Weak optimal inverse problems of interval linear programming based on KKT conditions

In this paper,weak optimal inverse problems of interval linear programming(IvLP)are studied based on KKT conditions.Firstly,the problem is precisely defined.Specifically,by adjusting the minimum change of the current cost coefficient,a given weak solution can become optimal.Then,an equivalent characterization of weak optimal inverse IvLP problems is obtained.Finally,the problem is simplified without adjusting the cost coefficient of null variable.

Checking weak and strong optimality of the solution to interval convex quadratic program

In this paper,we investigate three canonical forms of interval convex quadratic pro-gramming problems.Necessary and suficient conditions for checking weak and strong optimality of given vector corresponding to various forms of feasible region,are established respectively.By using the concept of feasible direction,these conditions are formulated in the form of linear systems with both equations and inequalities.In addition,we provide two specific examples to illustrate the efficiency of the conditions.

An Optimal Model for Carbon Sinks of CDM Project to Build a New Countryside Based on Cyclic Economy under Uncertainty

Based on the status and characteristics of Clean Development Mechanism （CDM） renewable energy project and the mode of cyclic economy, aimed at achieving the maximum capacity of carbon sinks in the system, Lvjin Jiayuan—New Countryside Distripark CDM project in Wuchuan County was taken as an example for developing an interval linear programming （ILP） model to optimize the crops planting scheme and cows breeding scheme by using interval optimal method. The case showed that the optimized crops planting scheme and cows breeding scheme obtained from the optimal model was reasonable with relatively preferable overall performance. In the context of meeting economic benefits and fertilizer, electricity demand, [231 287.8, 273 312.7] t of CO2 could be absorbed and fixed, which had increased by [12.94, 33.46]% compared with the feasibility scheme of case project and provided technical support for making the decision in CDM project.

A Hybrid Inexact Optimization Model for Land-use Allocation of China

Land scarcity has become the prominent obstacle on the way to sustainable development for China. Under the constraints of land shortage, how to allocate the finite land resources to the multiple land users in China considering various political, environmental, ecological and economic conditions have become research topics with great significance. In this study, an interval fuzzy national-scale land-use model(IFNLM) was developed for optimizing land systems of China. IFNLM is based on an integration of existing interval linear programming(ILP), and fuzzy flexible programming(FFP) techniques. IFNLM allows uncertainties expressed as discrete interval values and fuzzy sets to be incorporated within a general optimization framework. It can also facilitate national-scale land-use planning under various environmental, ecological, social conditions within a multi-period and multi-option context. Then, IFNLM was applied to a real case study of land-use planning in China. The satisfaction degree of environmental constraints is between 0.69 and 0.97, the system benefit will between 198.25 × 1012 USD and 229.67 × 1012 USD. The results indicated that the hybrid model can help generate desired policies for land-use allocation with a maximized economic benefit and minimized environmental violation risk. Optimized land-use allocation patterns can be generated from the proposed IFNLM.

Predictive simulation and optimal allocation of surface water resources in reservoir basins under climate change

Predicting and allocating surface water resources are becoming increasingly important tasks for addressing the risk of water shortages and challenges of climate change,especially in reservoir basins.However,surface water resource management includes many systematic uncertainties and complexities that are difficult to address.Thus,advanced models must be developed to support predictive simulations and optimal allocations of surface water resources,which are urgently required to ensure regional water supply security and sustainable socioeconomic development.In this study,a soil and water assessment tool-based interval linear multi-objective programming(SWAT-ILMP)model was developed and integrated with climate change scenarios,SWAT,interval parameter programming,and multi-objective programming.The developed model was applied to the Xinfengjiang Reservoir basin in South China and was able to identify optimal allocation schemes for water resources under different climate change scenarios.In the forecast year 2025,the optimal water quantity for power generation would be the highest and account for∼60%of all water resources,the optimal water quantity for water supply would account for∼35%,while the optimal surplus water released from the reservoir would be the lowest at≤5%.In addition,climate change and reservoir initial storage would greatly affect the surplus water quantity but not the power generation or water supply quantity.In general,the SWAT-ILMP model is applicable and effective for water resource prediction and management systems.The results from different scenarios can provide multiple alternatives to support rational water resource allocation in the study area.

Minimum Resistance Ship Hull Uncertainty Optimization Design Based on Simulation-Based Design Method

In the ship hull optimization design based on simulation-based design(SBD) technology, low precision of the approximate model leads to an uncertainty form of optimization model. In order to enable the approximate model with finite precision to maximize the effectiveness, uncertainty optimization method is introduced here.Wave resistance coefficient approximation model, built by back propagation(BP) neural network, is represented as a form of interval. Afterwards, a minimum resistance optimization model is established with the design space constituted by principal dimensions and ship form coefficients. Double-level nested optimization architecture is proposed: for outer layer, improved particle swarm optimization(IPSO) algorithm with learning factor improvement strategy is used to generate design variables, and for inner layer, modified very fast simulated annealing(MVFSA) algorithm is used to solve the objective function interval with uncertainty region. Cases calculation proves the effectiveness and superiority of uncertainty optimization method for ship hull SBD optimization design,thus providing a good way for finding optimal designs.