Multi-criteria Optimization Research Articles

Advantages of IMRT optimization with MCO compared to IMRT optimization without MCO in reducing small bowel high dose index for cervical cancer patients-individualized treatment options.

Traditional intensity-modulated radiation therapy (IMRT) planning for cervical cancer is time-consuming and require iterative repeated optimization. In this study, we focused on leveraging multi-criteria optimization (MCO) to reduce the impact of small bowel high-dose indices on other optimization targets, thereby providing a rapid approach to individualized IMRT for cervical cancer patients. Our research involved a cohort of 25 cervical cancer patients who underwent IMRT radiotherapy. The patient inclusion criteria were as follows: (I) histopathological confirmation of cervical cancer, (II) underwent IMRT radiation therapy, and (III) a prescribed dose of 180 cGy/28 fractions for the patient. All plans were replanned by an experienced dosimetrist without the MCO (W-IMRT). On the basis of the W-IMRT plan, the individualized IMRT (I-IMRT) plan was generated under the priority trade-off of reducing the D2cc (D2cc is the minimal dose to the 2 cm3 of the small bowel receiving the maximal dose) index of the small bowel using the MCO method, maintaining target coverage and protecting other organs at risk (OARs) as much as possible. Statistical analysis was performed using the Wilcoxon signature rank test. When the MCO method was applied to the IMRT plan, the high dose index decreased in the overlapping area between the small bowel and the planning treatment volume (PTV) (P<0.001, respectively). The D2cc index of the small bowel decreased to below 5,200 cGy in all I-IMRT plans. On the other hand, in PTV, the I-IMRT plan achieved a better homogeneity index (HI) compared to the W-IMRT plan. Significant dose reductions were also observed in the bladder (Dmean 144.8 cGy and V40 1.45%) (P<0.001, respectively), rectum (Dmean 43.9 cGy and V40 2.7%) (P<0.001, respectively) and bilateral femur heads (Dmean 150 cGy) (P<0.001, respectively). Dosimetric differences suggest that the I-IMRT plan using the MCO method provides better protection of other OARs and equivalently in PTV coverage, while lowering the high-dose index in the small bowel as much as possible for patients with cervical cancer, thus providing a rapid approach to achieving individualized IMRT for cervical cancer patients.

The method for solving the multi-criteria linear-fractional optimization problem in integers

In the papers we propose a method for solving the linear-fractional multi-criteria optimization model with identical denominators in whole numbers. Such models are in increasing demand, especially from an application point of view. The solving procedure of these models initially involves assigning utilities (weights) to each criterion [15] and building the optimization model with a single criterion, which is a synthetic function of all criteria weighted. It was found that the optimal solution of the model does not depend on the values optimum of the criteria obtained in R+ or in Z+. So, the decision maker can combinatorially select the types of optimal values of criteria, a fact that represents the essential priority of the algorithm. By changing the utility values, at the decision maker's discretion, we will obtain a new optimal compromise solution of the model. Theoretical justification of the algorithm as well as a solved example are brought to work.

The method for solving the multi-criteria linear-fractional optimization problem in integers

In the papers we propose a method for solving the linear-fractional multi-criteria optimization model with identical denominators in whole numbers. Such models are in increasing demand, especially from an application point of view. The solving procedure of these models initially involves assigning utilities (weights) to each criterion [15] and building the optimization model with a single criterion, which is a synthetic function of all criteria weighted. It was found that the optimal solution of the model does not depend on the values optimum of the criteria obtained in R+ or in Z+. So, the decision maker can combinatorially select the types of optimal values of criteria, a fact that represents the essential priority of the algorithm. By changing the utility values, at the decision maker's discretion, we will obtain a new optimal compromise solution of the model. Theoretical justification of the algorithm as well as a solved example are brought to work.

Optimization of a Self-Compacting Paste Based on Glass Powder Using Mixture Design and the Desirability Function

Abstract The partial replacement of cement by supplementary cementitious materials is an opportunity for reducing fossil energy consumption and greenhouse gas emissions. In this study, forty (40) pastes were formulated by applying a 4-factor mixture plan, consisting of cement, glass powder (GP), superplasticizer and water. Third order models “special cubic” established for the flow time, spreading diameter, and flow velocity, responses were statistically significant. The analysis of the models allowed the study of the individual and combined effects of the different factors, highlighting the predominant effect of the superplasticizer on the dispersion GP fines. The multi-criteria optimization allowed the development of two optimal pastes SCP1 and SCP2 incorporating 25 and 7% GP, respectively. SCP1 was chosen because at this GP amount, unlike at 28 days, the paste presents the best strengths at 90 days with 4.5% increase for flexural tensile strength and 15.69% increase for compressive strength while maintaining satisfactory workability.

Multi-criteria optimization and thermo-economic analysis of a heat pump-organic Rankine cycle Carnot battery system

Energy storage is a crucial solution for the intermittency and instability of renewable energy. Carnot batteries, a novel electrical energy storage technology, promise to address the challenges of renewable electrical energy storage worldwide. Rankine-based Carnot batteries, which are geographically unconstrained and effectively store energy at low temperatures, have attracted considerable attention in recent years. In this study, a mathematical model was developed, and a multi-objective optimization with power-to-power-efficiency, exergy efficiency, and levelized cost of storage was performed. Moreover, the investment cost and exergy loss of the optimized system components were investigated in detail and analyzed. The results showed that the optimal power-to-power-efficiency, exergy efficiency, and levelized cost of the storage system can be achieved at 60.3%, 33%, and 0.373 $/kWh based on single-objective optimization, and the operating parameters of the proposed system are different. Therefore, there is a strong trade-off relationship between the three objective functions mentioned above. Under the same weighting for the two approaches, they are 25.8%, 23%, and 0.437 $/kWh, and 39.3%, 29.1%, and 0.549 $/kWh, respectively. Furthermore, this study observed that the exergy destruction in the charge mode was nearly 95 kW larger than that in the discharge mode, and the exergy destruction of the throttle valve was the largest at 95.83 kW, accounting for 28.32%. The expander was the component with the highest cost (35.84% of the total cost) in the proposed system, followed by the compressor.

Design of Performance Characteristics on Laser Treated Denim Fabric

The current paper covers an experimental study, mathematical modelling, and design optimization of the laser treatment process of denim fabrics. Laser fading is used in the finishing phase of garment production, unfortunately, it decreases fabric durability. Denim fabric is known as a cotton fabric but nowadays it is blended with other fibres to improve fabric properties. For this reason, the main purpose of this study was to test multicomponent fabric longevity after laser treatment. The knowledge from this study is used by garment production company. The tear force, abrasion resistance, and colour difference are considered as performance characteristics of laser treated denim fabrics subjected to maximization. To achieve the goals, novel, mathematical models were developed. In the preliminary tests, the design space was determined. The full factorial design of experiments was utilized in the experimental study and the values of the performance characteristics are measured. Based on the results of the experimental study the artificial neural network and Haar wavelet based mathematical models were developed to predict the behaviour of the tear force, abrasion resistance, and colour difference. The artificial intelligence-based multicriteria design optimization procedure is developed.

Mixed H&lt;sub&gt;2&lt;/sub&gt;/H&lt;sub&gt;∞&lt;/sub&gt; robust controllers in aircraft control problem

A leading cause of accidents during the landing phase of a flight lies in a considerable altitude loss by an aircraft as a result of the impact of a microburst of wind. One of the significant factors focuses primarily on the need to simultaneously satisfy various requirements regarding conditions of environmental disturbances and a wide range of systemic changes. The paper presents an algorithm for synthesizing an optimal controller that solves the mixed H&lt;sub&gt;2&lt;/sub&gt;/H&lt;sub&gt;∞&lt;/sub&gt; control problem for the stabilization of aircraft in glide-path landing mode in the presence of uncertainty. Firstly, the principles of multi-criteria optimization are presented, and the mixed H&lt;sub&gt;2&lt;/sub&gt;/H&lt;sub&gt;∞&lt;/sub&gt; problem is interpreted as the synthesis of a system with optimal quadratic performance, subject to its readiness to operate with the worst disturbance. Then, the ensuing section expounds upon the mathematical depiction of the vertical trajectory of aircraft, duly considering the perturbations imposed by wind phenomena. Subsequently, the effectiveness of mixed H&lt;sub&gt;2&lt;/sub&gt;/H&lt;sub&gt;∞&lt;/sub&gt; control is confirmed compared to autonomous H&lt;sub&gt;2&lt;/sub&gt; or H&lt;sub&gt;∞&lt;/sub&gt; regulators through simulation outcomes acquired from the created system. Optimization based on a hybrid (mixed) criterion allowed combining the strengths of locally optimal systems based only on H&lt;sub&gt;2&lt;/sub&gt; or H&lt;sub&gt;∞&lt;/sub&gt; theory.

Industrial Process Control Using DPCA and Hierarchical Pareto Optimization

The control of large-scale industrial systems has several criteria, such as ensuring high productivity, low production costs and the lowest possible environmental impact. These criteria must be established for all subsystems of the large-scale system. This study is devoted to the development of a hierarchical control system that meets several of these criteria and allows for the separate optimization of each subsystem. Multicriteria optimization is based on the processing of data characterizing production processes, which makes it possible to organize a multidimensional statistical control process. Using neural networks to model the technological processes of subsystems and the method of dynamic principal component analysis (DPCA) to reduce the dimensionality of control problems allows us to find more efficient solutions. Using the example of a two-level hierarchy, we showed a variant of the connection between two subsystems by parameters.

Multicriteria Optimization of Lower Limb Exoskeleton Mechanism

Typical leg exoskeletons employ open-loop kinematic chains with motors placed directly on movable joints; while this design offers flexibility, it leads to increased costs and heightened control complexity due to the high number of degrees of freedom. The use of heavy servo-motors to handle torque in active joints results in complex and bulky designs, as highlighted in the existing literature. In this analytical study, we introduced a novel synthesis method with analytical solutions provided for synthesizing the lower-limb exoskeleton. Furthermore, we proposed a mathematical model of multicriteria optimization; as a result, we obtained several lower-limb exoskeleton mechanisms comprising only six links, well-suited to the human anatomical structure, exhibit superior trajectory accuracy, efficient force transmission, satisfactory step height, and having internal transfer segment of the foot.

A linearized approach for solving differentiable vector optimization problems with vanishing constraints

In this paper, two mathematical methods are used for solving a complex multicriteria optimization problem as the considered convex differentiable vector optimization problem with vanishing constraints. First of them is the linearized approach in which, for the original vector optimization problem with vanishing constraints, its associated multiobjective programming problem is constructed at the given feasible solution. Since the aforesaid multiobjective programming problem constructed in the linearized method is linear, one of the existing methods for solving linear vector optimization problems is applied for solving it. Thus, the procedure for solving the considered differentiable vector optimization problems with vanishing constraints is presented in the paper.

A numerical study of the multicriteria parametric optimization of the displacement and weight of a two-connected conical shell of minimal surface under thermal and power loading

Various methods and approaches are used to solve the problem of optimal design. Problems of this type are used for the optimal design of spatial coverings, which in modern architecture are progressive structures that are of interest to the whole world. Spatial coatings allow to give the building architectural expressiveness, cover large spans and combine load-bearing and enclosing functions.&#x0D; The hulls of minimal surfaces are the hulls of negative Gaussian curvature. In general, the geometry of minimal surfaces cannot be described analytically. To solve this problem, which is associated with solving the differential equation that describes the minimal surface in general, under appropriate boundary conditions, one has to use methods of numerical analysis. This approach allows us to build a point frame of the shell, which is a matrix of discrete solutions of functions that searches for a given minimum surface. In view of this, its geometric characteristics can be obtained only in numerical form.&#x0D; The basic relations of the linear theory of thin elastic shells of minimal surface are highlighted in the numerical study of parametric optimization. The mathematical justifications of how the external load is perceived and the process of creating the stress-strain state of the shells of minimal surfaces are highlighted.&#x0D; For the numerical implementation of the multicriteria parametric optimization of a double-connected conical shell of minimal surface, a finite element model was built from plate finite elements in the amount of 4824 pieces and 4896 nodes. The perimeter is rigidly clamped to the ground disk. The thermal force load is set, which consists of a combination of static and temperature loads.&#x0D; The developed methodology shows quite good results that coincide with the works of other authors and makes it possible to use two types of optimization for one research object simultaneously. The first stage is shape optimization, and the second stage is multicriteria parametric optimization.&#x0D; This methodology makes it possible to perform optimization processes in an automated mode, which is an important applied task for construction and applied mechanics.

Multi-criteria thermoeconomic optimization of a geothermal energy-driven green hydrogen production plant coupled to an alkaline electrolyzer

Among the various technologies for hydrogen production, the renewable energy driven water electrolysis has emerged as a favorable method. In this respect, the present research proposes and analyses a novel and efficient medium-temperature driven geothermal system for green hydrogen production. An alkaline electrolyzer is deployed for hydrogen production which is powered by a double flash steam geothermal power cycle. To boost the power generation (and hence the hydrogen production amount) the double flash cycle is equipped with a self-superheating process, which superheats the saturated vapor at turbine inlet without using another external heat source. Thermodynamic evaluations, based on exergy concept, along with economic analysis are carried out to assess the hydrogen production amount, plant exergy efficiency and total cost rate, and the unit hydrogen price. In order to represent a comprehensive investigation of the plant performance, parametric analyses along with single- and multi-criteria optimizations were conducted. The results revealed that, for 1kg/s of geothermal brine, the capacity of hydrogen production of the proposed plant is ∼1.5−3kg/h under various operating conditions. It is found that, under multi-objective optimum operating conditions, the plant yields 12.63% exergy efficiency and its total cost rate is calculated to be 10.42 $/h. However, if the plant is to be optimized for maximum exergy efficiency, the value of 14.25% is achievable which will result in increment of total cost rate to 11.97 $/h.

An investigation and multi-criteria optimization of an innovative compressed air energy storage

Compressed air energy storage, a well-known technique for energy storage purposes on a large scale, has recently attracted substantial interest due to the development and long-term viability of smart grids. The current research focus on the design and thorough examination of a compressed air energy storage system utilizing a constant pressure tank. Various aspects, including energy, exergy, economic, and exergoeconomic factors, have been extensively investigated in this study. The goal of the referenced design is to maximize the utilization of air's energy stored in the tank, minimize exergy destruction, enhance production capacity and energy storage density, optimize system performance, and recover waste heat efficiently. Additionally, through the utilization of artificial neural networks and genetic algorithms, this study provides an analysis of optimal operational conditions, taking into account both thermodynamic and economic performance considerations. The referenced system, which stores 209 MWh of excess power from the grid as compressed air and heat throughout off-peak times and utilizes it to produce 137 MWh of electrical power during peak demand periods, demonstrates remarkable performance compared to the conventional storage methods. The findings indicate that the total electrical efficiency, round trip efficiency, and exergy round trip efficiency of the referenced system are equal to 65.63 %, 68.28 %, and 66.01 %, respectively. The total cost of the products of the system is 21.15 $/GJ, while exhibiting a value of 190.4 $/MWh for its levelized cost of electricity. The system's payback period is approximately 5.11 years, and the ultimate profit amounts to around $40 million.

Optimization methods for multi-criteria decisions in pharmacy

Optimization methods for multi-criteria decisions in pharmacy&#x0D; In pharmaceutical technological research, the determination of the quantitative composition of granules is considered as a task of multi-criteria selection. Today, to solve this problem, the regression analysis and multi-criteria optimization methods are widely used; they are based on mathematical models obtained for the object under study.&#x0D; Aim. To identify a decision-making method in a multi-criteria space that is effective for use in pharmaceutical technology research with quantitative factors.&#x0D; Materials and methods. The study uses tools of the popular computer mathematics system Mathcad (MathSoft Ins., USA) to automate the solution of mathematical problems. To automatically search for the type and coefficients of regression equations, the MS Excel application was used, namely: the data analysis package (regression analysis). The MS Word processor was used to edit the code.&#x0D; Results. A variety of approaches to the formalization of the multi-criteria optimization task have been studied. The optimal quantitative content of excipients when developing the granule technology has been found using two different optimization criteria, which are formed according to different methodical approaches. The method proposed does not provide for the mandatory introduction of gradation of individual criteria or their weighting factors.&#x0D; Conclusions. As a result of the comparison of multi-criteria optimization methods, the effectiveness of the decision-making method in the multi-criteria space has been shown; it synthesizes a mathematical procedure related to the vector of criteria and is based on determining the ideal point and introducing the concept of a norm into the space of functionals; it has not been mathematically proven, but it is practically useful decision-making algorithm compared to the mathematical method of convolution of criteria. The optimization method proposed has advantages that are manifested in the possibility of using a relatively simple mathematical apparatus and simplified logic of obtaining a solution.

Formulation of inexpensive and green reactive powder concrete by using milled-waste-glass and micro calcium-carbonate – A multi-criteria optimization approach

In view of its high strength and durability, reactive powder concrete (RPC) is a promising construction material. The replacement of cement and silica fume with sustainable alternatives to RPC may provide significant benefits, however, there are challenges to overcome. In this study, calcium carbonate and ground waste glass powder were introduced as mineral mixtures to develop an environmentally friendly and cost-effective RPC mixture. The best flowability, proper compressive strength, and reduced cement content were achieved using a multi-objective simultaneous optimization approach based on the Derringer & Suich methodology. As a result of the study, 603 kg/m3 of cement was determined as the most suitable dosage for RPC. Additionally, the optimized mix contained 368 kg/m3 of waste glass and 118 kg/m3 of calcium carbonate, which had a beneficial impact on both cost and environmental considerations. As a result of numerous experimental tests, including compressive strength, elasticity modulus, chloride ion penetration, and drying shrinkage, the developed RPC's properties were validated and were comparable to the control mixture while showing superior drying shrinkage behavior. A further benefit of adding these admixtures was the reduction of superplasticizer dosage. Despite the optimized RPC's lower mechanical and chloride ion penetration performance at early ages, the performance discrepancy diminished over time due to the pozzolanic properties of waste glass powder. A significant characteristic of the optimized RPC was its superior drying shrinkage behavior throughout the testing period resulting from its reduced water dosage. Ultimately, the study highlights the potential of the addition of calcium carbonate and waste glass powder to RPC for sustainable concrete production at a low cost.

Protection system planning in distribution networks with microgrids using a bi-level multi-objective and multi-criteria optimization technique

Microgrids are able to improve several features of power systems, such as energy efficiencies, operating costs and environmental impacts. Nevertheless, microgrids’ protection must work congruently with power distribution protection to safely take all advantages. This research contributes to enable their protection by proposing a bi-level method to simultaneously solve the allocation and coordination problems, where the proposed scheme also includes local protections of distributed energy resources. The uncertainties associated with generation and loads are categorized by the k-means method, as well. The non-dominated sorting genetic algorithm II is employed in the upper-level task to solve the protection and control devices allocation problem with two opposing objectives. In the lower-level task, a genetic algorithm ensures their coordination. Protection devices include reclosers and fuses from the network, and directional relays for the point of common coupling of microgrids, while control devices consist of remote-controlled switches. In contrast to related works, local devices installed at the point of coupling of distributed generation units are considered as well, such as voltage-restrained overcurrent relays and frequency relays. The optimal solution for the decision-maker is achieved by utilizing the compromise programming technique. Results show the importance of solving the allocation and coordination problems simultaneously, achieving up to $25,000 cost savings compared to cases that solve these problems separately. The integrated strategy allows the network operator to select the optimum solution for the protective system and avoid corrective actions afterward. The results also show the viability of the islanding operation depending on the decision maker's criteria.

TRANSACTIVE LOCAL ELECTRICAL ENERGY SYSTEMS: FUNCTIONING FEATURES AND DEVELOPMENT PROSPECTS

Due to global concerns about climate change, the deployment of distributed energy resources and electrical and thermal energy storage systems has been accelerated to minimize CO2 emissions. In addition, the need for optimal energy management of these energy resources was emphasized in order to reduce the need for new energy resources. The concept of transactional energy and, accordingly, transactional systems was introduced for modern energy systems as a system of economic and control mechanisms that allow for dynamic balancing of supply and demand in the entire electrical infrastructure using cost as a key indicator. This ensures cost-effective integration of renewable energy sources and creates incentives for investment and innovative renewal of local energy systems, allowing for management of both supply and demand for electricity. The article discusses the architecture of transactional systems and its components. The main objective function of transactional systems is to minimize the total annual costs of the local system, which supports the continuity of energy supply. To estimate the current cost of electricity, it is necessary to have information on the distribution of investments invested in the project before the start of its implementation, between the periods of project implementation. Considered optimization criteria, the use of which depends on specific goals. It is important to use multi-criteria optimization and control methods to determine the structure of the system and the optimal distribution of energy obtained from different sources in order to maximize the efficiency of the entire system, while contributing to the maximum reduction of emissions to the environment, while minimizing the cost of energy production.

Mean values as nondominated multicriterial points

AbstractIn this paper, we introduce new notions of mean values based on ideas of multicriteria optimization. The distances between the current point to all points in the sample are regarded as elements of a vector estimate. Such vector estimates are usually scalarized, for example, by taking the sum of all components. In contrast, we introduce preference relations on the set of all such vectors, based on the information about the preferences of the decision maker who could be a statistician, analyst or researcher. Such preference relations reflect the distances between points, including the case in which all distances are equally important. We define the mean values as the points whose corresponding vector estimates are nondominated with respect to the defined preference relation, and investigate their properties. Such mean values turn out to be multi‐valued. We further explore the relationship between the new notions of mean values with their conventional definitions and suggest computational approaches to the calculation of the suggested new means. We also outline generalisations of the suggested approach to the case of multidimensional data.

Multicriteria Optimization of Software Development Platform Selection

The problem of multicriteria optimization of tech stack selection in a non-linear software development environment is formalized. Approaches to solving the problem based on the formation of a compromise area of local quality criteria, additive convolution of vector criteria and their scalarization are considered. An aggregate quality criterion of the software development platform is proposed. It allows taking into account the nonlinearities of the external environment in the framework of solving the problem of extremal control. The coordinates of the vector criteria are piecewise continuous functions A comparative analysis of various approaches to changing the software development tech stack in the face of significant disturbances in the development tools market has been carried out. The possibilities of boxed solutions, custom development and Open Source software development in ensuring information security of the software development environment are shown. The information stability of a software development project using Less Code tools is established and the advantages of technological solutions are shown. The analysis of the adequacy of the obtained solutions was carried out using the Open Source Less Code of the Jmix platform. The data of a comparative analysis of the budgets of the Less Code platform and custom software from vendors are given, which showed the benefits of using Open Source software development tools for long-term operation of the development platform.

Optimisasi Program Linear Pada Permasalahan Multikriteria Menggunakan Metode ε-constraint

The purpose of this study is to solve multi-criteria problems using the ε-constraint method with the help of an excel solver. The multi-criteria optimization problem is an optimization problem that has more than one objective function. A multi-criteria optimization problem can be said to be a multiple criteria decision making (MCDM) if there is more than one thing that must be considered in the model as a goal or criterion. In general, the weighting method and the ε-constraint method are the most widely used. The weighting method converts a set of options into options by multiplying each option by the inventory weight. On the other hand, the ε-constraint method only saves one of the existing goals and limits the goals with a certain number of values to get an efficient limit.