Multi-objective Nonlinear Programming Research Articles

Distributed AquaCrop simulation-nonlinear multi-objective dependent-chance programming for irrigation water resources management under uncertainty

In the agricultural water resources system, the regional yield is hard to be simulated accurately under the impacts of spatial heterogeneities of soil, weather, and crop types. The optimal water allocation schemes may be not in accordance with actual conditions due to neglecting the actual crop growth process. Meanwhile, the uncertainties in the simulation-optimization models are not easy to be addressed. To deal with the above problems, this paper develops a framework of the distributed AquaCrop simulation nonlinear multi-objective dependent-chance programming (distributed AquaCrop NMOFDCP) for irrigation water resources management under uncertainties. This developed model is applied to a case study of irrigation water resources management in the middle reaches of the Heihe River Basin in China. The 134 homogeneous decision-making units (DMUs) are divided to depict the spatial heterogeneities of the study area, and 472 decision variables (irrigation amount) for 134 DMUs are optimized. Moreover, the model deals with uncertainties expressed as fuzzy goals and tradeoffs relationships between objectives of the yield and water productivity, and measures the satisfactory degrees between objectives and their fuzzy goals. Two groups of Pareto solutions corresponding to the maximum satisfactory degree of the yield, and the maximum satisfactory degree of the water productivity are obtained by the parallel genetic algorithm (PGA) method respectively. In addition, water allocation, satisfactory degree of the yield, and satisfactory degree of water productivity are analyzed at the decision-making unit scale, crop scale, and irrigation-district scale separately. Besides the effects of three weather conditions and four soil types on the system’s outputs are conducted. The results show that weather conditions and soil types have obvious effects on the system’s outputs at three analysis scales, and different water allocation patterns at the growth period affect the yield and water productivity.

A supervised method for scheduling multi-objective job shop systems in the presence of market uncertainties

In real industries, managers usually consider more than one objective in scheduling process. Minimizing completion time, operational costs and average of machine loads are amongst the main concerns of managers during production scheduling in practice. The purpose of this research is to develop a new scheduling method for job-shop systems in the presence of uncertain demands while optimizing completion time, operational costs and machine load average are taken into account simultaneously. In this research a new multi-objective nonlinear mixed integer programming method is developed for job-shop scheduling in the presence of product demand uncertainty. The objectives of the proposed method are minimizing cost, production time and average of machine loads index. To solve the model, a hybrid NSGA-II and Simulated Annealing algorithms is proposed where the core of the solving algorithm is set based on weighting method. In continue a Taguchi method is set for design of experiments and also estimate the best initial parameters for small, medium and large scale case studies. Then comprehensive computational experiments have been carried out to verify the effectiveness of the proposed solution approaches in terms of the quality of the solutions and the solving times. The outcomes are then compared with a classic Genetic Algorithm. The outcomes indicated that the proposed algorithm could successfully solve large-scale experiments less than 2 min (123 s) that is noticeable. While performance of the solving algorithm are taken into consideration, the proposed algorithm could improve the outcomes in a range between 9.07% and 64.96% depending on the input data. The results also showed that considering multi-objective simultaneously more reasonable results would be reached in practice. The results showed that the market demand uncertainty can significantly affect to the process of job shop scheduling and impose harms in manufacturing systems both in terms of completion time and machine load variation. Operational costs, however, did not reflect significantly to market demand changes. The algorithm is then applied for a manufacturing firm. The outcomes showed that the proposed algorithm is flexible enough to be used easily in real industries.

Solution of some multi-objective nonlinear programming problems*

Solution of some multi-objective nonlinear programming problems*

Integrated Algorithm-based Credit Risk Assessment and Credit Decision Guidance

This paper investigates helping banks to assess the strength and creditworthiness of firms based on limited data on MSMEs, which leads to credit risk assessment and lending decisions. In the data of enterprise invoice with complete information, four indicators of annual profit, annual profit rate, annual profit growth rate and reputation rating were selected as independent variables (the last one symbolizes enterprise reputation, the other three symbolize enterprise strength), and whether to default or not as the dichotomous dependent variable, six single classifiers such as LDA, KNeighborsClassifier, NB, SVM, LR and MLP classifiers were trained with one The integrated classifier was finally selected through performance evaluation. For the data with missing reputation ratings, we use three indicators such as enterprise capital turnover, order completion rate, and effective invoicing rate from the data with complete information as features and reputation ratings as labels, and fit a classification prediction model by fisher linear discriminant, and then make predictions for the data with missing information. After excluding firms with a credit rating of D and a high risk factor, we allocated the loan amount to the total amount of the three types of firms according to their size. After fitting the equation for the relationship between APR and customer churn rate, a multi-objective nonlinear programming model was developed to solve the credit strategy with minimum customer churn rate and maximum profit as the objectives and loan amount and APR as the decision variables.

Scenario-Based Network Reconfiguration and Renewable Energy Resources Integration in Large-Scale Distribution Systems Considering Parameters Uncertainty

Renewable energy integration has been recently promoted by many countries as a cleaner alternative to fossil fuels. In many research works, the optimal allocation of distributed generations (DGs) has been modeled mathematically as a DG injecting power without considering its intermittent nature. In this work, a novel probabilistic bilevel multi-objective nonlinear programming optimization problem is formulated to maximize the penetration of renewable distributed generations via distribution network reconfiguration while ensuring the thermal line and voltage limits. Moreover, solar, wind, and load uncertainties are considered in this paper to provide a more realistic mathematical programming model for the optimization problem under study. Case studies are conducted on the 16-, 59-, 69-, 83-, 415-, and 880-node distribution networks, where the 59- and 83-node distribution networks are real distribution networks in Cairo and Taiwan, respectively. The obtained results validate the effectiveness of the proposed optimization approach in maximizing the hosting capacity of DGs and power loss reduction by greater than 17% and 74%, respectively, for the studied distribution networks.

Portfolio optimization of bank credits with interval returns: Empirical evidence from Iran

Bank credit is one of the main sources of spending on productivity and economic services. However, because of the limitations in its amount, accurate planning is essential to optimize its allocation to applicants. Despite the total volume of credits allocated to the agricultural sector, as well as the large number of applicants and sub-sectors applying for these facilities, there is still no clear pattern for the optimal allocation of agricultural bank credits in Iran. It is bank managers who must decide on the distribution of financial capital in a competitive environment. Based on this fact, the paper investigates the optimum portfolio composition of the Agricultural Bank credits in accordance with optimistic, pessimistic, and collaborative strategies by using an interval non-linear multi-objective programming model and considering three different states in determining the rate of return using a genetic algorithm. The results showed that the current pattern of the distribution of bank credits is estimated as different from the optimal one. In the optimum patterns estimated in all states, the agriculture, agricultural services, animal husbandry, aviculture and greenhouses sections were assigned the largest shares in their optimum portfolio combination. Managers can choose their desired model according to three studied strategies and depending on the importance, different estimates of return, and risk of each of them.

Operational mine planning in block cave mining: a simulation-optimisation approach

ABSTRACT Block cave mining operations face challenges to meet daily operational production targets. The optimistic long-term and medium-term plans along with uncertainty and the synergistic effect of the mechanical and structural failures in operational levels of the mine cause a significant deviation from production plan targets. The on-site tuning of the mining production targets in real time are neither the best practice nor the optimum approach to compensate for shortfalls in production. The objective of this paper is to develop a methodology that generates practical and near-optimal short-term mine plans for block caving operations in the presence of operational uncertainty. To accomplish this goal, we propose a simulation-optimisation approach using a Monte Carlo simulation model and a multi-objective non-linear goal programming model that takes into consideration operational constraints and uncertainties. In a case study, we compare the results of the proposed methodology against the mine plan and the historical production data of a copper block cave operation. The strengths and weaknesses of the model are presented and discussed.

A Hybrid Mehta-Heuristic algorithm for optimization location-routing problem of facilities in four echelon supply chain

During the last three decades, the concept of integrated decision making in the supply chain becomes one of the essential aspects of supply chain management (SCM). This concept explores the interdependence between facility location, flow allocation between facilities, transportation system structure, and inventory control system. This study presents a new form of the location-routing problem of facilities under uncertainty in a supply chain network for deteriorating items through taking environmental considerations, cost, and procurement time and customer satisfaction into account, to simultaneously minimize total system costs, maximal delivery time and emissions across the entire network and maximize customer satisfaction. The research problem is formulated in a mixed-integer nonlinear multi-objective programming. In order to solve the model, the combination of the two Benders decomposition algorithm and Lagrange multiplier liberalization, as well as the combination of red deer algorithm and annealing simulation, was proposed. For validation, the results of the proposed algorithm in different size examples are compared with the results of the exact method solution by MATLAB software. The mean error of the proposed algorithm for the objective function is less than 4% compared to the exact method in solving the sample problems. Besides, the results of the algorithm performance are investigated based on standard indices. The computational results show the efficiency of the algorithm for a wide range of problems with different sizes. The location decisions are interdependent, and the process of determining the optimal values of these variables interact together, which can lead to an optimal system.

On optimistic, pessimistic and mixed approaches under different membership functions for fully intuitionistic fuzzy multiobjective nonlinear programming problems

The concept of measuring the membership degree along with a non-membership degree, gives rise to the intuitionistic fuzzy set theory. The present study formulates a nonlinear programming problem with multiple objectives, including all the parameters and decision variables as intuitionistic fuzzy numbers. The problem is further investigated subject to optimistic, pessimistic and mixed approaches under linear, exponential and hyperbolic membership functions. The article redefines pessimistic and mixed point of view to be in the true spirit compatible with the definition of an intuitionistic fuzzy number. Accuracy function is used to reduce the problem to an equivalent crisp multiobjective nonlinear programming problem and then optimal compromise solution is obtained under different approaches using various membership/non-membership functions. At appropriate places, theorems have also been proved to establish the equivalence between the original formulation and its crisp counterparts under each approach. Further, practical applications in production planning and transportation problem are illustrated to explain the optimistic, pessimistic and mixed approaches using the proposed algorithm and finally a comparison is also drawn.

Bi-Objective Optimization of Service-Oriented Location-Pricing Model Using Electromagnetism-Like Mechanism Algorithm

This paper develops a multi-objective multi-layer location-pricing (MLLP) model with congested facilities in which the facilities act like a classic queuing system. The customers who arrive to this system receive service at all layers in a predetermined order to fulfill their demands. The goal is to determine (1) optimal number of the facilities required at each layer, (2) optimal allocation of customers to facilities, and (3) optimal price of providing service at each layer. The objective functions are to maximize the total profit of the system and to minimize the sum of travel and waiting times, simultaneously. The problem is formulated as a multi-objective nonlinear integer mathematical programming model. Since the problem is hard to be solved analytically, we present a multi-objective meta-heuristic algorithm (MHA) based on an electromagnetism-like mechanism (ELM) as a solution for multi-objective MLLP. This algorithm used an elitist mechanism to strengthen the structure of search engine in order to find better quality solutions. The results indicate the efficiency and effectiveness of the proposed algorithm in comparison with the traditional ELM.

Optimal design of the water-energy-food nexus for rural communities

People from rural areas face some limitations to reach sustainable development, such as the lack of electricity. In this work, we propose a multi-objective nonlinear programming model to find the optimal design and operation of water, energy, and food systems for agricultural communities. To this aim, we develop, using a bottom-up approach, a mathematical formulation of a superstructure that includes renewable power technologies, water management devices, and food and energy crops. Numerical experiments are carried out using data from a community in Michoacan, Mexico. The results from the sensitivity analyses show that selling bioethanol as an economic activity can be attractive for this community by slightly increasing the biofuel price and the sugarcane yield. Moreover, the epsilon-constraint method, along with a Pareto filter, is applied to obtain compromised solutions. Some of these solutions represent a significant improvement in social and environmental dimensions while maintaining an acceptable economic index. These results show this methodology’s usefulness for analyzing economic opportunities and obtaining strategies to manage the Water-Energy-Food Nexus (WEFN), especially the land distribution between food and energy crops. The model proposed constitutes a contribution, as a decision-making tool, to the sustainable development of rural communities.

Evaluation of environmental consequences affecting human health in the current and optimal cropping patterns in the eastern Lorestan Province, Iran.

Planning for optimal use of resources and reduction of environmental impacts, in addition to resource protection, is associated with increasing farmers' revenues and boosting the regional economy. Given the limited resources and environmental impacts of agricultural activities on human health, it is necessary to determine an appropriate cropping pattern. The present research aimed to maximize net profit and minimize environmental impacts, including the releases of carcinogens, noncarcinogens, ozone layer depletion, ionizing radiation, and respiratory inorganics and organics on human health. In this study, an optimal cropping pattern of irrigated and rainfed crops was proposed for the east of Lorestan Province using multi-objective nonlinear programming (MOP). Results showed that the cropping areas of chickpea, rapeseed, and potatoes decreased by 50% in the irrigated crop of MOP model and that of lentil in the MOP model of rainfed crops compared with the current pattern. Another important result was increases in the cropping areas of lentil and bean in the MOP pattern of irrigated crops and wheat in the rainfed MOP model. The environmental impacts of agricultural sector on human health can be reduced by determining an optimal cropping pattern. The implementation of this model in the region reduced the emissions of carcinogens (4%), noncarcinogens (9%), respiratory inorganics (17%), ionizing radiation (14%), ozone layer depletion (17%), and respiratory organics (15%) compared with the existing situation along with an increased net profit of $968,483. According to the findings, consideration of environmental objectives affecting human health is essential in the optimization of the cropping pattern. In addition to optimal use of water and land resources, using the proposed model helps to increase profits and reduce environmental consequences on human health.

Regional Integrated Energy Site Layout Optimization Based on Improved Artificial Immune Algorithm

Regional integrated energy site layout optimization involves multi-energy coupling, multi-data processing and multi-objective decision making, among other things. It is essentially a kind of non-convex multi-objective nonlinear programming problem, which is very difficult to solve by traditional methods. This paper proposes a decentralized optimization and comprehensive decision-making planning strategy and preprocesses the data information, so as to reduce the difficulty of solving the problem and improve operational efficiency. Three objective functions, namely the number of energy stations to be built, the coverage rate and the transmission load capacity of pipeline network, are constructed, normalized by linear weighting method, and solved by the improved p-median model to obtain the optimal value of comprehensive benefits. The artificial immune algorithm was improved from the three aspects of the initial population screening mechanism, population updating and bidirectional crossover-mutation, and its performance was preliminarily verified by test function. Finally, an improved artificial immune algorithm is used to solve and optimize the regional integrated energy site layout model. The results show that the strategies, models and methods presented in this paper are feasible and can meet the interest needs and planning objectives of different decision-makers.

Multiobjective Optimization on Hierarchical Refugee Evacuation and Resource Allocation for Disaster Management

This paper studies a location-allocation problem to determine the selection of emergency shelters, medical centers, and distribution centers after the disaster. The evacuation of refugees and allocation of relief resources are also considered. A mixed-integer nonlinear multiobjective programming model is proposed to characterize the problem. The hierarchical demand of different refugees and the limitations of relief resources are considered in the model. We employ a combination of the simulated annealing (SA) algorithm and the particle swarm optimization (PSO) algorithm method to solve the complex model. To optimize the result of our proposed algorithm, we absorb the group search, crossover, and mutation operator of GA into SA. We conduct a case study in a district of Beijing in China to validate the proposed methodology. Some computational experiments are conducted to analyze the impact of different factors, such as the target weight setting, selection of candidate shelters, and quantity of relief resources.

Solving matrix games with hesitant fuzzy pay-offs

The objective of this paper is to develop matrix games with pay-offs of triangular hesitant fuzzy elements (THFEs). To solve such games, a new methodology has been derived based on the notion of weighted average operator and score function of THFEs. Firstly, we formulate two non-linear programming problems with THFEs. Then applying the score function of THFEs, we transform these two problems into two non-linear multi-objective programming problems with triangular fuzzy numbers (TFNs). Finally, the Lexicographic method is used to solve these two multi-objective programming problems. A market share problem is considered to show the validity and applicability of the proposed methodology.

A multi-stage activated carbon impregnation system: Isotherms, kinetics and multi-objective modeling optimization

A multi-stage activated carbon impregnation system, with a special emphasis on solvent reuse, is introduced and optimized in this study. Experiments and modeling optimization are combined to simultaneously minimize the solute consumption and operating time for the system. The adsorption isotherm and kinetic models are well regressed based on a series of experiments on activated carbon impregnated in triethylene tetramine solution. A multi-objective nonlinear programming optimization framework is then formulated based on the regressed isotherm and kinetic models and material balance, including activated carbon, solute, water and impurities at each stage in the system. The AUGMECON method and global solver ANTIGONE are used to solve the challenging optimization problem, and the pareto optimal solutions are obtained. Additionally, a new dimensionless number is presented to further coordinate the operating parameters for the system. The result shows that the specific solute consumption and operating time are decreased by 65.11% and 85.88%, respectively.

Optimization for multi-objective sum of linear and linear fractional programming problem: fuzzy nonlinear programming approach

Multi-objective linear plus linear fractional programming problem is an emerging tool for solving problems in different environments such as production planning, financial and corporate planning and healthcare and hospital planning which has attracted many researchers in recent years. This paper presents a method to find a Pareto optimal solution for the multi-objective linear plus linear fractional programming problem through nonlinear membership function. The proposed approach defines a fuzzy goal for each objective through a nonlinear membership function. By means of nonlinear membership function, the multi-objective linear plus linear fractional programming problem transformed into a multi-objective nonlinear programming problem. Applying the linear approximation method, the nonlinear objectives are converted into linear. In order to solve the multi-objective linear programming problem, the fuzzy goal programming model is formulated by minimizing the negative deviational variables. The proposed procedure is illustrated through numerical examples and a real-life application problem. Further, it is compared with the existing methods. Finally, the Euclidean distance function has been used to prove the efficiency of the proposed method.

Developing a novel inverse data envelopment analysis (DEA) model for evaluating after‐sales units

AbstractThis paper proposes a novel model of inverse data envelopment analysis (IDEA) based on the slack‐based measure (SBM) approach. The developed inverse SBM model can maintain relative efficiency of decision making units (DMUs) with new input and output. This model can also measure the input and output volumes when a decision maker (DM) increases efficiency score. The inverse SBM model is a kind of multi‐objective non‐linear programming (MONLP) problem, which is not easy to solve. Therefore, we suggest a linear programming model for solving inverse SBM model. In this model efficiency score of DMU under evaluation remains unchanged. Furthermore, we suggest an optimal combination of inputs and outputs in the production possibility set (PPS). A case study is presented to demonstrate the efficacy of our proposed model.

Immune optimization algorithm for nonlinear multi-objective probabilistic constrained programming

Immune optimization algorithm for nonlinear multi-objective probabilistic constrained programming

(1905-5222) Solving Matrix Games with Hesitant Fuzzy Pay-offs

The objective of this paper is to develop matrix games with pay-offs of triangular hesitant fuzzy elements (THFEs).To solve such games, a new methodology has been derived based on the notion of weighted average operator and scorefunction of THFEs. Firstly, we formulate two non-linear programming problems with THFEs. Then applying thescore function of THFEs, we transform these two problems into two non-linear multi-objective programming problemswith triangular fuzzy numbers (TFNs). Finally, the Lexicographic method is used to solve these two multi-objectiveprogramming problems. A market share problem is considered to show the validity and applicability of the proposedmethodology.