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.

An Optimization Approach for Convolutional Neural Network Using Non-Dominated Sorted Genetic Algorithm-Ⅱ

In computer vision,convolutional neural networks have a wide range of uses.Images representmost of today’s data,so it’s important to know how to handle these large amounts of data efficiently.Convolutional neural networks have been shown to solve image processing problems effectively.However,when designing the network structure for a particular problem,you need to adjust the hyperparameters for higher accuracy.This technique is time consuming and requires a lot of work and domain knowledge.Designing a convolutional neural network architecture is a classic NP-hard optimization challenge.On the other hand,different datasets require different combinations of models or hyperparameters,which can be time consuming and inconvenient.Various approaches have been proposed to overcome this problem,such as grid search limited to low-dimensional space and queuing by random selection.To address this issue,we propose an evolutionary algorithm-based approach that dynamically enhances the structure of Convolution Neural Networks(CNNs)using optimized hyperparameters.This study proposes a method using Non-dominated sorted genetic algorithms(NSGA)to improve the hyperparameters of the CNN model.In addition,different types and parameter ranges of existing genetic algorithms are used.Acomparative study was conducted with various state-of-the-art methodologies and algorithms.Experiments have shown that our proposed approach is superior to previous methods in terms of classification accuracy,and the results are published in modern computing literature.

Bi-Objective Optimization: A Pareto Method with Analytical Solutions

Multiple objectives to be optimized simultaneously are prevalent in real-life problems. This paper develops a new Pareto Method for bi-objective optimization which yields analytical solutions. The Pareto optimal front is obtained in closed-form, enabling the derivation of various solutions in a convenient and efficient way. The advantage of analytical solution is the possibility of deriving accurate, exact and well-understood solutions, which is especially useful for policy analysis. An extension of the method to include multiple objectives is provided with the objectives being classified into two types. Such an extension expands the applicability of the developed techniques.

A FLEXIBLE OBJECTIVE-CONSTRAINT APPROACH AND A NEW ALGORITHM FOR CONSTRUCTING THE PARETO FRONT OF MULTIOBJECTIVE OPTIMIZATION PROBLEMS

In this article, a novel scalarization technique, called the improved objective-constraint approach, is introduced to find efficient solutions of a given multiobjective programming problem. The presented scalarized problem extends the objective-constraint problem. It is demonstrated that how adding variables to the scalarized problem, can lead to find conditions for (weakly, properly) Pareto optimal solutions. Applying the obtained necessary and sufficient conditions, two algorithms for generating the Pareto front approximation of bi-objective and three-objective programming problems are designed. These algorithms are easy to implement and can achieve an even approximation of (weakly, properly) Pareto optimal solutions. These algorithms can be generalized for optimization problems with more than three criterion functions, too. The effectiveness and capability of the algorithms are demonstrated in test problems.

A Multi-Objective Optimization for Locating Maintenance Stations and Operator Dispatching of Corrective Maintenance

In this study,we introduce a novel multi-objective optimization model tailored for modern manufacturing,aiming to mitigate the cost impacts of operational disruptions through optimized corrective maintenance.Central to our approach is the strategic placement of maintenance stations and the efficient allocation of personnel,addressing a crucial gap in the integration of maintenance personnel dispatching and station selection.Our model uniquely combines the spatial distribution of machinery with the expertise of operators to achieve a harmonious balance between maintenance efficiency and cost-effectiveness.The core of our methodology is the NSGA Ⅲ+Dispatch,an advanced adaptation of the Non-Dominated Sorting Genetic Algorithm Ⅲ(NSGA-Ⅲ),meticulously designed for the selection of maintenance stations and effective operator dispatching.This method integrates a comprehensive coding process,crossover operator,and mutation operator to efficiently manage multiple objectives.Rigorous empirical testing,including a detailed analysis from a taiwan region electronic equipment manufacturer,validated the effectiveness of our approach across various scenarios of machine failure frequencies and operator configurations.The findings reveal that the proposed model significantly outperforms current practices by reducing response times by up to 23%in low-frequency and 28.23%in high-frequency machine failure scenarios,leading to notable improvements in efficiency and cost reduction.Additionally,it demonstrates significant improvements in oper-ational efficiency,particularly in selective high-frequency failure contexts,while ensuring substantial manpower cost savings without compromising on operational effectiveness.This research significantly advances maintenance strategies in production environments,providing the manufacturing industry with practical,optimized solutions for diverse machine malfunction situations.Furthermore,the methodologies and principles developed in this study have potential applications in various other sectors,including healthcare,transportation,and energy,where maintenance efficiency and resource optimization are equally critical.

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.

Improved non-dominated sorting genetic algorithm (NSGA)-II in multi-objective optimization studies of wind turbine blades

The non-dominated sorting genetic algorithm （NSGA） is improved with the controlled elitism and dynamic crowding distance. A novel multi-objective optimization algorithm is obtained for wind turbine blades. As an example, a 5 MW wind turbine blade design is presented by taking the maximum power coefficient and the minimum blade mass as the optimization objectives. The optimal results show that this algorithm has good performance in handling the multi-objective optimization of wind turbines, and it gives a Pareto-optimal solution set rather than the optimum solutions to the conventional multi objective optimization problems. The wind turbine blade optimization method presented in this paper provides a new and general algorithm for the multi-objective optimization of wind turbines.

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.

Copper smelter slag treatment by ammonia solution:Leaching process optimization

The feasibility of copper smelter slag processing by ammonia solution treatment was investigated. The central composite rotatable design(CCRD) and approximation method were used to determine the optimum conditions of zinc and copper recovery to a solution. The experimental design was done at five levels of the four operating parameters which were the initial concentration of NH–3, the initial Cl ions concentration, leaching time and solid/liquid ratio. Two mathematical models describing dependence of metal recovery on the operating parameters were obtained. The models are successful in predicting the responses. It was found that optimal parameters for zinc and copper recovery are as follows(values for copper are given in brackets): initial CNH3 17.1%(19.9%), initial CCl– 160 g/L(160 g/L), leaching process duration 4.56 h(4.13 h), solid/liquid ratio 0.39(0.53). The maximum Zn and Cu recoveries to solution, obtained experimentally under the conditions, are 81.16% and 56.48%, respectively.

CHARACTERIZATION OF EFFICIENT SOLUTIONS FOR MULTI-OBJECTIVE OPTIMIZATION PROBLEMS INVOLVING SEMI-STRONG AND GENERALIZED SEMI-STRONG E-CONVEXITY

The authors of this article are interested in characterization of efficient solutions for special classes of problems. These classes consider semi-strong E-convexity of involved functions. Sufficient and necessary conditions for a feasible solution to be an efficient or properly efficient solution are obtained.

Non-dominated sorting quantum particle swarm optimization and its application in cognitive radio spectrum allocation

In order to solve discrete multi-objective optimization problems, a non-dominated sorting quantum particle swarm optimization (NSQPSO) based on non-dominated sorting and quantum particle swarm optimization is proposed, and the performance of the NSQPSO is evaluated through five classical benchmark functions. The quantum particle swarm optimization (QPSO) applies the quantum computing theory to particle swarm optimization, and thus has the advantages of both quantum computing theory and particle swarm optimization, so it has a faster convergence rate and a more accurate convergence value. Therefore, QPSO is used as the evolutionary method of the proposed NSQPSO. Also NSQPSO is used to solve cognitive radio spectrum allocation problem. The methods to complete spectrum allocation in previous literature only consider one objective, i.e. network utilization or fairness, but the proposed NSQPSO method, can consider both network utilization and fairness simultaneously through obtaining Pareto front solutions. Cognitive radio systems can select one solution from the Pareto front solutions according to the weight of network reward and fairness. If one weight is unit and the other is zero, then it becomes single objective optimization, so the proposed NSQPSO method has a much wider application range. The experimental research results show that the NSQPS can obtain the same non-dominated solutions as exhaustive search but takes much less time in small dimensions; while in large dimensions, where the problem cannot be solved by exhaustive search, the NSQPSO can still solve the problem, which proves the effectiveness of NSQPSO.

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.

ε-strongly Efficient Solutions for Vector Optimization with Set-valued Maps

In locally convex Hausdorff topological vector spaces,ε-strongly efficient solutions for vector optimization with set-valued maps are discussed.Firstly,ε-strongly efficient point of set is introduced.Secondly,under the nearly cone-subconvexlike set-valued maps,the theorem of scalarization for vector optimization is obtained.Finally,optimality conditions of ε-strongly efficient solutions for vector optimization with generalized inequality constraints and equality constraints are obtained.

Multi-objective optimization of water supply network rehabilitation with non-dominated sorting Genetic Algorithm-II

Through the transformation of hydraulic constraints into the objective functions associated with a water supply network rehabilitation problem, a non-dominated sorting Genetic Algorithm-II (NSGA-II) can be used to solve the altered multi-objective optimization model. The introduction of NSGA-II into water supply network optimal rehabilitation problem solves the conflict between one fitness value of standard genetic algorithm (SGA) and multi-objectives of rehabilitation problem. And the uncertainties brought by using weight coefficients or punish functions in conventional methods are controlled. And also by in-troduction of artificial inducement mutation (AIM) operation, the convergence speed of population is accelerated;this operation not only improves the convergence speed, but also improves the rationality and feasibility of solutions.

Multi-Objective Optimization of Water-Sedimentation-Power in Reservoir Based on Pareto-Optimal Solution

A multi-objective optimal operation model of water-sedimentation-power in reservoir is established with power-generation, sedimentation and water storage taken into account. Moreover, the inertia weight self-adjusting mechanism and Pareto-optimal archive are introduced into the particle swarm optimization and an improved multi-objective particle swarm optimization （IMOPSO） is proposed. The IMOPSO is employed to solve the optimal model and obtain the Pareto-optimal front. The multi-objective optimal operation of Wanjiazhai Reservoir during the spring breakup was investigated with three typical flood hydrographs. The results show that the former method is able to obtain the Pareto-optimal front with a uniform distribution property. Different regions （A, B, C） of the Pareto-optimal front correspond to the optimized schemes in terms of the objectives of sediment deposition, sediment deposition and power generation, and power generation, respectively. The level hydrographs and outflow hydrographs show the operation of the reservoir in details. Compared with the non-dominated sorting genetic algorithm-Ⅱ （NSGA-Ⅱ）, IMOPSO has close global optimization capability and is suitable for multi-objective optimization problems.

Solution of Chemical Dynamic Optimization Using the Simultaneous Strategies

An approach of simultaneous strategies with two novel techniques is proposed to improve the solution accuracy of chemical dynamic optimization problems. The first technique is to handle constraints on control vari- ables based on the finite-element collocation so as to control the approximation error for discrete optimal problems, where a set of control constraints at dement knots are integrated with the procedure for optimization leading to a significant gain in the accuracy of the simultaneous strategies. The second technique is to make the mesh refine- ment more feasible and reliable by introducing length constraints and guideline in designing appropriate element length boundaries, so that the proposed approach becomes more efficient in adjusting dements to track optimal control profile breakpoints and ensure accurate state and centrol profiles. Four classic benchmarks of dynamic op- timization problems are used as illustrations, and the proposed approach is compared with literature reports. The research results reveal that the proposed approach is preferz,ble in improving the solution accuracy of chemical dy- namic optimization problem.

Near-Infrared Spectroscopy Combined with Absorbance Upper Optimization Partial Least Squares Applied to Rapid Analysis of Polysaccharide for Proprietary Chinese Medicine Oral Solution

Near-infrared (NIR) spectroscopy was applied to reagent-free quantitative analysis of polysaccharide of a brand product of proprietary Chinese medicine (PCM) oral solution samples. A novel method, called absorbance upper optimization partial least squares (AUO-PLS), was proposed and successfully applied to the wavelength selection. Based on varied partitioning of the calibration and prediction sample sets, the parameter optimization was performed to achieve stability. On the basis of the AUO-PLS method, the selected upper bound of appropriate absorbance was 1.53 and the corresponding wavebands combination was 400 - 1880 & 2088 - 2346 nm. With the use of random validation samples excluded from the modeling process, the root-mean-square error and correlation coefficient of prediction for polysaccharide were 27.09 mg·L-1 and 0.888, respectively. The results indicate that the NIR prediction values are close to those of the measured values. NIR spectroscopy combined with AUO-PLS method provided a promising tool for quantification of the polysaccharide for PCM oral solution and this technique is rapid and simple when compared with conventional methods.

Finding Symbolic and All Numerical Solutions for Design Optimization Based on Monotonicity Analysis and Solving Polynomial Systems

A method for determining symbolic and all numerical solutions in design optimization based on monotonicity analysis and solving polynomial systems is presented in this paper. Groebner Bases of the algebraic system equivalent to the subproblem of the design optimization is taken as the symbolic (analytical) expression of the optimum solution for the symbolic optimization, i.e. the problem with symbolic coefficients. A method based on substituting and eliminating for determining Groebner Bases is also proposed, and method for finding all numerical optimum solutions is discussed. Finally an example is given, demonstrating the strategy and efficiency of the method.

Optimization of separation processing of copper and iron of dump bioleaching solution by Lix 984N in Dexing Copper Mine

The effects of the concentration of Lix 984N,phase ratio,initial pH value of aqueous phase and extraction time on the extraction of copper and iron under the condition of low Cu2+ /Fe3+ ratio in dump bioleaching solution of Dexing Copper Mine were explored.The optimal conditions of extraction are as follows: the concentration of Lix 984N 10%; the phase ratio (O/A) 1:1; the initial pH value of aqueous phase 1.5 and the mixing time 2 min.The stripping experiments show that H2SO4 solution could efficiently recover copper from the organic phase under the optimal conditions.

Optimal Power Flow Solution Using Particle Swarm Optimization Technique with Global-Local Best Parameters

This paper proposes an efficient method for optimal power flow solution （OPF） using particle swarm optimization （PSO） technique. The objective of the proposed method is to find the steady state operation point in a power system which minimizes the fuel cost, while maintaining an acceptable system performance in terms of limits on generator power, line flow limits and voltage limits. In order to improvise the performance of the conventional PSO （cPSO）, the fine tuning parameters- the inertia weight and acceleration coefficients are formulated in terms of global-local best values of the objective function. These global-local best inertia weight （GLBestlW） and global-local best acceleration coefficient （GLBestAC） are incorporated into PSO in order to compute the optimal power flow solution. The proposed method has been tested on the standard IEEE 30 bus test system to prove its efficacy. The results are compared with those obtained through cPSO. It is observed that the proposed algorithm is computationally faster, in terms of the number of load flows executed and provides better results than the conventional heuristic techniques.