Multi-objective Optimization Solution Research Articles

Interactive influences of ecosystem services and socioeconomic factors on watershed eco-compensation standard “popularization” based on natural based solutions

Watershed eco-compensation is a policy tool to realize watershed environment improvement and regional economic development. It is important to eliminate the influence of economic differences between upstream & downstream regions and realize the fairness of regional social development based on Natural based Solutions (NbS). At present, lack of clarity in coupling and coordination analysis of ecosystem services & socioeconomic based on NbS could hamper watershed eco-compensation standards “popularization” and reduce the ability to successfully ecological governance. To meet the needs of economic development and ecological service value realization, dynamic equilibrium game research based on multidimensional relationship coordination and a multi-objective optimization solution of economic benefit distribution was carried out. To achieve the bargaining Bayesian/Nash equilibrium of the watershed eco-compensation standard in the game, the existence conditions of the equilibrium solution of the eco-compensation standard based on the mixed equilibrium game implementation process were studied. To carry out the complete information dynamic game, the equilibrium solution of the watershed eco-compensation standard based on the dynamic transfer payment was solved, and the rational analysis of the dynamic Bayesian equilibrium game of bargaining based on the incentive compatibility mechanism was also discussed. Water quantity and quality eco-compensation can ensure balanced development between ecological protection and the social economy in the Mihe River Basin. Combined with the variation law of socioeconomic water intake-utilization standards and the water use value, the city of Shouguang City & Qingzhou City should pay Linqu County 4.78 million US$ and 1.29 million US$ as watershed eco-compensation standards per year based on NbS, respectively. To verify the rationality of the results derived from the economically optimal model, two modes of “bargaining” & “perfect competition”, were used to study the characteristics of the protocols generated by the equilibrium game, and the applicable conditions of the nonzero-sum game solution upstream and downstream of the watershed were also explored. Based on the nonzero-sum processing of the survey results, the current relationship between the input value of eco-compensation and the willingness to pay satisfies v≥c+1/4. Based on the dynamic game & Bayesian equilibrium solution of bargaining, the watershed eco-compensation quota of water quantity & quality is 6.07 million US$, the willingness to pay is 65.63 US$/month. These findings contribute to the quantifying process of bargaining & dynamic equilibrium by transforming “ambiguous” information to achieve sustainable ecosystem service management and develop socioeconomic strategies associated with different compensation features based on NbS, thus helping to inform watershed management.

On approximate solutions for robust semi-infinite multi-objective convex symmetric cone optimization

On approximate solutions for robust semi-infinite multi-objective convex symmetric cone optimization

Multi-Objective Resource Scheduling for IoT Systems Using Reinforcement Learning

IoT embedded systems have multiple objectives that need to be maximized simultaneously. These objectives conflict with each other due to limited resources and tradeoffs that need to be made. This requires multi-objective optimization (MOO) and multiple Pareto-optimal solutions are possible. In such a case, tradeoffs are made w.r.t. a user-defined preference. This work presents a general Multi-objective Reinforcement Learning (MORL) framework for MOO of IoT embedded systems. This framework comprises a general Multi-objective Markov Decision Process (MOMDP) formulation and two novel low-compute MORL algorithms. The algorithms learn policies to tradeoff between multiple objectives using a single preference parameter. We take the energy scheduling problem in general Energy Harvesting Wireless Sensor Nodes (EHWSNs) as a case example in which a sensor node is required to maximize its sensing rate, and transmission performance as well as ensure long-term uninterrupted operation within a very tight energy budget. We simulate single-task and dual-task EHWSN systems to evaluate our framework. The results demonstrate that our MORL algorithms can learn better policies at lower learning costs and successfully tradeoff between multiple objectives at runtime.

Multi-response optimization of AISI H11 using Taguchi and Grey relational analysis

Tool & Die is one of the important department in the manufacturing industries that takes care of proper designing and fabrication of tools and dies required for the production. In this sector, tool steels are used as the primary source of materials. These tool steels belongs to the family of carbon and alloy steels. Mostly used alloying elements are chromium, tungsten, molybdenum and vanadium and are heat-treated. The objective of the work involves machinability study of AISI H11 chromium hot-worked steel extensively used for tool & die making. It deals with the analysis of machining parameters and its influences on the responses considered. Here the controlling parameters considered are cutting speed (Cs), feed rate (Fr) and depth of cut (Dc) and responses as surface roughness (Ra) and material removal rate (Mrr). Each controlling parameters are assigned with 3 levels and experimental runs were executed as per taguchi robust design. To determine multi-objective optimal solution, grey relational analysis (GRA) is employed. GRA is used as it provides a feasible platform for converting a multi-objective function into single-objective function. The experimental runs were performed as per L27 orthogonal array sequence in CNC end-milling. The responses recorded are then analyzed using analysis of variance (ANOVA) and optimal solutions are validated through confirmatory runs. The entire machinability study of AISI H11 is performed in two conditions involving rough machining and finish machining. This has been addressed based on the machining scenario followed in industries taking up job orders. The confirmatory results for rough machining recorded was found to be 0.7871 microns against predicted value of 0.7654 microns resulting with a deviation error of 2.88%. Similarly, for finish machining, confirmatory runs recorded 0.8579 microns against predicted value of 0.8357 microns resulting with a deviation error of 2.66%. The deviation level indicated above between predicted and observed values are minimum, which shows the reliability of the optimal solutions arrived in.

Online Microservice Orchestration for IoT via Multiobjective Deep Reinforcement Learning

By providing loosely coupled, lightweight, and independent services, the microservice architecture is promising for large-scale and complex service provision requirements in the Internet of Things (IoT). However, it requires more fine-grained resource management and orchestration for service provision. Most of the existing microservice orchestration solutions are based on those designed for the traditional cloud. They can only provide coarse-grained resource allocation using possibly conflicting weighted objectives. In this article, we present a fine-grained microservice orchestration approach to provide services online for dynamic requests of IoT applications. By using a fine-grained resource model of energy cost and service end-to-end response time of orchestrated microservices, we formulate the microservice orchestration problem as a multiobjective Markov decision process. We then propose a multiobjective optimization solution based on deep reinforcement learning (DRL) to simultaneously reduce energy consumption and response time. Through extensive experiments, our proposed algorithm presents significant performance results than the state of the art. To the best of our knowledge, this is the first work that addresses microservice orchestration using DRL for multiple conflicting objectives.

Intelligent optimization framework of near zero energy consumption building performance based on a hybrid machine learning algorithm

The realization of a near zero energy consumption building (NZEB) is one of the important goals to promote the sustainable development of green buildings. To achieve the goal of NZEB and to allow for factors such as building comfort, environmental protection and cost, an intelligent optimization framework that combines Building Information Modeling DesignBuilder(BIM-DB) and random forest-nondominated sorting genetic algorithm-III (RF-NSGA-III) is proposed to study the multiobjective optimization of NZEB performance. The data in this paper are simulated by BIM-DB through orthogonal experimental design. RF is used to establish the complex relationship between building design parameters and NZEB performance. After the accuracy of the model is verified by the goodness of fit (R2) and the root mean square error (RMSE), the obtained nonlinear mapping relationship is taken as the fitness function of NSGA-III, and the multiobjective Pareto optimal solution set is obtained by using the proposed RF-NSGA-III intelligent optimization framework. Taking a teaching building in Wuhan as an example, the effectiveness of this method is verified. The results show that (1) the RF prediction accuracy is good, the RMSE range for the performance of NZEB is 0.015–0.035, and the R2 range is 0.91–0.93. (2) After optimization, the energy-saving rate of the building body is 21.25%, which meets the near zero energy consumption standard. (3) The proposed RF-NSGA-III intelligent optimization framework can achieve multiobjective optimization, and the comprehensive optimization rate of five objectives is the best compared with three and four objectives. Accordingly, this intelligent method that combines BIM-DB and RF-NSGA-III provides an effective idea for the design optimization of NZEB.

Application of combined optimization strategy and system of CNC machining parameter

This paper presents an efficient optimization method of combining off-line optimization with on-line adaptive control for CNC (Computerized Numerical Control) machining parameter, and develops the corresponding system, aims to multi-objective optimization and cutting force stability. Firstly, the multi-objective optimization solution of machining parameters is obtained by off-line optimization based on Pareto genetic algorithm and TRIZ theory. Then, on this basis, feed speed is adjusted online based on adaptive control system. Next, current is used as feedback to control cutting force, and cutting force can be kept at a set value by the on-line adjusting. We obtain the relationship between off-line optimization and on-line adaptive control. Finally, we build the combined optimization module and embed the self-developed CNC machining system. Based on the system, the experimental results verify that the optimized process parameters make the processing time reduced by 14 s, and no matter how cutting conditions change, cutting force can be stabilized as soon as possible by adjusting feed speed online for keeping the cutting process stability. From the perspective of building the parameter optimization function module, it provides a new idea for the self-development of CNC machining system.

Multi-Objective Optimal Power Flow Solution Using a Non-Dominated Sorting Hybrid Fruit Fly-Based Artificial Bee Colony

A new optimization technique is proposed for solving optimization problems having single and multiple objectives, with objective functions such as generation cost, loss, and severity value. This algorithm was developed to satisfy the constraints, such as OPF constraints, and practical constraints, such as ram rate limits. Single and multi-objective optimization problems were implemented with the proposed hybrid fruit fly-based artificial bee colony (HFABC) algorithm and the non-dominated sorting hybrid fruit fly-based artificial bee colony (NSHFABC) algorithm. HFABC is a hybrid model of the fruit fly and ABC algorithms. Selecting the user choice-based solution from the Pareto set by the proposed NSHFABC algorithm is performed by a fuzzy decision-based mechanism. The proposed HFABC method for single-objective optimization was analyzed using the Himmelblau test function, Booth’s test function, and IEEE 30 and IEEE 118 bus standard test systems. The proposed NSHFABC method for multi-objective optimization was analyzed using Schaffer1, Schaffer2, and Kursawe test functions, and the IEEE 30 bus test system. The obtained results of the proposed methods were compared with the existing literature.

Multi-objective optimization of micro-energy network considering exergy efficiency

Compared with energy networks that only distribute a single kind of energy, the unique feature of micro-energy networks lies in the efficient and coordinated utilization of heterogeneous energy. To measure the quality of energy and to compare the capability of different energy sources or systems, exergy is a generally accepted tool in thermodynamics. Therefore, it is of great significance to introduce exergy to analyze energy utilization in quality. First, based on exergy analysis of a micro-energy network, a multi-objective optimal scheduling strategy considering exergy efficiency and economic costs is proposed, and a multi-objective optimal scheduling model is established. Second, the specified weights cannot be adjusted flexibly during the scheduling process; the optimal model can update the weights hourly and find the multi-objective optimal solution. The hunting algorithm is used to solve the optimization problem of this scheduling model, which has multiple constraints and variables. Finally, the simulation results show that the operating cost of the multi-objective scheduling model is reduced by 3.93% in summer, 7.87% in winter, and the overall exergy efficiency of the proposed model is increased by 1.92% in summer, 2.46% in winter, compared to single-objective optimization models. The results prove that the proposed multi-objective optimal scheduling strategy is effective and feasible.

A multi-objective evolutionary algorithm based on niche selection in solving irregular Pareto fronts

The key characteristic of multi-objective evolutionary algorithm is that it can find a good approximate multi-objective optimal solution set when solving multi-objective optimization problems(MOPs). However, most multi-objective evolutionary algorithms perform well on regular multi-objective optimization problems, but their performance on irregular fronts deteriorates. In order to remedy this issue, this paper studies the existing algorithms and proposes a multi-objective evolutionary based on niche selection to deal with irregular Pareto fronts. In this paper, the crowding degree is calculated by the niche method in the process of selecting parents when the non-dominated solutions converge to the first front, which improves the the quality of offspring solutions and which is beneficial to local search. In addition, niche selection is adopted into the process of environmental selection through considering the number and the location of the individuals in its niche radius, which improve the diversity of population. Finally, experimental results on 23 benchmark problems including MaF and IMOP show that the proposed algorithm exhibits better performance than the compared MOEAs.

Balancing daylight in office spaces with respect to the indoor thermal environment through optimization of light shelves design parameters in the tropics

The study aims to investigate the preferred daylighting availability ranges for the best visual and thermal comfort in office workspace through optimal modifications light-shelve parameters, grounded on parametric design and optimization, with a focus on its visual and thermal indices. To identify the final optimal solutions, single and multi-optimization scenarios were used. The findings revealed that optimizing for a single objective might obstruct the attainment of other goals. In other words, the first scenario, optimization only for daylight availability, results in an increase in temperature. While optimizing for indoor thermal performance solely, none of the preset daylight availability acceptance requirements were met. However, multi-objective optimization solutions were the final optimal solutions nearest to the ideal. Final optimum solutions of the best design parameters of light shelves can improve the total average of daylight availability by 56.25%, 50.63%, 57.50% and 71.88%, and the indoor thermal performance was improved by decreasing the average temperature for thermal environmental performance indicators by 4.15%, 3.27%, 3.17% and 4.76%, respectively, in March, June, September and December. The study concludes that daylighting levels of 500 lux to1300 lux provide the best range of optimal daylighting for visual and thermal comfort indicators for office spaces in the tropics.

A note on characterization of (weakly/properly/robust) efficient solutions in nonsmooth semi-infinite multiobjective optimization using convexificators

This note concerns with Theorem 4.1 in [Kabgani A, Soleimani-damaneh M. Characterization of (weakly/properly/robust) efficient solutions in nonsmooth semi-infinite multiobjective optimization using convexificators. Optimization, 2018; 67: 217–235]. We present this theorem in a correct way and show that the error does not influence other results of the paper. Moreover, we provide some new corollaries for this theorem.

Evaluation of Product Innovation Practice of Chinese Internet Companies Based on DANP Model

Purpose. Internet companies have played an important supporting role in China’s economic growth and social resource allocation in the advent of an exogenous shock: the coronavirus disease (COVID-19) pandemic. This is owing to their digital, networked, and platform-based characteristics amidst an environment of intensified competition and stagnation of innovation activities due to the pandemic shock. Thus, based on the social network theory and resource-based theory, this study combines the DANP model with corporate innovation to build a product innovation performance evaluation framework for Chinese Internet companies. From a value network perspective, this study considers the different performance aspects of network embeddedness, knowledge management, environmental triggering, and organizational effectiveness. Methodology. The performance of Internet enterprise product innovation may be considered a complex multicriteria decision-making problem. This study used the decision-making trial and evaluation laboratory-based analytic network algorithms to analyze the complex influencing relationship among the factors and calculate their weights. Preference ranking organization method for enrichment evaluation was used for selecting the final solution of multiobjective optimization. Three representative and influential Internet companies in China were selected for empirical analysis and practical evaluation, to find the gap between product innovation performance and expectations and present development suggestions. Findings. The study results reveal that relational embeddedness, knowledge sharing degree, cognitive embeddedness, structural embeddedness, knowledge absorptive capacity, and corporate strategic orientation are important to Chinese Internet enterprise product innovation performance. Practical Implications. This Internet enterprise product innovation performance evaluation framework can be used by Internet business operators to assess product innovation performance and identify areas of improvement. This study provides new product innovation ideas for Chinese Internet companies during an epidemic situation. Originality/Value. This study contributes to the present body of knowledge by using the DANP model to conduct empirical analysis, considering value network-related performance aspects to evaluate the product innovation performance of Internet enterprise in China.

Research on Multi-Objective Reactive Power Optimization of Power Grid With High Proportion of New Energy

The integration of large-scale wind power and photovoltaics into the power system will aggravate the voltage fluctuation of grid nodes, while when the reactive power of new energy units participates in the optimization of reactive power and voltage of the system, it will promote the consumption of new energy while effectively improving the stable operation level of the system. In this work, the grey wolf algorithm (GWO) of entropy weight is introduced to solve the optimal compromise solution of multi-objective reactive power optimization of transmission network, and the network loss and voltage deviation and static voltage stability margin are taken as three objective functions to evaluate and make use of the reactive power regulation performance of new energy units. Specifically, the cooperative optimization of reactive power regulation performance of wind turbine and photovoltaic generating set and reactive power compensation of original power system is adopted, the efficient GWO) is incorporated to solve the multi-objective reactive power optimization model, the entropy method is introduced to obtain the optimal compromise solution of reactive power optimization, and a numerical example is analyzed by using IEEE39 transmission network system. Simulation results confirmed that the proposed multi-objective reactive power and voltage optimization model and grey wolf optimization algorithm can effectively improve the system node voltage quality and improve the stable operation level of the system.

Establishing Best Pedestrian Paths considering SARS-CoV-2 contagions: Mathematical Optimization Model and Mobile Application Approach

Given the modern SARS-CoV-2 coronavirus pandemic and the Universidad de Los Andes needs to protect their students against possible contagions at the university campus, we established and design a mobile application to obtain the best route between two places in the campus university for a student. The resulting path obtained by our proposed solution reduces the distance traveled by the student as well as a possible coronavirus contagion during his journey through the university campus. Therefore, we modeled two types of costs: a transport cost that models the distance to travel the campus by a student, and the contagion risk cost that models the contagion susceptibility that a student has during a displacement through the campus. As a result, we developed and validated a solution algorithm that minimizes the two modeled costs. The algorithm results were compared against a Multi-Objective mathematical optimization solution were findings show an solution approximation between the algorithm and the mathematical model. Finally, a mobile application was developed to map the optimal routes to displace between two points in the university campus given the solution algorithm.

Evaluation of Multi-Objective Optimization Techniques for Resilience Enhancement of Electric Vehicles

The pervasiveness of electric vehicles (EVs) has increased recently, which results in the interdependence of power and transport networks. Power outages may adversely impact the transportation sector, and the available energy may not be sufficient to meet the needs of all EVs during such events. In addition, EVs will be used for diverse purposes in the future, ranging from personal usage to emergency response. Therefore, the allocation of energy to different EVs may have different degrees of societal-, community-, and individual-level benefits. To capture these diverse aspects, the energy allocation problem to EVs during outages is modeled as a multiobjective optimization (MOO) problem in this study. Three indices are formulated to quantify the value of different EVs for societies, communities, and individuals during outages, and, correspondingly, three objective functions are formulated. The formulated MOO problem is solved using the five most widely used MOO solution methods, and their performance is evaluated. These methods include the weighted-sum method, lexicographic method, normal boundary intersection method, min–max method, and nondominated sorting genetic algorithm II. To compare the performance of these methods, two indices are proposed in this study, which include the demand fulfillment index and total demand fulfillment index. The former is for analyzing the demand fulfillment ratio of different priority EVs, while the latter is for the demand fulfillment analysis of the whole EV fleet requiring a recharge. In addition, the computational complexity, variance, and additional constraints required by each method are also analyzed. The simulation results have shown that the lexicographic method has the best performance when the relative priorities are known, while the min–max method is the most suitable method if the priorities are not known.

Simulation and experiment investigation of a heating and power double function system with multi-objective optimization

As conventional organic Rankine cycle (ORC) power generation and reverse Carnot cycle (RCC) heat pump systems have some limitations for a fixed heat source. This study proposed a novel RCC and ORC double function system which can work in the ORC power generation mode and RCC heat pump mode for district heating and power output, respectively. The energy model is firstly established to analyze the system thermal performance and then a test rig is built to verify the performance of the system and validate the mathematical model. The economic and environmental analysis are conducted and the multi-objective optimization (MOP) method has been conducted to solve the conflicting problem between the capital cost and payback period under the different operating conditions. Results indicate that the system has good feasibility and stability which can provide 5.96 kW power output with the thermal efficiency of 5.23 % and 60.02 kW heating capacity with the COP of 2.85. The errors of the experiment to simulation COP and the error of experiment to simulation thermal efficiency value are all less than 10%. The optimization consequences based on the TOPSIS decision-making and NSGA-II technology indicate that the MOP solution has a better performance compared with the single-objective optimization.

Output Space Entropy Search Framework for Multi-Objective Bayesian Optimization

We consider the problem of black-box multi-objective optimization (MOO) using expensive function evaluations (also referred to as experiments), where the goal is to approximate the true Pareto set of solutions by minimizing the total resource cost of experiments. For example, in hardware design optimization, we need to find the designs that trade-off performance, energy, and area overhead using expensive computational simulations. The key challenge is to select the sequence of experiments to uncover high-quality solutions using minimal resources. In this paper, we propose a general framework for solving MOO problems based on the principle of output space entropy (OSE) search: select the experiment that maximizes the information gained per unit resource cost about the true Pareto front. We appropriately instantiate the principle of OSE search to derive efficient algorithms for the following four MOO problem settings: 1) The most basic single-fidelity setting, where experiments are expensive and accurate; 2) Handling black-box constraints which cannot be evaluated without performing experiments; 3) The discrete multi-fidelity setting, where experiments can vary in the amount of resources consumed and their evaluation accuracy; and 4) The continuous-fidelity setting, where continuous function approximations result in a huge space of experiments. Experiments on diverse synthetic and real-world benchmarks show that our OSE search based algorithms improve over state-of-the-art methods in terms of both computational-efficiency and accuracy of MOO solutions.

Solving Multi-Objective Energy Management of a DC Microgrid using Multi-Objective Multiverse Optimization

This paper deals with the multi-objective optimization dispatch (MOOD) problem in a DC microgrid. The aim is to formulate the MOOD to simultaneously minimize the operating cost, pollutant emission level of (NOx, SO2 and CO2) and the power loss of conversion devices. Taking into account the equality and inequality constraints of the system. Two approaches have been adopted to solve the MOOD issue. The scalarization approach is first introduced, which combines the weighted sum method with price penalty factor to aggregate objective functions and obtain Pareto optimal solutions. Whilst, the Pareto approach is based on the implementation of evolutionary multi-objective optimization solution. Single and multi-objective versions of multi-verse optimizer algorithm are, respectively, employed in both approaches to handle the MOOD. For each time step, a fuzzy set theory is selected to find the best compromise solution in the Pareto optimal set. The simulation results reveal that the Pareto approach achieves the best performances with a considerable decrease of 28.96 $/day in the daily operating cost, a slight reduction in the power loss of conversion devices from 419.79 kWh to 419.29 kWh, and in less computational time. While, it is noticing a small increment in the pollutant emission level from 11.54 kg/day to 12.21 kg/day, for the daily microgrid operation. This deviation can be fully covered when comparing the cost related to the treatment of these pollutants, which is only 5.55 $/day, to the significant reduction in the operating cost obtained using the Pareto approach.

A model of multi-objective route optimization for a vessel in drifting ice

The paper suggests a three-dimensional graph model for a spatio-temporal representation of a water area with drifting ice objects. The article considers multi-objective route optimization with both additive and minimax criteria. The algorithmic solution of multi-objective optimization is proposed for a set of objective functions, which correspond to the following route parameters: the route length, risks along the route and the number of course direction changes. The method presented in the paper allows finding a set of Pareto-optimal solutions.The paper suggests the algorithm for arranging three-dimensional graph in relation to motion laws of ice objects existing in the considered water area. For illustrating the method, the article provides a computational example of path optimization. The paper also includes the discussion on the parameters influencing computational complexity of practical implementation of the developed method as well as on the approach in general.The developed model can be implemented in designing marine transportation systems and navigation assisting in ice infested water areas.