Values Of Decision Variables Research Articles

Bureaucracy in quest of feasibility

A bureaucracy has to determine the values of many decision variables while satisfying a set of constraints. The bureaucracy is not assumed to have any objective function beyond achieving a feasible solution, which can be viewed as “satisficing” à la Simon (1955). We assume that the variables are integer-valued and the constraints are linear. We show that simple and (arguably) natural versions of the problem are already NP-Hard. We therefore look at decentralized decisions, where each office controls but one decision variable and can determine its value as a function of its past values. However, an attempt to consult more than a single past case can lead to Condorcet-style consistency problems. We prove an Arrovian result, showing that, under certain conditions, feasibility is guaranteed only if all offices mimic their decisions in the same past case. This result can be viewed as explaining a status quo bias.

Multi-attribute optimization of eco-manufacturing based criteria in CNC manufacturing systems using an evolutionary algorithm

Manufacturing technology has evolved over the years with the development of CNC manufacturing systems, flexible manufacturing, rapid prototyping, smart manufacturing etc Simultaneously, the development of new and exotic materials to match specific requirements has shaped new problems in manufacturing. The materials developed thus far require special tools, lubricating agents, and extra-care in machining without compromising the quality. Further the study of carbon emissions in manufacturing sector has also gained unusual spotlight in view of their deleterious effect on the ecological balance. The manufacturing systems have to be consequently designed and developed, such that they generate minimal quantity of emissions without forfeiting the prime objectives of quality and tool morphology. The present work is principally intended to analyse the effect of cutting parameters on the emission rate of greenhouse gases, tool wear and work-piece temperature concurrently. These studies are accomplished in both dry and wet conditions on computer numerical control machining system. The machining process involved plain facing of a Ti-6Al-4V hardened material. The experimental studies are realized using both single point and multi-point cutting tools and are supplemented with the application of Multi-Objective Genetic Algorithm (MOGA). The MOGA generated set of pareto-fronts for the four machining conditions were subjected to VIKOR, TOPSIS and LINMAP decision making approaches to arrive at the optimum values of decision variables. The optimum cutting parameters obtained in single point cutting tool machining in dry conditions are speed (873.2 rpm), feed (0.199 mm rev−1) and depth of cut (0.25 mm), while the corresponding values of responses are tool wear (67.19 μm), work-piece temperature (39.36 °C) and carbon emission (0.138 Kg-CO2). The equivalent values for multi-point cutting were determined as 899.8 rpm, 0.195 mm rev−1 and 0.25 mm, while the responses for these optimal conditions are 69.92 μm, 39.48 °C and 0.137 Kg-CO2 in that order.

Comparative multi-objective optimization using neural networks for ejector refrigeration systems with LiBr and LiCl working agents

Education's evolution in the context of energy systems is essential for addressing sustainable energy challenges and developing a workforce equipped for future innovations, emphasizing both formal curricula and informal lifelong learning through successful energy case studies. As the global energy sector transforms to reduce carbon emissions and reliance on fossil fuels, innovations in renewable technologies like solar thermal are pivotal for promoting energy security and economic stability, supported by an educational foundation that fosters awareness and technical skills for sustainable development. Exposure to successful renewable energy systems, such as solar-powered refrigeration, offers an informal educational experience that enhances understanding and supports global educational goals, initiating with the innovative design and optimization of these systems using artificial intelligence (neural networks). Based on this formulation, the current article developed two sustainable energy systems by comparing the refrigeration cycles with two different operating fluids and various arrangements, and multi-objective optimization with an evolutionary genetic algorithm is performed for the proposed systems. The studied systems are refrigeration cycles using an ejector and without an ejector with two working fluids of lithium bromide and lithium chloride. The present work's main aim is to examine the working fluid and refrigeration system arrangements. Energy and economic modeling were performed for the proposed systems, and then parametric analysis and two-objective optimization were extracted. Parameters such as generator temperature, condenser temperature, absorber temperature, and evaporator temperature, which significantly impact the proposed system's performance, have been selected as decision parameters, and parametric analysis has been extracted for them. In addition to the mentioned parameters, diffusion mixing efficiency, nozzle efficiency, and heat exchanger have also been studied in the ejector asset system. To find the best values of decision variables, multi-objective optimization for both arrangements is conducted, and results are presented. The results have indicated that the refrigeration system using lithium chloride working fluid without an ejector achieves a coefficient of performance of 0.766 and a cost of 0.922 $/h at the optimal point, while the system with an ejector yields a higher coefficient of performance (1.047) and a slightly lower cost rate (0.991 $/h). The outcomes of this work can play a critical role for higher education institutions in advancing innovative solutions to pressing energy challenges. Lifelong learning, at the heart of educational innovation, can benefit from the integration of sustainable energy systems as a core component of informal education through the optimization of ejector refrigeration systems.

Inverse optimization in semi-definite programs to impute unknown constraint matrices

In a typical (forward) optimization problem, a decision-maker uses given values of model parameters to compute the values of decision variables. The goal in inverse optimization (IO) is instead to infer parameters that render given values of decision variables optimal. Most papers on IO utilize duality to impute objective function parameters. A corresponding literature for imputing constraint parameters is essentially non-existent, even for linear programs. The difficulty is that these IO problems include nonconvex bilinear constraints and/or objectives. We study inverse semi-definite programs (SDPs) where matrices on the left-hand-sides of constraints are unknown. These unknown matrices must satisfy some side constraints. We consider two types of such problems, depending on which SDP decision variable values are given: primal or dual. In each situation, we study three sub-cases based on whether both the right-hand-side coefficients and the objective function matrix are known or only one of these two is known. This creates six variants of the inverse problem. For each variant, we first look for sufficient conditions, either on the side constraints or on problem structure, under which the nonconvex bilinear inverse problem can be simplified substantially. In particular, it either has a trivial solution or can be reformulated as a (set of) convex program(s). When such conditions are not evident, we propose three tailored heuristics called the Convex–Concave Procedure, Sequential Semi-definite Programming, and Alternate Convex Search. We perform computational experiments to gain insights into the performance of these three methods.

Preventive maintenance for coherent systems considering postponed replacement

AbstractOne primary objective of reliability engineering is to achieve optimal maintenance of technical systems, which ensures they remain in good operating condition. This paper proposes an age‐based preventive optimal maintenance policy for ‐component coherent systems. Under this proposed strategy, the system begins operating at and undergoes preventative maintenance (PM) at a time . If the system fails before , it will be replaced with a new one. If the system is still functioning at time , an assessment is made based on the number of failed components to determine whether the system should be replaced or allowed to continue operating. If the number of failures at is below a predetermined threshold , the PM time is postponed and a new PM time will be scheduled, and the system continues operating in the interval . Otherwise, the entire system is preventively replaced at with a new one. In this scenario, we use a cost function to determine the optimal values of decision variables , , and . To examine the effectiveness of our proposed model, we analyze some examples of coherent systems using graphical and numerical methods.

A K-means Supported Reinforcement Learning Framework to Multi-dimensional Knapsack

In this paper, we address the difficulty of solving large-scale multi-dimensional knapsack instances (MKP), presenting a novel deep reinforcement learning (DRL) framework. In this DRL framework, we train different agents compatible with a discrete action space for sequential decision-making while still satisfying any resource constraint of the MKP. This novel framework incorporates the decision variable values in the 2D DRL where the agent is responsible for assigning a value of 1 or 0 to each of the variables. To the best of our knowledge, this is the first DRL model of its kind in which a 2D environment is formulated, and an element of the DRL solution matrix represents an item of the MKP. Our framework is configured to solve MKP instances of different dimensions and distributions. We propose a K-means approach to obtain an initial feasible solution that is used to train the DRL agent. We train four different agents in our framework and present the results comparing each of them with the CPLEX commercial solver. The results show that our agents can learn and generalize over instances with different sizes and distributions. Our DRL framework shows that it can solve medium-sized instances at least 45 times faster in CPU solution time and at least 10 times faster for large instances, with a maximum solution gap of 0.28% compared to the performance of CPLEX. Furthermore, at least 95% of the items are predicted in line with the CPLEX solution. Computations with DRL also provide a better optimality gap with respect to state-of-the-art approaches.

Application of new nanopolymer materials in intelligent thermal insulation system for building external walls

In response to the current problem of poor energy consumption control effect and overall high energy consumption of new nanopolymer materials for building exterior walls, the author proposes a thermal insulation energy consumption control technology based on the heat transfer performance model of exterior wall insulation panels. Calculate the current heat transfer performance parameters of exterior wall insulation panels using the reaction coefficient method, determine the proportional relationship between the effective heat transfer coefficients, and establish a heat transfer performance model for exterior wall insulation panels, based on the thermal conductivity index of the new nanopolymer material for the wall, the current control parameters are optimized. The optimal data algorithm is used to obtain the energy consumption decision variable value of the new nanopolymer material for the exterior wall of the building under the condition of clarifying the current heat transfer coefficient, and establish constraint conditions, based on the specific energy consumption data of new nanopolymer materials outside the current wall, establish the current thermal energy information transmission ratio relationship, analyze the current wall energy consumption hotspots, propose the K-means clustering analysis strategy, and apply it to the hot spot clustering control. Energy consumption control is achieved by locating the main cluster head parameters of the hot spot. Simulation results show that the hot spot fit of the aforementioned control methods has been improved by 29%, and the accuracy of the design method in cooling load control statistics is significantly higher than the two traditional methods used for comparison. Due to different weights, the final improvement ratio is determined to be 27%, further verifying the hypothesis. It has been proven that it can effectively improve the energy consumption control effect.

Multi-objective optimization of rectangular microchannel heat sink based on entropy generation and hydro-thermal performance using NSGA-II algorithm

In this study, multi-objective optimization of a rectangular microchannel heat sink is implemented based on two objective functions figure of merit (FOM) and entropy generation (Ṡgen). Decision variables are height ratio (α), width ratio (β) and number of channels (N). CFD simulations are conducted for different values of decision variables and the effects of each decision variable on hydro-thermal performance (FOM) and entropy generation are studied separately. To reduce the computational cost in multi-objective optimization process, a fourth-order multivariate polynomial regression model is used to predict the FOMαβ and Ṡgenαβ objective functions at each N. Non-Dominated Sorting Genetic Algorithm II coupled with predicted objective functions (FOM and Ṡgen) is implemented to maximize the FOM and minimize the Ṡgen at each N. Also, the decision variables related to the highest FOM are presented, which is 90% more than the reference point, and the hydrodynamic-thermal performance has improved. Decision variables related to the lowest Ṡgen are presented, which is 19% lower than the reference point. Finally, decision variables are presented to simultaneously satisfied the highest FOM and the lowest Ṡgen where FOM is 57% higher than the reference point and Ṡgen is 9.78% lower than the reference point.

An expandable machine learning-optimization framework to sequential decision-making

We present an integrated prediction-optimization (PredOpt) framework to efficiently solve sequential decision-making problems by predicting the values of binary decision variables in an optimal solution. We address the key issues of sequential dependence, infeasibility, and generalization in machine learning (ML) to make predictions for optimal solutions to combinatorial problems. The sequential nature of the combinatorial optimization problems considered is captured with recurrent neural networks and a sliding-attention window. We integrate an attention-based encoder–decoder neural network architecture with an infeasibility-elimination and generalization framework to learn high-quality feasible solutions to time-dependent optimization problems. In this framework, the required level of predictions is optimized to eliminate the infeasibility of the ML predictions. These predictions are then fixed in mixed-integer programming (MIP) problems to solve them quickly with the aid of a commercial solver. We demonstrate our approach to tackling the two well-known dynamic NP-Hard optimization problems: multi-item capacitated lot-sizing (MCLSP) and multi-dimensional knapsack (MSMK). Our results show that models trained on shorter and smaller-dimensional instances can be successfully used to predict longer and larger-dimensional problems. The solution time can be reduced by three orders of magnitude with an average optimality gap below 0.1%. We compare PredOpt with various specially designed heuristics and show that our framework outperforms them. PredOpt can be advantageous for solving dynamic MIP problems that need to be solved instantly and repetitively.

Metaheuristic based single and multiobjective optimization of thermoelectric generator

Analytical optimization methods are not applicable for some complex practical problems that lead to explore the numerical/metaheuristic optimization methods. Thermoelectric devices are also complex systems and need metaheuristic methods for their performance optimization. This paper analyses various metaheuristic techniques for performance optimization of thermoelectric generator (TEG). Single and multiobjective optimizations of TEG have been performed to optimize its power output and efficiency. The hot and cold side temperatures, load resistance, length of semiconductor legs, and fill factor of the TEG are used as performance parameters. Single-objective optimization is performed using 13-metaheuristic algorithms and their results are compared in terms of solution optimality and computational time acceptability. It has been observed that the cuckoo search (CS) algorithm is the most suitable in terms of accuracy and speed. CS produced the optimum power output and efficiency of 19.20837 W and 2.4427 % respectively in minimum time. The multiobjective optimization is also performed for simultaneous optimization of the power output and efficiency. Shannon entropy approach is found to be the best technique to determine optimal point on the Pareto front for multiobjective optimization. The optimal values of decision variables, Th Tc, RL, L and FF for multiobjective optimization are found to be 321.195 K, 281.195 K, 0.14250 Ω, 0.5 mm and 0.9 respectively and it produced optimum power output and efficiency of 19.20837 W and 2.25932 % respectively. The statistical and box plot analysis have also been carried out for all the algorithms. The determination of the most suitable algorithm for the faster performance optimization of the TEG, hereby provides the pathways to ascertain the most accurate solution for the power output and efficiency obtainable from the TEG system and hence, delivering the ability to decide the right parameters for the construction of the TEG system with the best performance.

Exergoeconomic analysis of an integrated electric power generation system based on biomass energy and Organic Rankine cycle

ABSTRACT The present study investigates the thermodynamics analysis of a trigeneration system using a gasifier system. An Organic Rankine Cycle (ORC) system is used to heat recovery and consequently, supplying the cooling demand. The first and second laws of thermodynamics are used to energy and exergy analysis of the system. Some thermodynamic parameters which affect the system performance including combustion temperature, gasifier temperature, compressor isentropic efficiency, gas turbine isentropic efficiency, compressor pressure ratio, and ORC pressure are parametrically analysed and their contribution in improving the efficiency and economy of the system is investigated. To the sustainable performance of the combined system, we need an evolutionary algorithm to identify the optimum values of thermodynamic parameters that have an impact on system performance. Hence, the Multi-Objective Particle Swarm Optimization (MOPSO) algorithm is used to find the best values of decision variables. The most striking result to emerge from the optimisation.optimisation is that implementing the MOPSO algorithm improves the exergy efficiency by 5.17% and reduces the total cost of the system by 1.9%.

A dynamic multi-objective optimization method based on classification strategies

The dynamic multi-objective optimization problem is a common problem in real life, which is characterized by conflicting objectives, the Pareto frontier (PF) and Pareto solution set (PS) will follow the changing environment. There are various dynamic multi-objective algorithms have been suggested to solve such problems, but most of the methods suffer from the inability to balance the diversity of populations with convergence. Prediction based method is a common approach to solve dynamic multi-objective optimization problems, but such methods only search for probabilistic models of optimal values of decision variables and do not consider whether the decision variables are related to diversity and convergence. Consequently, we present a prediction method based on the classification of decision variables for dynamic multi-objective optimization (DVC), where the decision variables are first pre-classified in the static phase, and then new variables are adjusted and predicted to adapt to the environmental changes. Compared with other advanced prediction strategies, dynamic multi-objective prediction methods based on classification of decision variables are more capable of balancing population diversity and convergence. The experimental results show that the proposed algorithm DVC can effectively handle DMOPs.

Simulation and multi-objective optimization of Claus process of sulfur recovery unit

Although natural gas can provide energy with minimum greenhouse gas emissions compared to other fossil-derived fuels, the sulfur removal is the major challenge associated with its use in various applications. In this work, sulfur recovery unit was simulated using the Aspen HYSYS. The environmental, energy, and economic analyses of the process based on special criteria (profit (PBT), weighted global warming potentials (WGWP), and energy consumption (NQ)) were analyzed. After consideration of the sensitivity analysis of the process, the single and multi-objective optimizations were carried out by integrating the HYSYS simulations with MATLAB codes with the Genetic Algorithm method. Feed temperature, feed molar flow rate, combustion air temperature, and reboiler temperature are decision variables in this work. The results show that with increasing the feed temperature, the energy consumption decreases, so, the cost of energy decreases. Also, with increasing the feed temperature, and reduction of consumed energy, the equivalent CO2 emission (which is calculated based on total energy consumption) reduces, so, WGWP decreases. Maximization of PBT, Minimization of WGWP, and Minimization of NQ were considered as the single objective optimizations, separately. Optimum values of decision variables were found. For multi-objective optimization, three different cases were considered: Case 1 (Max. PBT and Min. WGWP), Case 2 (Max. PBT and Min. NQ), Case 3 (Min. WGWP and Min. NQ). In all these cases, it can be found Pareto optimal frontier. The results show that the feed molar flow rate and air combustion temperature variables have more effect than other variables.

Parametric analysis and optimization of 660 MW supercritical power plant

The newly set up power plant has been committed to fulfilling the power supply demand of the world. Therefore, optimizing operating variables within constraints of varying power demand becomes necessary. The research aims to identify and optimize several parameters influencing the performance and efficiency of a 660 MW supercritical power plant at different operating conditions, such as steam temperature, pressure, feedwater flow rate, and fuel consumption. Ultimately, the research aims to contribute to developing sustainable and environmentally friendly power generation technologies. The present study covers the multi-objective optimization of a 660 MW capacity fossil fuel-fired SUPP. The overall plant efficiency, cost of electricity, and exergetic efficiency are taken as objective functions. The Particle Swarm Optimization (PSO) technique and a semi-empirical model of energy, economic, and exergy analysis of fossil fuel-fired SUPP have been employed. The varying power outputs, coal calorific value, amount of coal consumption, inlet temperature, and pressure conditions of turbines set are decision variables taken for the study. The parametric study was carried out with the variation in plant load and mass of coal consumption concerning the variation of the objective function. The lower temperature at the inlet of the low-pressure turbine is preferred for lowing the cost of electricity. The maximum value of plant efficiency of 41.643% and exergy efficiency of 39.834% with a minimum cost of electricity of 3.1456 INR/Unit have been evaluated using multi-objective PSO. The outcome of the present study is that the optimized value of decision variables will reduce the dependency on high-grade coal from an energy, exergy, and economic point of view. The outcome of the present study will explore the scope for future researchers and engineers.

Two-Agent Slack Due-Date Assignment Scheduling with Resource Allocations and Deteriorating Jobs

In enterprise management, there are often multiple agents competing for the same products to reduce production cost. On this basis, this paper investigates a two-agent slack due-date single-machine scheduling problem with deteriorating jobs, where the processing time of a job is extended as a function of position-dependent workload, resource allocation and a common deterioration rate. The goal is to find the optimal sequence and resource allocation that minimizes the maximal value of earliness, tardiness, and decision variables of one agent subject to an upper bound on cost value of the second agent. Through theoretical analysis, a polynomial time algorithm with O(N3) time is proposed for the problem, where N is the maximum number of jobs between the two agents.

Approaches Used In Adapting Metaheuristic Optimization Algorithms Developed For Continuous Problems to Discrete Problems

Many real-world problems such as determining the type and number of wind turbines, facility placement problems, job scheduling problems, are in the category of combinatorial optimization problems in terms of the type of decision variables. However, since many of the evolutionary optimization algorithms are developed for solving continuous optimization problems, they cannot be directly applied to optimization problems with discrete decision variables. Therefore, the continuous decision variable values generated by these metaheuristics need to be converted to binary values using some techniques. In other words, to apply such algorithms to discrete optimization problems, it is necessary to adapt the candidate solution vectors of the algorithms to discrete values and make changes in their working structures. In this study, firstly, adaptation methods that are frequently used in previous studies in transforming metaheuristic optimization algorithms designed for the solution of continuous optimization problems into discrete optimization algorithms are explained. Then, the popular location update strategies used in solving discrete optimization problems are explained. The presented work summarizes the process of adapting continuous optimization algorithms to solve combinatorial problems step by step.

Integrated Optimization Model for Maintenance Policies and Quality Control Parameters for Multi-Component System

The practical applications of integrated maintenance policies and quality for a multi-component system are more complicated, still rare, and incomplete to meet the requirements of Industry 4.0. Therefore, this work aims to extend the integration economic model for optimizing maintenance policies and quality control parameters by incorporating the Taguchi loss function for a multi-component system. An optimization model is developed based on preventive maintenance, corrective maintenance policies, and quality control parameters with the CUSUM (Cumulative Sum) chart, which is widely used for detecting small shifts in the process mean. The model was developed to minimize the expected total cost per unit of time and to obtain the optimal values of decision variables: the size of samples, sample frequency, decision interval, coefficient of the CUSUM chart, and preventive and corrective maintenance intervals. The solution steps were employed by selecting a case study in the Alahlia Mineral Water Company (AMWC). Then, the design of experiments based on one-factor-at-a-time was used to evaluate the effect of selected decision variables on the expected total cost. Finally, sensitivity analysis was performed on the selected decision variables to demonstrate the robustness of the developed model. A predictive maintenance plan was developed based on the optimal value of preventive maintenance interval, and the results showed that the performance of the maintenance plan realizes the full potential of the integrated model. In addition, the case study results indicate that the extended integrated model for multicomponent is the new standard for the quality production of multi-component systems in future works.

Modeling and optimizing the maintenance schedule using dynamic quality and machine condition monitors in an unreliable single production system

This work attempted to propose an integrated approach for the joint control of production, quality and maintenance where a single machine would produce one type of product. The machine would be subject to degradation process that would produce non-conform units. Based on the simultaneous operations of assessment of the machine degradation and that of the product quality, decisions to conduct maintenance activities would be proposed to improve the machine reliability. The strategy adopted in this work was to establish a link between the information from the quality indicator and the level of the machine degradation using a coupling function h(x,y) to generate a maintenance schedule. The ultimate objective of this work was to minimize the average total cost per unit of time in function of cost of maintenance and cost of production. For this purpose, a mathematical model was developed and numerical examples were implemented where optimal values of decision variables were computed.

Performance investigation on novel combined power generation and refrigeration system

This article aims to examine a novel combined power and refrigeration system, using renewable and waste heat sources suitable for low-temperature applications. The present system is an integrated Kalina cycle and ejector refrigeration system to generate power and refrigeration simultaneously. To improve the vapour generation, the separator vapour fraction is used as a decision variable. Relative irreversibility and efficiency defect as two important parameters considered in this system for an investigation to identify the weaker components. The combined system generates power and refrigeration with two different mediums by the incorporation of the heat exchanger at the turbine exhaust. The novel system's energy and conventional exergy evaluation are carried out through Python Software. The optimum values of decision variables: turbine concentration, separator vapour fraction, entrainment ratio, expander ratio, split ratio and turbine concentration are identified using Python software from an opted range of variables. The maximum value of net power output, first law efficiency for power generation system, combined system, second law efficiency for power generation system, combined system, refrigeration effect and coefficient of performance are obtained as 113 kW, 8.85%, 11.83%, 93.44%, 81.29%, 38.07% and 0.118, respectively, at higher separator vapour fraction. Among the components considered in the combined power generation system, the condenser and LTRGN account for the higher exergy destruction rate of 30.41% and 25.53%. The coefficient of performance is maximized at a higher value of the refrigeration effect. The turbine pressure at the inlet is increased with increments in turbine work on choosing the higher value of the expander ratio. The higher exergetic value components are not emphasized to focus on improvement.

Optimization of bakery production by using branch and bound approach

Mommy Ai Kitchen is one the businesses specializing in the bakery business, producing cupcakes, birthday cakes, brownies, and donuts. However, it does not optimally determine each bakery’s production quantity, so it offers fewer profits and becomes a problem. This research aims to find the optimal production quantity so that this business maximizes profits. The method used was integer programming using the branch and bound approach, which counts the decision variable value using the simplex method. This research was based on the number of raw materials on hand wheat flour, sugar, eggs, modal, and the profits of each bakery. Based on the analysis of the branch and bound approach, it was known that the maximum profit value was IDR 253,200, with eight alternative options for the bakeries that were produced. One of them was Mommy Ai Kitchen, which could produce three cupcakes, five birthday cakes, one brownie, and nine donuts to get that maximum profit. Meanwhile, Mommy Ai Kitchen’s estimation could produce one cupcake, one brownie, and six donuts using available materials with a profit of IDR 78,800. As a result, the profit difference before and after integer programming was IDR 174,400.