Multi-objective Dynamic Programming Research Articles

Automated pricing and replenishment decisions for vegetable products based on evaluation optimization models

Based on the commodity information of the supermarket in the annex, the detailed data of historical sales flow, the wholesale price of vegetable commodities and the recent loss rate of vegetable commodities, and through the data analysis of each category and each single product, the automatic pricing and replenishment decision-making model of commodities is established. Use the optimization evaluation algorithm to formulate the total daily replenishment and pricing strategy of each category and each single product. In order to solve the first problem, firstly, the outliers in the original data of Annexes 2 and 3 are cleaned, normalized, feature selected and dimensionally reduced. Secondly, a quarter is taken as a sales cycle of supermarkets, so as to find the proportion of sales volume of a certain category in the same quarter of three years to the total sales volume, and give the distribution law of sales volume of different categories, the results are shown. Considering different periods again, the daily sales volume distribution law is calculated by taking one day as a sales cycle, and the results are shown. Finally, the Pearson grade correlation coefficient is used to judge the relationship between the processing indicators, and the matrix heat map is obtained. According to the two results, it was concluded that there was a significant positive correlation between the sales volume of mosaic and cauliflower vegetables, and a significant negative correlation between the sales volume of nightshade and aquatic root vegetables. In view of the second problem, firstly, considering the functional relationship between the total sales volume and the cost pricing, the correlation analysis and linear fitting were carried out to obtain the linear relationship between the sales price of each category and the maximum value of the sales volume of each category in July of the previous year can be described as Through further nonlinear fitting and optimization problem solving, the total daily replenishment volume and pricing strategy of each vegetable category in the coming week (July 1-7, 2023) are shown in Table 1 and Table 2, which makes the supermarket have the largest revenue In response to the third question, based on the known data, we can analyze the data requirements for each data: we need to know the sales volume of various vegetables during this period, we need to determine the purchase cost of each vegetable, we need to understand the past pricing strategy and response, and we need to know the inventory of various vegetables on June 30. On this basis, a multi-objective dynamic programming model is established, and the total number of saleable items is 30 by using the greedy algorithm to obtain the replenishment quantity of single items on July 1, and the pricing strategy is further solved by using the linear equation fitted in problem 2. In response to the fourth problem , on the basis of the existing sales, wholesale price and loss rate data, in order to better formulate the replenishment and pricing decisions of vegetable products, supermarkets also need to consider and collect the following 12 aspects of relevant data to assist in planning the pricing and replenishment decisions of vegetable products, such as: customer preference and satisfaction survey, seasonality and availability of vegetables, competitor information, inventory costs and storage conditions, historical sales data and trend analysis, customer flow and purchase period, nutritional value and health benefits of vegetables, Socio-economic factors, external environmental factors, policy and regulatory factors, technological and innovation factors, and supply chain and logistics information to ensure more comprehensive and accurate decision-making. Among them, the analysis of historical sales data and trends is mainly carried out.

Energy optimization in freight train operations: Algorithmic development and testing

This research applies multi-objective dynamic programming – specifically, goal programming – solved using a computationally efficient heuristic minimum path-finding algorithm (A*) to improve energy efficiency in freight train operations. The investigation focuses on the U.S. freight network, evaluating the impact of the proposed system on six powertrain technologies, namely diesel, biodiesel, diesel-hybrid, biodiesel-hybrid, hydrogen fuel cell, and battery electric on energy consumption and travel time. The primary findings indicate that when prioritizing energy reduction, diesel and biodiesel hybrids emerge as the most effective, achieving a 47% decrease in energy consumption compared to scenarios without optimization. Hydrogen and battery electric technologies demonstrate a 26% energy saving. In contrast, diesel and biodiesel powertrains show the least improvement, with a 21.5% reduction in energy consumption, accompanied by a 60% increase in travel time for all powertrains except hydrogen, which incurs only a 29% increase. Furthermore, when the multi-objective optimization model incorporates travel time, assigning a 70% weight to energy consumption and a 30% weight to travel time, the results are consistent. In this scenario, diesel and biodiesel hybrids yield an 11% reduction in energy consumption, followed by a 7% reduction for hydrogen fuel cells and a 6% reduction for battery electric trains, with diesel and biodiesel powertrains achieving a 5% reduction. This optimization leads to a mere 7% increase in travel time compared to the non-optimized scenario.

Neutrosophic parametric study of piecewise quadratic fuzzy multi-objective dynamic programming problems

The goal of this research is to investigate fuzzy multiobjective dynamic programming issues with fuzzy parameters in the objective functions and single valued trapezoidal neutrosophic numbers in the left hand side of the constraints. Piecewise quadratic fuzzy numbers characterize these fuzzy parameters. In addition, applying the score function of the neutrosophic numbers to convert the constraints parameters into its crisp . Some basic notions in the problem under the pareto optimal solution concept is redefined and analyzed to study the stability of the problem. Furthermore, a technique is presented for obtaining a subset of the parametric space that has the same pareto optimal solution. For a better understanding and comprehension of the suggested concept, a numerical example is provided.

Research on Multistage Dynamic Trading Model Based on Gray Model and Auto-Regressive Integrated Moving Average Model

Quantitative portfolio investment mainly depends on historical data analysis and market trend prediction to make appropriate decisions, which is an important mean to reduce risks and increase returns. Based on summarizing the existing traditional single forecasting models and multiobjective dynamic programming models, this paper puts forward a new quantitative portfolio model to improve the accuracy of asset price forecasting results and the appropriateness of investment trading strategies, to better realize the maximization of investment returns. This model analyzes and forecasts daily price data by establishing a combination forecasting model of the gray GM (1,1) model and the ARIMA time series model and establishes a multiobjective dynamic programming model with moving average convergence divergence (MACD) and Sharpe ratio indicators as risk constraints to formulate appropriate investment trading strategies. The results show that by solving the quantitative portfolio trading model established in this paper and analyzing the sensitivity and robustness of the model, the price of gold and Bitcoin, two volatile assets, can be accurately predicted, and the best investment portfolio trading strategy can be effectively worked out on the premise of considering the risk level.

Multi-objective dynamic programming with limited precision

This paper addresses the problem of approximating the set of all solutions for Multi-objective Markov Decision Processes. We show that in the vast majority of interesting cases, the number of solutions is exponential or even infinite. In order to overcome this difficulty we propose to approximate the set of all solutions by means of a limited precision approach based on White’s multi-objective value-iteration dynamic programming algorithm. We prove that the number of calculated solutions is tractable and show experimentally that the solutions obtained are a good approximation of the true Pareto front.

Environmental and economic trade-off-based approaches towards urban household waste and crop straw disposal for biogas power generation project -a case study from China

Development and utilization of biomass waste for energy, especially urban household waste and crop straw waste, has garnered global attention. To enable the clean recycling of biomass waste, this study designed a biogas power generation project with a single/mixed raw material input, and established a multi-objective dynamic programming model under an uncertain environment to compare the economic and environmental differences between biogas production and landfill/incineration. Fuzzy membership function was used to deal with the uncertainty problems of daily crop straw yield and methane content in produced biogas. The proposed project and model were then utilized for an actual case area, and scenario analyses were conducted. Through the sensitivity analysis of the profitability expectations and straw input levels, it was found that single-feedstock anaerobic digestion could improve economic benefits while mixed-feedstock anaerobic digestion was more beneficial to reduce carbon emissions. This revealed a mechanism that the project’s objectives of environmental protection and economic development could be regulated through the raw material procurement scheme for urban household waste and crop straw, and the allocation plan of processing capacity for anaerobic digestion with single/mixed raw materials. The results showed that the proposed methodology was efficient for the disposal of the biomass waste, and carbon emissions were only about 30% of that achieve via landfill/incineration. The economic benefits included the achievement of 6.74 ×106 CNY per year. Compared with previous studies, this study reported the successful development of a practical and effective biogas power generation project for treating biomass waste. Effective management methods have been proposed to optimize the processes of anaerobic digestion and power generation to ensure stable project operations.

Methodology of emergency medical logistics for multiple epidemic areas in public health emergency.

Coronavirus disease 2019(COVID-19) has brought great disasters to humanity, and its influence continues to intensify. In response to the public health emergencies, prompt relief supplies are key to reduce the damage. This paper presents a method of emergency medical logistics to quick response to emergency epidemics. The methodology includes two recursive mechanisms: (1) the time-varying forecasting of medical relief demand according to a modified susceptible-exposed-infected- Asymptomatic- recovered (SEIAR) epidemic diffusion model, (2) the relief supplies distribution based on a multi-objective dynamic stochastic programming model. Specially, the distribution model addresses a hypothetical network of emergency medical logistics with considering emergency medical reserve centers (EMRCs), epidemic areas and e-commerce warehousing centers as the rescue points. Numerical studies are conducted. The results show that with the cooperation of different epidemic areas and e-commerce warehousing centers, the total cost is 6% lower than without considering cooperation of different epidemic areas, and 9.7% lower than without considering cooperation of e-commerce warehousing centers. Particularly, the total cost is 20% lower than without considering any cooperation. This study demonstrates the importance of cooperation in epidemic prevention, and provides the government with a new idea of emergency relief supplies dispatching, that the rescue efficiency can be improved by mutual rescue between epidemic areas in public health emergency.

Dynamic multi-objective programming model for improving consumer satisfaction within water supply system under uncertain environment

Water scarcity poses a real crisis for decision makers of water supply system because satisfying growing demand and, as a result, achieving full consumer satisfaction in different sectors of the system remains a major problem. Therefore, this study develops a dynamic multi-objective model of water supply optimization under different scenarios to improve multisectoral consumer satisfaction. To diminish the negative effects of the water crisis on long-term consumer satisfaction, the performance of the dynamic water supply system is evaluated and optimized, which can change the situation from a state of dissatisfaction to satisfaction. In this regard, to analyze the developed model, a real case study of the Hamoun wetland in southeastern Iran is considered. According to the proposed model, various strategies are performed along with the analysis of two scenarios related to runoff uncertainty in order to investigate the consumer satisfaction status in detail. However, given to the final results, which show the greater impact of the two sensitive factors of reliability and vulnerability on consumer satisfaction, the highest level of dissatisfaction is related to the agricultural sector because it has less reliability and higher vulnerability compared to other sectors. In this regard, by proposing policies such as weight scenarios and demand reduction scheme, the situation of consumer satisfaction has improved much more desirable.

Multiobjective Land-Use Optimization Allocation in Eucalyptus-Introduced Regions Based on the GMDP–ACO Model

Large-scale artificial forests have replaced original land cover types such as arable land, garden land, evergreen broad-leaved forest, and Pinus khasya forest. In particular, the widespread introduction of Eucalyptus has caused great changes in land-use patterns and affected ecosystem service functions. How to rationally allocate land, improve the land utilization rate, and ecosystem service functions in a limited land area have become research hotspots. This paper mainly studies the land-use optimization in Lancang County, a large-scale eucalyptus-introduced region, by using the gray multiobjective dynamic programming (GMDP) model and the ant colony optimization (ACO) algorithm. The maximization of social, economic, and ecological benefits is used as the quantitative structure optimization objective in this model, while land-use suitability and spatial compactness are used as the spatial optimization rules. The results show the following: (1) The economic and ecological benefits are significantly improved after optimization compared with those of the current situation and the integrated land-use planning in Lancang County (i.e., the overall plan hereafter or the overall planning of land use by government departments). The social benefits are lower than those in the current situation and overall plan. (2) The suitability of the land-use spatial structure after optimization is improved to some extent compared with the land-use structures of the current situation and overall plan. In particular, the suitability of urban construction land is significantly improved after optimization. (3) The patch density (PD) index of each land-use type is significantly reduced after optimization. The fractal dimension (FRAC) indexes of urban construction land and natural reserves are increased compared with those in the current situation and in the overall plan. The compactness index (CI) of land use increases after optimization, and the degree of land-use fragmentation is improved significantly. (4) Land transfer is greater for arable land, garden land, forests, and natural reserves after optimization. Compared with the overall plan, more high-quality arable land and forest resources may be protected. In conclusion, optimized land use is conducive to promoting the rational use of land resources, socioeconomic development, and environmental protection in eucalyptus-introduced regions.

Multiobjective dynamic programming in bipolar multistage method

The multicriteria Bipolar method can be extended and used to control multicriteria, multistage decision processes. In this extension, at each stage of the given multistage process two sets of reference points are determined, constituting a reference system for the evaluation of stage alternatives. Multistage alternatives, which are compositions of stage alternatives, are assigned to one of six predefined hierarchical classes and then ranked. The aim of this paper is to show the possibility of finding the best multistage alternative, using Bellman’s optimality principle and optimality equations. Of particular importance is a theorem on the non-dominance of the best multistage alternative, proven here. The methodology proposed allows to avoid reviewing each multistage alternative, which is important in large-size problems. The method is illustrated by a numerical example and a brief description of the sustainable regional development problem. The problem can be solved by means of the proposed procedure.

A trade-off multiobjective dynamic programming procedure and its application to project portfolio selection

We consider a stochastic discrete multiobjective programming process with a finite number of stages. The number of states at each stage and the number of feasible decisions at each state are also finite. The aim of the paper is to propose a new interactive procedure for such a problem based on trade-off analysis. The procedure is illustrated with project portfolio selection. There are many organizations with moderately large portfolios of projects. Although the problem under discussion is not very large, it is difficult to solve, since projects are not implemented simultaneously. Moreover, the companies must take into account the risk that a particular project, which is planned to start in the future, may not be ready for implementation. We present an interactive trade-off procedure, based on the stochastic approach, as a new proposition to solve such a problem.

Optimal allocation of regional water resources based on multi-objective dynamic equilibrium strategy

Raising water demand, insufficient freshwater resources and uneven precipitation are the main causes of water conflicts in the river basin. The main challenges in water resources allocation are the following: first, the uncertainty of water supply caused by climate change; second, the dynamic allocation of water resources is not considered; third, there is a lack of equitable water allocation, which may lead to intensified conflicts among the water user sectors. Based on the above challenges, a multi-objective dynamic programming optimal water resources allocation model under uncertainties is established in this paper, which could be a resolution for water disputes as it addresses simultaneously economic, social and environmental benefits. The proposed model considers maximizing the minimum satisfaction degree of each water sector, maximizing the utilization efficiency of water resources in the basin, and maximizing economic benefits. Satisfaction degree function is introduced to optimize water allocation equality in water use sectors (agricultural, domestic, and industrial sectors), and economic efficiency loss acceptance is integrated into the model constraints to control the economic loss corresponding to variations in water availability. In addition, a case study demonstrated the practicality and rationality of the proposed model, and the model results proposed herein show significantly help for a single river basin. Most importantly, the results show that model with dynamic constraint ensures a greater overall economic return for the entire basin, and a larger variation in water resources of sub-area leads to a larger maximum economic efficiency loss. Moreover, the proposed model herein is flexible and can be used in other developing countries/regions only by modifying the parameters according to the actual situation.

Roadmap of green transformation for a steel-manufacturing intensive city in China driven by air pollution control

Steel-manufacturing cities are facing slow economic development and an increasing pressure for improving and protecting their environment, making green economic transformation priority. Located in the capital region, Tangshan is the largest steel producer and is ranked in the top 10 cities in China that have the worst air quality. This study aims to explore an optimisation path to pursue the green transformation of economic development and air-pollution control with incentives on industrial restructure and the implementation of a cleaner production approach. In this study, we construct a green economy transformation decision-making model to establish dynamic optimisation simulation for the period 2016 to 2025. For this purpose, we use integrating methods of system dynamics, input-output modelling, and dynamic multi-objective programming. The simulation results verify the existing a negative development trend under the current situation along with the positive economic development (with acceptable levels of environmental pollution) when there is an increase of investments in clean production technologies. Technology advancement and cost reduction values are explored further. When the technological cost was reduced by 15%, both the highest economic elasticity and an optimal air pollutant control capacity can be achieved simultaneously. Additionally, the growth rate of Tangshan’s GRP can reach 39%, while the NOX and SO2 emissions can be simultaneously reduced by 42% and 36%, respectively by the year 2025 (compared to the emission levels and GRP in 2016). Our study has improved upon previous research methods to put forward a specific optimisation path to achieve green economic transformation for steel-manufacturing cities through industrial structure adjustments and technological updates. This is also conducive to the sustainable development of similar cities that are characterized by heavy industries.

Ensemble Based Forecasting and Optimization Framework to Optimize Releases from Water Supply Reservoirs for Flood Control

Water supply reservoir management is based on long-term management policies which depend on customer demands and seasonal hydrologic changes. However, increasing frequency and intensity of precipitation events is necessitating the short-term management of such reservoirs to reduce downstream flooding. Operational management of reservoirs at hourly/daily timescales is challenging due to the uncertainty associated with the inflow forecasts and the volumes in the reservoir. We present an ensemble-based streamflow prediction and optimization framework consisting of a regional scale hydrologic model forced with ensemble precipitation inputs to obtain probabilistic inflows to the reservoir. A multi-objective dynamic programming model was used to obtain optimized release strategies accounting for the inflow uncertainties. The proposed framework was evaluated at a water supply reservoir in the Hackensack River basin in New Jersey during Hurricanes Irene and Sandy. Hurricane Irene resulted in the overtopping of the dam despite releases made in anticipation of the event and resulted in severe downstream flooding. Hurricane Sandy was characterized by low rainfall, however, raised significant concerns of flooding given the nature of the event. The improvement in NSE for the Hurricane Irene inflows from 0.5 to 0.76 and reduction of the spread of PBIAS with decreasing lead times resulted in improvements in the forecast informed releases. This study provides perspectives on the benefits of the proposed forecasting and optimization framework in reducing the decision making burden on the operator by providing the uncertainties associated with the inflows, releases and the water levels in the reservoir.

Optimization of the National Land Space Based on the Coordination of Urban-Agricultural-Ecological Functions in the Karst Areas of Southwest China

National land spatial planning is dominated by urban-agricultural-ecological functions and has become a Chinese national strategic issue. However, the three functional spaces have serious conflicts in the karst areas, causing inconsistencies in regional development and triggering poverty and a more serious situation for the ecological environment. In this study, we used the gray multi-objective dynamic programming model and the conversion of land use and its effects at small region extent model to simulate the developmental structures of future land use in the karst areas of Southwest China under a socioeconomic development scenario, an arable land protection scenario and an ecological security scenario. Finally, based on the coordination of the urban-agricultural-ecological functions, we used a functional space classification method to optimize the spatial structures of the national land space for 2035 year and to identify different functional areas. The results showed that the three scenarios with different objectives had differences in the quantities and spatial structures of land use but that the area of forestland was the largest and the area of water was the smallest in each scenario. The optimization of the national land space was divided into seven functional areas—urban space, agricultural space, ecological space, urban-agricultural space, urban-ecological space, agricultural-ecological space and urban-agricultural-ecological space. The ecological space was the largest and the urban-ecological space was the smallest among seven functional areas. The different types of functional spaces had significant differentiation characteristics in the layouts. The urban-agricultural space, urban-ecological space, agricultural-ecological space and urban-agricultural-ecological space can effectively alleviate the impacts of human activities and agricultural production activities in karst areas, promote the improvement of rocky desertification and improve the quality of the regional ecological environment. The results of this research can provide support for decisions about the balanced development of the national land space and the improvement of environmental quality in the karst areas.

Evasive Path Planning Under Surveillance Uncertainty

The classical setting of optimal control theory assumes full knowledge of the process dynamics and the costs associated with every control strategy. The problem becomes much harder if the controller only knows a finite set of possible running cost functions, but has no way of checking which of these running costs is actually in place. In this paper we address this challenge for a class of evasive path planning problems on a continuous domain, in which an evader needs to reach a target while minimizing his exposure to an enemy observer, who is in turn selecting from a finite set of known surveillance plans. Our key assumption is that both the evader and the observer need to commit to their (possibly probabilistic) strategies in advance and cannot immediately change their actions based on any newly discovered information about the opponent’s current position. We consider two types of evader behavior: in the first one, a completely risk-averse evader seeks a trajectory minimizing his worst-case cumulative observability, and in the second, the evader is concerned with minimizing the average-case cumulative observability. The latter version is naturally interpreted as a semi-infinite strategic game, and we provide an efficient method for approximating its Nash equilibrium. The proposed approach draws on methods from game theory, convex optimization, optimal control, and multiobjective dynamic programming. We illustrate our algorithm using numerical examples and discuss the computational complexity, including for the generalized version with multiple evaders.

Multiobjective Reservoir Operation Optimization Using Improved Multiobjective Dynamic Programming Based on Reference Lines

Reservoir optimal operation (ROO) needs to coordinate various profit-making objectives, which is a typical multiobjective optimization problem (MOP) with complex constraints. With the development of multiobjective evolutionary algorithms (MOEAs) in the past decades, more and more research has focused on MOEAs to solve MOP. Considering that multiobjective ROO is also a typical multi-stage Markov decision-making problem, this paper introduces the application of multiobjective dynamic programming (MODP) for multiobjective ROO in detail. On this basis, an improved MODP with selection mechanism of non-dominated solutions based on reference lines (MODP-BRL) is proposed to improve the convergence efficiency of MODP. The experimental results show that the proposed MODP-BRL is a reliable and effective tool in solving multiobjective ROO. In addition, MODP-BRL has better performance in convergence effect and efficiency in comparison experiments with NSGAII, NSGAIII, and SPEA2. It is noteworthy that MODP and MODP-BRL are very sensitive to the discrete step. With the decrease of the discrete step (the higher the discrete precision), the computing time increases nonlinearly. The appropriate discrete step of the state variable is key presets to balance the superiority and computational efficiency of non-dominated solutions with the application of MODP and MODP-BRL.

A novel multi-objective Dynamic Programming optimization method: Performance management of a solar thermal power plant as a case study

Due to the intermittent nature of solar irradiance, solar power plants are usually equipped with energy storage systems. Suitable charge and discharge management of the storage systems can considerably help increase the reliability and profitability of the solar systems. In this regard, various optimization approaches, with their own strengths and limitations, have been employed by literature. Dynamic Programming (DP) is one of the fittest approaches for the wide range of engineering problems which exhibit the properties of overlapping sub-problems. DP is a simple, gradient-free, efficient, and deterministic optimization method that guarantees the optimal solution. However, this method has not been developed for multi-objective problems. This study develops a multi-objective DP method and employs it for the performance management of a solar power plant equipped with thermal energy storage system. “Daily electricity generation” and “daily revenue obtained from selling electricity” are considered to be the objective functions. The superiority of the developed method is shown through a comparison with one of the most commonly used multi-objective optimization approaches, NSGA-II. This comparison indicates that the multi-objective DP attains 3.0%–7.5% greater values of electricity generation and 3.1%–12.6% higher values of revenue than NSGA-II, for the different levels of solar radiation.

Hamiltonian Formalism for the Problem of Optimal Motion Control under Multiple Criteria

This paper describes methods for optimizing solutions to problems of controlled dynamics under multiple criteria. Such problems are usually solved by reduction to scalarized costs. However, preferable in realistic cases is the analysis of the whole Pareto front with description of its evolutionary dynamics. This is done via the introduction of vector-valued multiobjective dynamic programming similar to the classical approach described in [1]. It is shown that, under certain conditions, a multiobjective analogue of the classical principle of optimality holds for the introduced vector-valued cost function. As a result, a vector-valued version of the Hamilton–Jacobi–Bellman equation is introduced and the dynamics of the whole Pareto front is presented.

Application of multiobjective dynamic programming to the allocation and reliability problem

Application of multiobjective dynamic programming to the allocation and reliability problem