and operation time of each piece of equipment. Subsequently, we formulated a robust MILP model to minimize the energy consumption of the process. This model incorporates several constraints, including starting time, operation time, shutdown time, safety limits, and ladder electricity prices for each piece of equipment. Finally, we divided the uncertain feeding condition into three scenarios to solve the robust coordinated optimization problem. Case studies show that the proposed method can effectively mitigate constraint violations, and reduce safety risks.

A Study on a New Way of Thinking Based on Linear Programming to Analyze Civic Education in Colleges and Universities

Abstract This paper intends to construct a new multi-dimensional preference analysis model for learners by using the improved linear programming method of multi-dimensional preference analysis (LINMAP) to get the weight vector of attributes under the situation that the weights of attributes are completely unknown and for the uncertain multi-attribute decision-making problem that the elements of decision-making matrix are triangular fuzzy numbers, and the preference information is ordered pairs. The data of subjective or objective Civics education learning preferences are aggregated, and the statistical analysis of the data is carried out using SPSS.21 to generate the Civics education learning preference input degree weighting system. The results show that the offline behavioral input weight in the college Civics course is 0.5769, which is greater compared to the online input. And the attribute weights of course Civics preference are calculated to get Z max = 2.29, Z min = 0.73. Multiple feasible solutions can be obtained by taking any value between [0,1]. Based on the development law of the times, this paper makes a new thinking on ideological and political education and actively explores a new road suitable for the development of ideological and political education in colleges and universities.

Bidual Representation of Expectiles

Downside risk measures play a very interesting role in risk management problems. In particular, the value at risk (VaR) and the conditional value at risk (CVaR) have become very important instruments to address problems such as risk optimization, capital requirements, portfolio selection, pricing and hedging issues, risk transference, risk sharing, etc. In contrast, expectile risk measures are not as widely used, even though they are both coherent and elicitable. This paper addresses the bidual representation of expectiles in order to prove further important properties of these risk measures. Indeed, the bidual representation of expectiles enables us to estimate and optimize them by linear programming methods, deal with optimization problems involving expectile-linked constraints, relate expectiles with VaR and CVaR by means of both equalities and inequalities, give VaR and CVaR hyperbolic upper bounds beyond the level of confidence, and analyze whether co-monotonic additivity holds for expectiles. Illustrative applications are presented.

Uncertain linear programming with cloud set constraints integrating fuzziness and randomness

In reality, there is a significant need for processing methods of uncertain programming problems with fuzziness and randomness. Although there are many extensions of fuzzy sets to handle uncertain information, it is rare to organically integrate randomness and fuzziness, such as the cloud set which is the set extension of cloud model. To address the limitations of uncertain linear programming, which lacks consideration of fuzziness and randomness, a new approach called uncertain linear programming with cloud set constraints is proposed. This approach integrates both fuzziness and randomness properties. Firstly, the definition of uncertain linear programming model with cloud set constraints integrating fuzzy and randomness properties is given. Secondly, the construction method of cloud set membership function of uncertain linear programming model is studied. Thirdly, the solution method for uncertain linear programming model based on Ioperation and P operation in cloud set is argued. Finally, the effectiveness of the method is verified through a specific application example and a comparison case with other linear programs. This method of uncertain linear programming with cloud set constraints utilizes the normal cloud set to represent the objective and conditional constraints, effectively capturing the fuzziness and randomness inherent in these constraints. The contribution of this study is that it proposes the use of random membership degree to replace the subjective fixed single membership in the constraints of linear programming. The membership degree of normal cloud set is expressed by a normal random number with a stable tendency, which integrates fuzziness and randomness with a regular, discrete, sparse thickness instead of a fixed curve. It can more effectively express and adapt to the inherent uncertainty of the objective world because various variables in natural science and social science typically follow a normal distribution. So, it has good objectivity and universality.