An Efficient Approach for Transforming Unbalanced Transportation Problems into Balanced Problems in Order to Find Optimal Solutions

In operations research, the transportation problem (TP) is among the earliest and most effective applications of the linear programming problem. Unbalanced transportation problems reflect the reality of supply chain and logistics situations where the available supply of goods may not precisely match the demand at different locations. To deal with an unbalanced transportation problem (UTP), it is essential first to convert it into a balanced transportation problem (BTP) to find an initial basic feasible solution (IBFS) and hence the optimal solution. The present paper is concerned with introducing a new approach to convert an unbalanced transportation problem into a balanced one and as a consequence to obtain optimum total transportation cost. Numerical examples are provided to demonstrate the suggested method.

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.

Analysis of the Impact of Optimal Solutions to the Transportation Problems for Variations in Cost Using Two Reliable Approaches

In this paper, we have used two reliable approaches (theorems) to find the optimal solutions to transportation problems, using variations in costs. In real-life scenarios, transportation costs can fluctuate due to different factors. Finding optimal solutions to the transportation problem in the context of variations in cost is vital for ensuring cost efficiency, resource allocation, customer satisfaction, competitive advantage, environmental responsibility, risk mitigation, and operational fortitude in practical situations. This paper opens up new directions for the solution of transportation problems by introducing two key theorems. By using these theorems, we can develop an algorithm for identifying the optimal solution attributes and permitting accurate quantification of changes in overall transportation costs through the addition or subtraction of constants to specific rows or columns, as well as multiplication by constants inside the cost matrix. It is anticipated that the two reliable techniques presented in this study will provide theoretical insights and practical solutions to enhance the efficiency and cost-effectiveness of transportation systems. Finally, numerical illustrations are presented to verify the proposed approaches.

Research on the Optimization of Green Building Performance Based on BIM Technology

With the acceleration of urbanization,the construction industry has developed rapidly worldwide but has also brought serious environmental problems.Traditional architectural design methods often only focus on the function and beauty of the building while ignoring its impact on the environment.In addition,the lack of effective design and construction management methods also led to high resource and energy consumption.To overcome this challenge,the concept of green building came into being.Green buildings emphasize reducing the negative impact of buildings on the environment and improving resource utilization efficiency throughout the entire life cycle.BIM technology provides strong support for achieving this goal.Based on this,starting from the role of BIM technology in green building performance optimization,this article analyzes the optimization of green building performance solutions based on BIM technology in detail to promote the sustainable development of buildings.

ON ALTERNATIVE OPTIMAL SOLUTIONS TO QUASIMONOTONIC PROGRAMMING WITH LINEAR CONSTRAINTS

In this paper, the nonlinear programming problem with quasimonotonic （ both quasiconvex and quasiconcave ）objective function and linear constraints is considered. With the decomposition theorem of polyhedral sets, the structure of optimal solution set for the programming problem is depicted. Based on a simplified version of the convex simplex method, the uniqueness condition of optimal solution and the computational procedures to determine all optimal solutions are given, if the uniqueness condition is not satisfied. An illustrative example is also presented.

Multiple optimal solutions to a sort of nonlinear optimization problem

The optimization problem is considered in which the objective function is pseudolinear（both pseudoconvex and pseudoconcave） and the constraints are linear. The general expression for the optimal solutions to the problem is derived with the representation theorem of polyhedral sets, and the uniqueness condition of the optimal solution and the computational procedures to determine all optimal solutions （if the uniqueness condition is not satisfied ） are provided. Finally, an illustrative example is also given.

Continuity of the optimal value function and optimal solutions of parametric mixed-integer quadratic programs

To properly describe and solve complex decision problems, research on theoretical properties and solution of mixed-integer quadratic programs is becoming very important. We establish in this paper different Lipschitz-type continuity results about the optimal value function and optimal solutions of mixed-integer parametric quadratic programs with parameters in the linear part of the objective function and in the right-hand sides of the linear constraints. The obtained results extend some existing results for continuous quadratic programs, and, more importantly, lay the foundation for further theoretical study and corresponding algorithm analysis on mixed-integer quadratic programs.

A Way to Find All the Optimal Solutions in Linear Programming

With the expression theorem of convex polyhedron, this paper gives the general expression for the solutions in standard linear programming problems. And the calculation procedures in determining the optimal solutions are also given.

The Optimal Solution of the Model with Physical and Human Capital Adjustment Costs

We prove that the model with physical and human capital adjustment costs has optimal solution when the production function is increasing return and the structure of vetor fields of the model changes substantially when the prodution function from decreasing return turns to increasing return. And it is shown that the economy is improved when the coefficients of adjustment costs become small. Key words optimal solution - nonzero equilibrium - adjustment costs CLC number O 29 Foundation item: Supported by the National Natural Science Foundation of China (79970104)Biography: RAO Lan-lan (1978-), female, Master candidate, research direction: mathematical economy.

Dykstra’s Algorithm for the Optimal Approximate Symmetric Positive Semidefinite Solution of a Class of Matrix Equations

Dykstra’s alternating projection algorithm was proposed to treat the problem of finding the projection of a given point onto the intersection of some closed convex sets. In this paper, we first apply Dykstra’s alternating projection algorithm to compute the optimal approximate symmetric positive semidefinite solution of the matrix equations AXB = E, CXD = F. If we choose the initial iterative matrix X0 = 0, the least Frobenius norm symmetric positive semidefinite solution of these matrix equations is obtained. A numerical example shows that the new algorithm is feasible and effective.

Spacecraft Pose Estimation Based on Different Camera Models

Spacecraft pose estimation is an important technology to maintain or change the spacecraft orientation in space.For spacecraft pose estimation,when two spacecraft are relatively distant,the depth information of the space point is less than that of the measuring distance,so the camera model can be seen as a weak perspective projection model.In this paper,a spacecraft pose estimation algorithm based on four symmetrical points of the spacecraft outline is proposed.The analytical solution of the spacecraft pose is obtained by solving the weak perspective projection model,which can satisfy the requirements of the measurement model when the measurement distance is long.The optimal solution is obtained from the weak perspective projection model to the perspective projection model,which can meet the measurement requirements when the measuring distance is small.The simulation results show that the proposed algorithm can obtain better results,even though the noise is large.

An Adaptive Sequential Replacement Method for Variable Selection in Linear Regression Analysis

With the rapid development of DNA technologies, high throughput genomic data have become a powerful leverage to locate desirable genetic loci associated with traits of importance in various crop species. However, current genetic association mapping analyses are focused on identifying individual QTLs. This study aimed to identify a set of QTLs or genetic markers, which can capture genetic variability for marker-assisted selection. Selecting a set with k loci that can maximize genetic variation out of high throughput genomic data is a challenging issue. In this study, we proposed an adaptive sequential replacement (ASR) method, which is considered a variant of the sequential replacement (SR) method. Through Monte Carlo simulation and comparing with four other selection methods: exhaustive, SR method, forward, and backward methods we found that the ASR method sustains consistent and repeatable results comparable to the exhaustive method with much reduced computational intensity.

Orthogonal genetic algorithm for solving quadratic bilevel programming problems

A quadratic bilevel programming problem is transformed into a single level complementarity slackness problem by applying Karush-Kuhn-Tucker（KKT） conditions.To cope with the complementarity constraints,a binary encoding scheme is adopted for KKT multipliers,and then the complementarity slackness problem is simplified to successive quadratic programming problems,which can be solved by many algorithms available.Based on 0-1 binary encoding,an orthogonal genetic algorithm,in which the orthogonal experimental design with both two-level orthogonal array and factor analysis is used as crossover operator,is proposed.Numerical experiments on 10 benchmark examples show that the orthogonal genetic algorithm can find global optimal solutions of quadratic bilevel programming problems with high accuracy in a small number of iterations.

Multi-Objective Task Assignment for Maximizing Social Welfare in Spatio-Temporal Crowdsourcing

With the development of the Internet of Things(IoT),spatio-temporal crowdsourcing(mobile crowdsourcing)has become an emerging paradigm for addressing location-based sensing tasks.However,the delay caused by network transmission has led to low data processing efficiency.Fortunately,edge computing can solve this problem,effectively reduce the delay of data transmission,and improve data processing capacity,so that the crowdsourcing platform can make better decisions faster.Therefore,this paper combines spatio-temporal crowdsourcing and edge computing to study the Multi-Objective Optimization Task Assignment(MOO-TA)problem in the edge computing environment.The proposed online incentive mechanism considers the task difficulty attribute to motivate crowd workers to perform sensing tasks in the unpopular area.In this paper,the Weighted and Multi-Objective Particle Swarm Combination(WAMOPSC)algorithm is proposed to maximize both platform’s and crowd workers’utility,so as to maximize social welfare.The algorithm combines the traditional Linear Weighted Summation(LWS)algorithm and Multi-Objective Particle Swarm Optimization(MOPSO)algorithm to find pareto optimal solutions of multi-objective optimization task assignment problem as much as possible for crowdsourcing platform to choose.Through comparison experiments on real data sets,the effectiveness and feasibility of the proposed method are evaluated.

Multiobjective evolutionary algorithm for dynamic nonlinear constrained optimization problems

A new method to solve dynamic nonlinear constrained optimization problems （DNCOP） is proposed. First, the time （environment） variable period of DNCOP is divided into several equal subperiods. In each subperiod, the DNCOP is approximated by a static nonlinear constrained optimization problem （SNCOP）. Second, for each SNCOP, inspired by the idea of multiobjective optimization, it is transformed into a static bi-objective optimization problem. As a result, the original DNCOP is approximately transformed into several static bi-objective optimization problems. Third, a new multiobjective evolutionary algorithm is proposed based on a new selection operator and an improved nonuniformity mutation operator. The simulation results indicate that the proposed algorithm is effective for DNCOP.

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.

Optimal design of feeding system in steel casting by constrained optimization algorithms based on InteCAST

The traditional foundry industry has developed rapidly in recently years due to advancements in computer technology. Modifying and designing the feeding system has become more convenient with the help of the casting software, Inte CAST. A common method of designing a feeding system is to first design the initial systems, run simulations with casting software, analyze the feedback, and then redesign. In this work, genetic, fruit fly, and interior point optimizer(IPOPT) algorithms were introduced to guide the optimal riser design for the feeding system. The results calculated by the three optimal algorithms indicate that the riser volume has a weak relationship with the modulus constraint; while it has a close relationship with the volume constraint. Based on the convergence rate, the fruit fly algorithm was obviously faster than the genetic algorithm. The optimized riser was also applied during casting, and was simulated using Inte CAST. The numerical simulation results reveal that with the same riser volume, the riser optimized by the genetic and fruit fly algorithms has a similar improvement on casting shrinkage. The IPOPT algorithm has the advantage of causing the smallest shrinkage porosities, compared to those of the genetic and fruit fly algorithms, which were almost the same.

Time variant multi-objective linear fractional interval-valued transportation problem

This paper studies a time-variant multi-objective linear fractional transportation problem. In reality, transported goods should reach in destinations within a specific time. Considering the importance of time, a time-variant multi-objective linear fractional transportation problem is formulated here. We take into account the parameters as cost, supply and demand are interval valued that involved in the proposed model, so we treat the model as a multi-objective linear fractional interval transportation problem. To solve the formulated model, we first convert it into a deterministic form using a new transformation technique and then apply fuzzy programming to solve it. The applicability of our proposed method is shown by considering two numerical examples. At last, conclusions and future research directions regarding our study is included.

Novel electromagnetism-like mechanism method for multiobjective optimization problems

As a new-style stochastic algorithm, the electromagnetism-like mechanism（EM） method gains more and more attention from many researchers in recent years. A novel model based on EM（NMEM） for multiobjective optimization problems is proposed, which regards the charge of all particles as the constraints in the current population and the measure of the uniformity of non-dominated solutions as the objective function. The charge of the particle is evaluated based on the dominated concept, and its magnitude determines the direction of a force between two particles. Numerical studies are carried out on six complex test functions and the experimental results demonstrate that the proposed NMEM algorithm is a very robust method for solving the multiobjective optimization problems.