Search

Constrained multiobjective optimization problems (CMOPs) involve both conflicting objective functions and various constraints. Due to the presence of constraints, CMOPs' Pareto-optimal solutions are very likely lying on constraint boundaries. The experience from the constrained single-objective optimization has shown that to quickly obtain such an optimal solution, the search should surround the boundary of the feasible region from both the feasible and infeasible sides. In this article, we extend this idea to cope with CMOPs and, accordingly, we propose a novel constrained multiobjective evolutionary algorithm with bidirectional coevolution, called BiCo. BiCo maintains two populations, that is: 1) the main population and 2) the archive population. To update the main population, the constraint-domination principle is equipped with an NSGA-II variant to move the population into the feasible region and then to guide the population toward the Pareto front (PF) from the feasible side of the search space. While for updating the archive population, a nondominated sorting procedure and an angle-based selection scheme are conducted in sequence to drive the population toward the PF within the infeasible region while maintaining good diversity. As a result, BiCo can get close to the PF from two complementary directions. In addition, to coordinate the interaction between the main and archive populations, in BiCo, a restricted mating selection mechanism is developed to choose appropriate mating parents. Comprehensive experiments have been conducted on three sets of CMOP benchmark functions and six real-world CMOPs. The experimental results suggest that BiCo can obtain quite competitive performance in comparison to eight state-of-the-art-constrained multiobjective evolutionary optimizers.

During the last two decades, the notion of multiobjective optimization (MOO) has been successfully adopted to solve the nonconvex constrained optimization problems (COPs) in their most general forms. However, such works mainly utilized the Pareto dominance-based MOO framework while the other successful MOO frameworks, such as the reference vector (RV) and the decomposition-based ones, have not drawn sufficient attention from the COP researchers. In this article, we utilize the concepts of the RV-based MOO to design a ranking strategy for the solutions of a COP. We first transform the COP into a biobjective optimization problem (BOP) and then solve it by using the covariance matrix adaptation evolution strategy (CMA-ES), which is arguably one of the most competitive evolutionary algorithms of current interest. We propose an RV-based ranking strategy to calculate the mean and update the covariance matrix in CMA-ES. Besides, the RV is explicitly tuned during the optimization process based on the characteristics of COPs in a RV-based MOO framework. We also propose a repair mechanism for the infeasible solutions and a restart strategy to facilitate the population to escape from the infeasible region. We test the proposal extensively on two well-known benchmark suites comprised of 36 and 112 test problems (at different scales) from the IEEE CEC (Congress on Evolutionary Computation) 2010 and 2017 competitions along with a real-world problem related to power flow. Our experimental results suggest that the proposed algorithm can meet or beat several other state-of-the-art constrained optimizers in terms of the performance on a wide variety of problems.

Performance of multi/many-objective evolutionary algorithms (MOEAs) based on decomposition is highly impacted by the Pareto front (PF) shapes of multi/many-objective optimization problems (MOPs), as their adopted weight vectors may not properly fit the PF shapes. To avoid this mismatch, some MOEAs treat solutions as weight vectors to guide the evolutionary search, which can adapt to the target MOP's PF automatically. However, their performance is still affected by the similarity metric used to select weight vectors. To address this issue, this article proposes a fuzzy decomposition-based MOEA. First, a fuzzy prediction is designed to estimate the population's shape, which helps to exactly reflect the similarities of solutions. Then, N least similar solutions are extracted as weight vectors to obtain N constrained fuzzy subproblems ( N is the population size), and accordingly, a shared weight vector is calculated for all subproblems to provide a stable search direction. Finally, the corner solution for each of m least similar subproblems ( m is the objective number) is preserved to maintain diversity, while one solution having the best aggregated value on the shared weight vector is selected for each of the remaining subproblems to speed up convergence. When compared to several competitive MOEAs in solving a variety of test MOPs, the proposed algorithm shows some advantages at fitting their different PF shapes.

Natural ice accretion on the lifting surface of an aircraft is detrimental to its aerodynamic performance, as it changes the effective streamlined body. The main focus of this work considers the optimization design of airfoils under atmospheric icing conditions for the Unmanned Aerial Vehicle (UAV). The ice formation process is simulated by the Eulerian approach and the three-dimensional Myers model. A three-equation turbulence model is implemented to accurately predict the stall performance of the iced airfoil. In recognition of the real atmospheric variability in the icing parameters, the medium volume diameter of supercooled water droplets is treated as an uncertainty with an assumed probability density function. A technique of polynomial chaos expansion is used to propagate the input uncertainty through the deterministic system. The numerical results show that the multipoint/multiobjective optimization strategy can efficiently improve both the ice tolerance and the cruise performance of an airfoil. The reason for the focus on robust optimization is that the ice angle of the optimized airfoil becomes less critical to the incoming flow. The optimized airfoils are applied to a UAV platform, in which the performance improvement and the relevant key flow feature are both preserved.

In this paper, we investigate the relationships between proper efficiency and the solutions of a general scalarization problem in multi-objective optimization. We provide some conditions under which the solutions of the dealt with scalar program are properly efficient and vice versa. We also show that, under some conditions, if the considered general scalar problem is unbounded, then the original multi-objective problem does not have any properly efficient solution. In another part of the work, we investigate a general transformation of the objective functions which preserves proper efficiency. We show that several important results existing in the literature are direct consequences of the results of the present paper.

In this paper good consensus is associated with a high level of group satisfaction and a low level of dissatisfaction. A new method to improve consensus through a reformulation of the original group multi-objective optimization problem is introduced. For each point in the feasible decision set, the level of satisfaction or dissatisfaction from each group member is determined by multi-criteria ordinal classification approaches. Intense satisfaction and dissatisfaction are both modeled. Group satisfaction (respectively, dissatisfaction) is maximized (resp. minimized), finding the best possible consensus solutions in correspondence with a current stage of closeness among group members’ preferences, judgments, beliefs, and conservatism attitudes. Logic models are introduced to evaluate conditions for best consensus. Imperfect information (imprecision, uncertainty, ill-definition, arbitrariness) on the values of objective functions, required and available resources, and decision model parameters is handled by using interval numbers. Two different kinds of multi-criteria decision model are considered: i) an interval outranking approach and ii) an interval weighted-sum value function. The proposal can handle very general cases of group multi-objective optimization problems. The method is illustrated by solving a real size multi-objective project portfolio optimization problem using evolutionary computation tools.

Current pulses are convenient to be actively implemented by a Battery Management System (BMS). However, the Short-Term Features (STF) from currentpulses originate from various sensors with uneven qualities, which hinders one powerful and strong learner with STF for the battery SOH estimation. This paper thus proposes an optimized weak learner formulation procedure for Lithium-ion (Li-ion) battery SOH estimation, which further enables the automatic initialization and integration of the weak learners with STF into an efficient SOH estimation framework. A Pareto Front-based Selection Strategy (PFSS) is designed to select the representative solutions from the non-dominated solutions fed by a Knee point driven Evolutionary Algorithm (KnEA), which guarantees both the diversity and accuracy of the weak learners. Afterwards, the weak learners, whose coefficients are obtained by Selfadaptive Differential Evolution (SaDE), are integrated by a weight-based structure. The proposed method utilizes the weak learners with STF to boost the overall performance of SOH estimation. The validation of the proposed method is proved by LiFePO4/C batteries under accelerated cycling ageing test including one mission profile providing Primary Frequency Regulation (PFR) service to the grid and one constant current profile.

The constant evolution of transportation systems and traffic in developing countries is nowadays confronted with a problem of road safety and therefore of a high accident rate, especially in the context of inter-urban road transport. In this work, we propose a communication architecture for an Intelligent Transport System (ITS) to provide surveillance in an inter-urban transport network in the context of developing countries. We introduce two types of control points: Relay Control Points (RCP) and Treatment Control Points (TrCP). We also designed two multi-objective models for the deployment of these points. In order to ensure good coverage, to minimize the cost of installation and to put more emphasis in the areas having a high number of accidents. To ensure optimal deployment of these points, we have used the Non-Dominated Sorted Genetic Algorithm II (NSGA-II) that will allow to realize the Pareto front of non-dominated solutions. The results of the simulations show the effectiveness of our proposal.

Budget allocation problems in portfolio management are inherently multi-objective as they entail different types of assets of which performance metrics are not directly comparable. Existing asset management methods that either consolidate multiple goals to form a single objective (a priori) or populate a Pareto optimal set (a posteriori) may not be sufficient because a decision maker (DM) may not possess comprehensive knowledge of the problem domain. Moreover, current techniques often present a Pareto optimal set with too many options, making it counter-productive. In order to provide the DM with a diverse yet compact solution set, this paper proposes a three-step approach. In the first step, we employ different approximation functions to capture investment-performance relationships at the asset-type level. These simplified relationships are then used as inputs for the multi-objective optimisation model in the second step. In the final step, Pareto optimal solutions generated by a selected evolutionary algorithm are pruned by a clustering method. To measure the spread of representative solutions over the Pareto front, we present two novel indicators based on average Euclidean distance and cosine similarity between original Pareto solutions and representative solutions. Through numerical examples, we demonstrate that this approach can provide a set of representative solutions that maintain high integrity of the original Pareto front. We also put forward suggestions on choosing appropriate approximation functions, pruning methods, and indicators.

Offspring generation plays an important role in evolutionary multiobjective optimization. However, generating promising candidate solutions effectively in high-dimensional spaces is particularly challenging. To address this issue, we propose an adaptive offspring generation method for large-scale multiobjective optimization. First, a preselection strategy is proposed to select a balanced parent population, and then these parent solutions are used to construct direction vectors in the decision spaces for reproducing promising offspring solutions. Specifically, two kinds of direction vectors are adaptively used to generate offspring solutions. The first kind takes advantage of the dominated solutions to generate offspring solutions toward the Pareto optimal set (PS) for convergence enhancement, while the other kind uses those nondominated solutions to spread the solutions over the PS for diversity maintenance. The proposed offspring generation method can be embedded in many existing multiobjective evolutionary algorithms (EAs) for large-scale multiobjective optimization. Experiments are conducted to reveal the mechanism of our proposed adaptive reproduction strategy and validate its effectiveness. Experimental results on some large-scale multiobjective optimization problems have demonstrated the competitive performance of our proposed algorithm in comparison with five state-of-the-art large-scale EAs.

Techniques to reduce the energy burden of an industrial ecosystem often require solving a multiobjective optimization problem. However, collecting experimental data can often be either expensive or time-consuming. In such cases, statistical methods can be helpful. This article proposes Pareto Front (PF) and Pareto Set (PS) estimation methods using Bayesian Additive Regression Trees (BART), which is a non-parametric model whose assumptions are typically less restrictive than popular alternatives, such as Gaussian Processes (GPs). These less restrictive assumptions allow BART to handle scenarios (e.g. high-dimensional input spaces, nonsmooth responses, large datasets) that GPs find difficult. The performance of our BART-based method is compared to a GP-based method using analytic test functions, demonstrating convincing advantages. Finally, our BART-based methodology is applied to a motivating engineering problem. Supplementary materials, which include a theorem proof, algorithms, and R code, for this article are available online., Comment: 27 pages, 8 figures, submitted to Industry 4.0 special issue of Technometrics journal

Consider a multiobjective decision problem with uncertainty in the objective functions, given as a set of scenarios. In the single-criterion case, robust optimization methodology helps to identify solutions which remain feasible and of good quality for all possible scenarios. A well-known alternative method in the single-objective case is to compare possible decisions under uncertainty with the optimal decision with the benefit of hindsight, i.e. to minimize the (possibly scaled) regret of not having chosen the optimal decision. In this contribution, we extend the concept of regret from the single-objective case to the multiobjective setting and introduce a proper definition of multivariate (robust) (relative) regret. In contrast to the few existing ideas that mix scalarization and optimization, we clearly separate the modelling of multiobjective (robust) regret from its numerical solution. Moreover, our approach is not limited to a finite uncertainty set or interval uncertainty and furthermore, computations or at least approximations remain tractable in several important special cases. We illustrate all approaches based on a biobjective shortest path problem under uncertainty.

In many cases, some programs often have some milestone activities that decision makers need to pay attention to. In this case, managers must efficiently describe these different decision-making spaces and use this as a basis to optimize possible solutions. Choosing a suitable decision-making space has always been a major factor in decision-making management, and it is also one of the key factors that managers must determine when making plans. Multi-objective optimization is to optimize multiple objectives at the same time. Multi-objective optimization algorithms have been widely used in many technology industries. This article researched from two parts: model display and optimization algorithm. The first is to deepen the basic characteristics of project planning and decision-making when there are more decision-making spaces. Based on the existing decision-making network planning methods, combined with the situation analysis method, a decision-making network planning model that can show more decision-making space is established. Secondly, based on the actual improvement requirements, the multi-objective optimization method in the multi-decision network design model and the simulation model of activity exercise data are established. The purpose is to create a relatively complete project planning decision model and optimization algorithm that can select multiple decision spaces at the same time through the above experimental research.

The shape approximation method has been proven to be rapid and practicable in resolving low-thrust trajectory; however, it still faces the challenges of large deviation from the optimal solution and inability to satisfy the specific flight time and fuel mass constraints. In this paper, a modified shape approximation low-thrust model is presented, and a novel constrained optimization algorithm is developed to solve this problem. The proposed method aims at settling the bi-objective optimization orbit involving the twin objectives of minimum flight time and low fuel consumption and enhancing the accuracy of optimized orbit. In particular, a transformed high-order polynomial model based on finite Fourier series is proposed, which can be characterized as a multi-constraint optimization problem. Then, a novel optimization algorithm is specifically developed to optimize the large-scale multi-constraint dynamical equations of shape trajectory. The key performance indicators of the index include minimum flight time, low fuel consumption and bi-objective optimization of the two. Simulation results prove that this approach possesses both the high precision achievable by numerical methods and low computational complexity offered by shape approximation techniques. Besides, the Pareto front of the fuel-time bi-objective optimization orbit is firstly introduced to analyze an intact optimal solution set. Furthermore, we have demonstrated that our proposed approach is appropriate to generate the preliminary orbit for pseudo-spectral method.

The effect of numerous process variables has been explored for surface roughness and material removal rate during the magnetic abrasive finishing process. A hybrid approach was used in which the Taguchi technique is used in conjunction with grey relational analysis to reach the optimum combination of input variables. The L16 orthogonal array design was used to get a different combination of parameters. It was found that spindle speed of 200 rpm, the quantity of magnetic abrasives of 5 mg, mesh number of 270, and machining time 60 min caused minimum surface roughness of 0.066 µm during magnetic abrasive finishing of the brass plate. The percentage contribution of input parameters has been reported. Subsequently, the optimum results were obtained using multi-objective optimization techniques of grey relational analysis, and results were also validated using experimentation.

3D mesh subdivision is essential for geometry modeling of complex surfaces, which benefits many important applications in the fields of multimedia such as computer animation. However, in the ordinary adaptive subdivision, with the deepening of the subdivision level, the benefits gained from the improvement of smoothness cannot keep pace with the cost caused by the incremental number of faces. To mitigate the gap between the smoothness and the number of faces, this paper devises a novel improved mesh subdivision method to coordinate the smoothness and the number of faces in a harmonious way. First, this paper introduces a variable threshold, rather than a constant threshold used in existing adaptive subdivision methods, to reduce the number of redundant faces while keeping the smoothness in each subdivision iteration. Second, to achieve the above goal, a new crack-solving method is developed to remove the cracks by refining the adjacent faces of the subdivided area. Third, as a result, the problem of coordinating the smoothness and the number of faces can be formulated as a multi-objective optimization problem, in which the possible threshold sequences constitute the solution space. Finally, the Non-dominated sorting genetic algorithm II (NSGA-II) is improved to efficiently search the Pareto frontier. Extensive experiments demonstrate that the proposed method consistently outperforms existing mesh subdivision methods in different settings.

The rapid charging of lithium ion battery cells while minimizing degradation is a key challenge in battery management. Offline optimal control frameworks employing physics-based models provide a first-principles approach to this problem that provides critical insights and benchmarks for real-time oriented online optimization algorithms. In this letter, we approach the optimal control problem of minimizing both charging time and degradation of a NMC battery using the single shooting optimization framework, employing a coupled electrochemical-thermal-aging model. The aging mechanism used captures growth of the SEI layer, solvent diffusion. The effectiveness of the single shooting method using a piecewise polynomial control and the low sensitivity of the method to chosen numerical parameters in the multi-objective problem is illustrated. The tradeoff between charging time and degradation is investigated numerically.

The Control Rod Drive Mechanism (CRDM) is an essential part of the reactor, which realizes the start-stop and power adjustment of the reactor by lifting and lowering the control rod assembly. As a moving part in CRDM, the latch directly contacts with the control rod assembly, and the life of latch is closely related to the service life of the reactor. In this paper, the relationship between the life of the latch and the step stress, friction stress, and impact stress in the process of movement is analyzed, and the optimization methodology and process of latch life based on the approximate model are proposed. The design variables that affect the life of the latch are studied through the experimental design, and the optimization objective of design variables based on the latch life is established. Based on this, an approximate model of the life of the latch is built, and the multi-objective optimization of the life of the latch is optimized through the NSGA-II algorithm.

Nowadays, the problem of the proper charging of plug-in hybrid electric vehicles (PHEVs) has become increasingly difficult because there is high uncertainty on both the demand and supply sides of microgrid (MG) systems, which may reduce efficiency and increase the cost of MG systems. Available solutions to these challenges are the application of energy storage systems and energy exchange with the upstream utility grid (UUG). However, uncoordinated PHEV charging could have adverse effects on MGs, such as increasing the amounts of energy exchanged between the MGs and the UUG as well as decreasing the battery energy storage systems (BESSs) lifetime. This article proposes a smart charging scheme for PHEVs in ac MGs that can simultaneously minimize the energy drawn from the UUG to charge PHEVs and maximize the lifetime of BESSs based on a multiobjective optimization algorithm. For proving the validity of the proposed power management strategy (PMS), offline digital time-domain simulation studies are conducted based on the modified version of the IEEE 33-bus test system. The obtained results are compared with the results of other previously reported PMSs, which show that by increasing the output power of DER units (even when the penetration level of PHEVs increases), the proposed PMS can ensure proper charging of PHEVs while improving the lifetimes of BESSs and decreasing the energy drawn from the UUG.

Soil and water conservation practices have been extensively used in effective watershed management. The impact of each conservation practice is site specific and dependent on the implementation site in the watershed. In order to select cost effective placement of conservation practices with high impact, a large number of spatial combinations is needed to be compared. In this study, an optimization model framework is presented to find cost effective solutions for sediment yield and runoff control in the Fariman dam watershed in the Northeast of Iran. This was accomplished by integrating soil and water assessment tool (SWAT) for simulation of watershed hydrology and multi objective genetic algorithm (NSGA-II) for spatial optimization of soil and water conservation practices. The optimized solutions provided a trade-off between the two objective functions. The final Pareto-optimal shows that the impact of soil and water conservation practices on sediment yield is more than stream flow. The trade-offs between the objective functions show that the implementation of the median cost can lead to a significant decrease of 22.1% in the amount of sediment yield, and 10% in stream flow. Also, percent change achieved through median cost is very close to percent reduction with the highest cost. Results of low cost solution show that the vegetative practices are a suitable economic scenario for soil and water conservation. The introduced framework can be adapted as a suitable tool for selecting cost effective conservation practices in different regions.

Dynamic multi-objective optimization problems (DMOPs) contain multiple conflicting goals while tracking the changing Pareto-optimal front (PF) or Pareto-optimal set (PS). Most algorithms treat the solutions of DMOPs as if they were dealing with static multi-objective optimization problems. However, solutions under different environments may obey different distributions. To solve some of the existing limitations of currently available methods, a dynamic multi-objective optimization algorithm based on feature information prediction (FIP) is proposed. To identify the distribution of solutions after an environmental change, joint distribution adaptation (JDA) is used to construct a mapping function. The feature information, which is extracted from the objective space at the current time step, is mapped to a higher dimensional space. Then the feature information of decision space at the next time step is obtained using the interior point method. Based on this information, the initial population at the next time step is generated when a change is detected. The performance of FIP is validated by comparing it with respect to four state-of-the-art evolutionary algorithms on eight benchmark functions. Experimental results demonstrate that FIP can quickly cover the front with rapidly changing environments.

The hydrocarbon supply chain (HCSC) is a significant part of the world's energy sector. The energy market has experienced erratic behavior over the last few years results in financial risks such as exceeding certain limits of the budget or not achieving the desired levels of cash in-flow, i.e., revenue. In this work, robust optimization and multi-objective mathematical programming are used to develop a model that eliminates or at least mitigates the impact of uncertain market behavior. Robust optimization provides tactical plans that are feasible and robust over market scenarios. The model assesses the trade-offs between alternatives and guides the decision-maker towards the effective management of the HCSC. The economic objectives are to minimize total cost and maximize revenue, while the non-economic objective is to minimize the depletion rate. The model considers the environmental aspect by limiting the emission of CO2 and the sustainability aspect by reducing the depletion rate of natural resources. Uncertain behavior of the oil market is modeled on scenario representation. A case study based on real data from Saudi Arabia HCSC is provided to demonstrate the model's practicality, and a sensitivity analysis is conducted to provide some managerial insights. The results indicate that Saudi Arabia can cover its entire expenditure, break-even-point, by producing oil at 7.18 MMbbld and gas at 3,543.48 MMcftd. Besides, the robust approach provides a preferred plan with the highest cash inflow and the lowest sustainability over other approaches, e.g., deterministic, stochastic, and risk-based. The differences show that the robust model increases oil production to compensate for the variability of the scenario.

The ever increasing pressure to conserve the environment from global warming cannot be overemphasized. Emission from the inventory and production process contributes immensely to global warming and hence, the need to device a sustainable green inventory by the operational managers. In this paper, a multi-item multi-objective inventory model with back-ordered quantity incorporating green investment in order to save the environment is proposed. The model is formulated as a multi-objective fractional programming problem with four objectives: maximizing profit ratio to total back-ordered quantity, minimizing the holding cost in the system, minimizing total waste produced by the inventory system per cycle and minimizing the total penalty cost due to green investment. The constraints are included with budget limitation, space restrictions, a constraint on cost of ordering each item, environmental waste disposal restriction, cost of pollution control, electricity consumption cost during production and cost of greenhouse gas emission in the production process. The model effectiveness is illustrated numerically, and the solution obtained to give a useful suggestion to the decision-markers in the manufacturing sectors.

Segmentation is an important step of image processing that directly affects its success. Among the methods used for image segmentation, histogram-based thresholding is a very popular approach. To apply the thresholding approach, many methods such as Otsu, Kapur, Renyi etc. have been proposed in order to produce the thresholds that will segment the image optimally. These suggested methods usually have their own characteristics and are successful for particular images. It can be thought that better results may be obtained by using objective functions with different characteristics together. In this study, the thresholding which is originally applied as a single-objective problem has been considered as a multi-objective problem by using the Otsu and Kapur methods. Therefore, the discrete multi-objective shuffled gray wolf optimizer (D-MOSG) algorithm has been proposed for multi-level thresholding segmentation. Experiments have clearly shown that the D-MOSG algorithm has achieved superior results than the compared algorithms.

In this article, a distributed multiobjective optimization problem is formulated for the resource allocation of network-connected multiagent systems. The framework encompasses a group of distributed decision makers in the subagents, where each of them possesses a local preference index. Novel distributed algorithms are proposed to solve such a problem in a distributed manner. The weighted Lp preference index is utilized in each agent since it can provide a robust Pareto solution to the problem. By using distributed fixed-time optimization methods, the Lp preference index is constructed online without specifying the unknown parameters. Then, it is proved that the problem admits a unique Pareto solution. By exploiting consensus and gradient descent techniques, asymptotic convergence to the optimal solution is established via Lyapunov theories. Distinct from most of the current works, the proposed framework does not require any prior information in the formulation process, and private data can be well protected using this distributed approach. Numerical examples are included to validate the effectiveness of the proposed algorithms.

This paper aims to optimally design a PV/Wind/Diesel Hybrid Microgrid System (HMS) for a small number of houses considering load uncertainty for the city of Yanbu, Saudi Arabia. Designing such a hybrid system with all the renewable and non-renewable sources, storage devices, converters, and loads is a complicated task. A multiobjective approach has been adopted to optimize the microgrid design. Two methodologies are available for solving such multiobjective problems. In the first approach, the problem is transformed into a single objective one (using aggregation, for instance), whereas, the second technique treats objectives simultaneously and independently as adopted in this paper. The proposed approach offers the Pareto front; a set of solutions in one run opening the door of choosing the most suitable solution from the available options based on the experience, expertise and requirement of the designer. This paper presents a novel approach of using Decomposition Based Multiobjective Evolutionary Algorithm (MOEA/D) to optimally design the PV/Wind/Diesel HMS considering load uncertainty. Loss of Power Supply Probability (LPSP) and Cost of Electricity (COE) are considered as the objective functions of the optimization problem. Furthermore, two separate load cases of 5 and 10 houses are tested to verify the robustness of the approach. The obtained results are beneficial in assisting researchers and practitioners in selecting the optimal configuration of the microgrid.

The energy operation of the building can be enhanced by retrofitting actions considering that it influences the life quality of the residents. Since optimization of different retrofitting scenarios needs much time, a new method is proposed in this study to simplify the optimization process. Therefore, an integration of the parametric sensitivity evaluation at the early phases of the optimization procedure is employed to decrease the number of the needed computation. Two objectives of the optimization process are including interior thermal comfort without increasing greenhouse gas emissions as the environment-related effects. Four steps are involved in the process: initial energy operation evaluation of the housing prototype; suggesting retrofitting actions; parametric sensitivity evaluation for retrofitting measures to define the most effective actions; and multiple-criteria optimization. Finally, outer wall insulation, roof insulation, airtightness, and floor insulation have resulted as more significant parameters with considerable effect on energy operation. The next category is including performance schedule, artificial lighting, temperature setpoints, and window substitution with low effect on decreasing energy usage. For controlling multiple-objective retrofitting projections when handling the side effects an efficient approach is presented by best scenarios for decision-makers, especially for architects.

In order to improve the performance (low torque ripple, low suspension ripple, and high power factor) of the permanent magnet assisted bearingless synchronous reluctance motor (PMa-BSynRM), the multiobjective optimal design based on fast nondominated sorting genetic algorithm (NSGA-Ⅱ) of PMa-BSynRM rotor topology is investigated in this article. First, the structure and operation principle of the PMa-BSynRM are introduced. Second, the initial rotor design that gives optimizer the ability to produce a variety of barrier shapes and the comprehensive sensitive analysis that evaluates the influence of each design variable on optimization objectives are presented. Third, the optimal design is selected from the Pareto front, which is generated by NSGA-Ⅱ, and validated by finite-element analysis. The simulation results confirm that the torque and suspension force capacity of optimal motor are improved significantly in comparison with initial design, whereas the value of power factor reaches 0.81. Finally, the optimal prototype motor is manufactured, and experimental results confirm the validity and superiority of the optimized design.

In this research paper, we focus on developing a generation scheduling model using an intelligent soft-computing technique in a microgrid (MG) system. A multiobjective power management system with innovative features of the MG technology is presented The necessity and reason for undertaking this study is to optimize MG operation as well as address the uncertainty of random energy production from renewables by utilizing demand response (DR) programs. A meta-dynamic-approach-based multiobjective flower pollination algorithm is applied to solve this complex, nonlinear, multiobjective optimization (MOO) problem. Energy management in MGs utilizing renewable energy is a salient feature. DR schemes are conducted in residential, commercial, and industrial customers. Simulations are performed to achieve reduced prices and minimum emissions. Comparative studies were conducted wherein the metaheuristic algorithm demonstrated superior performance and higher efficiency compared to other technique. Operating costs reduced by 20.3% and emissions reduced by 5% after the implementation of DR programs using a meta-dynamic-approach-based flower pollination algorithm compared to particle swarm optimization (PSO). The results demonstrate the superiority of the proposed demand-side management modeling method.

Improving building performance is of great significance to protecting the ecology, saving energy and enhancing the living environment. This paper developed a comprehensive method for optimizing the design of a regular architectural space to improve building performance. The research aims to provide architects with robust and accurate design references when conducting design tasks. The entire optimization process is divided into three steps. The first step is to build a database by generating the research objects randomly and performing building simulations on them. The second step is to train artificial neural network (ANN) models as a substitute of the time-consuming building simulation in the multi-objective optimization to predict the building performance quickly. The last step is to perform multi-objective optimization based on the actual design constraints. To demonstrate the optimization process, a common type of classroom space defined by 30 design parameters was selected as a case study. The optimization objectives were set as energy demand, thermal environment and daylight environment. The accuracy of different ANN models was assessed. To imitate realistic design tasks, three design scenarios with constraints are used in the optimization. All the three optimizations finished in 350 s. Compared to the traditional optimization method based on simulation, the optimization calculation is accelerated by approximately 2,570 times. To ensure the reliability of the optimization results, several nondominated solutions of each case were validated by simulation, and there were good agreements between the simulation results and the optimization results. An integrated solution and a reference solution was defined for each case. Compared to the reference solution, the objectives of the integrated solution of the three cases have been improved by 24.6%, 18.7% and 14.2% on average, respectively, indicating that this method is feasible and effective to improve building design in actual tasks.

Green and efficient routes for a sustainable and renewable strategy in chemicals and energy delivery are highly demanded in the current status. Developing production routes from bio-alcohols is of immense interest. To achieve such a goal, an enhanced membrane-assisted dehydration reactor for the conversion of bio-alcohols (mainly made up of methanol and ethanol) is suggested. The system can eliminate the innate and produced water through the dehydration reaction, representing an intensified process that favors a conversion enhancement without needing a water purification unit. This study includes a rigorous feasibility study utilizing a validated mathematical model. The impacts of input variables such as feed flowrate, feed temperature, feed composition, and feed pressure, as well as the sweep gas flowrate and temperature, are examined. The sensitivity analysis is conducted in terms of feed conversion, temperature profiles, pressure drop, and desired product distributions. Then, an optimization strategy was developed to obtain the optimum operating conditions of each system leading to maximized conversion and product yields. According to the achievements of this study, the enhanced membrane-assisted dehydration reactor offers a great capacity for converting bio-alcohols and producing considerable quantities of DME from bio-methanol as well as DEE, ethylene, and butylene from bio-ethanol.

When solving constrained multiobjective optimization problems (CMOPs), the most commonly used way of measuring constraint violation is to calculate the sum of all constraint violations of a solution as its distance to feasibility. However, this kind of constraint violation measure may not reflect the distance of an infeasible solution from feasibility for some problems, for example, when an infeasible solution closer to a feasible region does not have a smaller constraint violation than the one farther away from a feasible region. Unfortunately, no set of artificial benchmark problems focusing on this area exists. To remedy this issue, a set of CMOPs with deceptive constraints is introduced in this article. It is the first attempt to consider CMOPs with deceptive constraints (DCMOPs). Based on our previous work, which designed a set of directed weight vectors to solve CMOPs, this article proposes a cooperative framework with an improved version of directed weight vectors to solve DCMOPs. Specifically, the cooperative framework consists of two switchable phases. The first phase uses two subpopulations-one to explore feasible regions and the other to explore the entire space. The two subpopulations provide useful information about the optimal direction of objective improvement to each other. The second phase aims mainly at finding Pareto-optimal solutions. Then an infeasibility utilization strategy is used to improve the objective function values. The two phases are switchable based on the information found to date at any time in the evolutionary process. The experimental results show that this method significantly outperforms the algorithms with which it is compared on most of the DCMOPs, in terms of reliability and stability in finding a set of well-distributed optimal solutions.

The purpose of this paper is to propose a novel combined cooling, heating, and power generation system driven by evacuated tube solar collectors for residential applications. Accordingly, evacuated tube collectors are employed to provide sufficient heat for cooling and power generation purposes, while the waste heat of the evacuated tube collectors is then exploited for heating. The proposed system is comprehensively analyzed from various standpoints i.e., energy, exergy, and exergoeconomic. Afterward, the multi-objective genetic algorithm optimization – as a suitable tool – is applied to the system to extract a trade-off between the competing objective functions. The results showed that R124 results in better exergetic efficiency compared to other refrigerants. The parametric study outcomes indicate that with increasing the collector area, total product cost reduces but the total cost rate increases dramatically. The results also show that input parameters can directly affect the exergetic sustainability index to be cautiously designed. The optimization results show that the system’s maximum exergy efficiency is 10.06% while the minimum total cost rate is obtained as 0.4835 $/h. Further, the decision factors’ scatter plots show that LiBr mass fraction should be around 25% for optimal operation. Overall, the proposed system can be employed for cooling, heating, and power generation as a potential cycle.

The objective of this work is to propose a machine-learning assisted multi-objective optimization protocol to design and optimize alkali–surfactant–polymer flooding processes in the presence of multiple technical and economic objective functions. Several universal multi-layer neural networks are trained, and they act as universal surrogate models of high-fidelity numerical simulator to evaluate the objective functions involved in the optimization workflow. The HLD-NAC equation is employed to model the microemulsion phase behavior of the crude oil/brine/surfactant system with the presence of alkali agents. The validity of the expert systems is confirmed via extensive blind testing applications with error margins of 9%, which includes the predictions of fluid production and pressure responses. A multi-objective optimization workflow is structured by coupling the expert systems with particle swarm optimizer, which employs Pareto optimum theory to carry comprehensive ASP injection assessments considering various technical and economic objective functions. Moreover, the proposed workflow enables the decision makers to comprehend the project risks by taking the inherent uncertainties from crude oil market into accounts. The robustness of the optimization protocol is verified by introducing a synthetic field case study, which validates the competence of optimizing ASP injection design considering project net present value as an objective function. A series of Pareto front solutions are generated when more objective functions such as chemical efficacies and water cut reductions are included. Subsequently, the workflow evaluates the project economic uncertainties from the fluctuation of oil price, which helps the decision makers investigate the project risks from technical and economic perspectives.

Lack of electricity networks in remote areas and also the high cost of connecting these areas to national networks due to the unfavorable geographical situation of the region leads to the use of other energy sources independent of the network in these areas. Today, the use of distributed generation sources is increasing due to the reduction of fossil fuel sources and heat problems. The output power of distributed generation sources, especially renewable energy sources, fluctuates under the influence of atmospheric conditions. The main purpose of the present study is to present a new optimal configuration for a hybrid photovoltaic/diesel generator/battery system to refine the load demand of a rural area in Hoxtolgay, China. The idea is to minimize the CO2 emissions value, the annualized cost, and the loss of load probability of the system. To simplify this system, e -constraint method is performed. The problem has been solved by an adaptive version of Marine Predators Algorithm (AMPA) to improve the optimization results. The total ACS for the optimal system is achieved 8224.15 $. Also, an optimal value of 451.30 kW for diesel generator, 4266$ for battery storage, and 2670.53 $ for PV generator are achieved. The initial capital cost of the system is achieved 47940 $ that is less than the NPC. In this case, the maximum cost of the system with 43.12% belongs to the PV system of total cost of the system. Finally, CO2 emission by the suggested AMPA with 1624 kg/year shows the minimum value with cleanest result among the others. Final results of the proposed technique are compared with PSO method and HOMER-based optimization to indicate its effectiveness. Sensitivity analysis has been also performed to determine the system efficiency.

The overall operational costs of home energy systems (HES) has been considered as an objective function (OF) by many articles. This paper shows that considering the energy cost as OF can lead to a decrease in the load elasticity against the electricity price, which can lead to demand response programs failure. So the distribution system operator (DSO) must stop this decline. A new index is introduced to calculate the responsiveness of the PV-integrated HES, based on which a new OF for home energy management system is proposed. This index shows the load elasticity against the electricity price. The relation between energy cost and load responsiveness index is investigated, and several scenarios are analyzed to demonstrate the applicability of the proposed approach in real cases. The proposed method is implemented to a PV- and ESS- integrated HES. The results show the relation between the responsiveness of the loads and the operational costs of home. A sensitivity analysis is added to the paper to show the robustness of the proposed control scheme.

Hybrid energy system is one main mean to deal with the energy crisis and its capacity optimization is a key to obtain an economical and reliable supply of energy. In this paper, the capacity optimization of a novel hybrid system composed of wind turbine, concentrated solar plant and electric heater is modeled as a multi-objective two-stage stochastic problem, where capacity optimization minimizing the life cycle cost (LCC) and energy management strategy optimization minimizing the loss of power supply probability (LPSP) are integrated. The scenario-based approach is applied to reflect the random characteristics of wind and solar resources. The Pareto set of the problem is obtained by non-dominated sorting genetic algorithm (NSGA-II), whose effectiveness is validated by algorithm comparisons with multi-objective particle swarm optimization (MOPSO) and multi-objective evolutionary algorithm based on decomposition (MOEA/D). Furthermore, techno-economic comparisons with a reference hybrid energy system without electric heater are performed to investigate economic benefits of the electric heater. The comparison results show that the electric heater is beneficial for a lower LCC which is reduced by 1.21%, 1.34%, 1.68%, 3.14%, 4.94% and 4.55% respectively when the LPSP is 0%, 1%, 2%, 3%, 4% and 5%.

Fair machine learning has been focusing on the development of equitable algorithms that address discrimination. Yet, many of these fairness-aware approaches aim to obtain a unique solution to the problem, which leads to a poor understanding of the statistical limits of bias mitigation interventions. In this study, a novel methodology is presented to explore the tradeoff in terms of a Pareto front between accuracy and fairness. To this end, we propose a multiobjective framework that seeks to optimize both measures. The experimental framework is focused on logistiregression and decision tree classifiers since they are well-known by the machine learning community. We conclude experimentally that our method can optimize classifiers by being fairer with a small cost on the classification accuracy. We believe that our contribution will help stakeholders of sociotechnical systems to assess how far they can go being fair and accurate, thus serving in the support of enhanced decision making where machine learning is used.

Mitigating bias in machine learning is a challenging task, due in large part to the presence of competing objectives. Namely, a fair algorithm often comes at the cost of lower predictive accuracy, and vice versa, a highly predictive algorithm may be one that incurs high bias. This work presents a methodology for estimating the fairness-accuracy Pareto front of a fully-connected feedforward neural network, for any accuracy measure and any fairness measure. Our experiments firstly reveal that for training data already exhibiting disparities, a newly introduced causal notion of fairness may be capable of traversing a greater part of the fairness-accuracy space, relative to more standard measures such as demographic parity and conditional parity. The experiments also reveal that tools from multi-objective optimisation are crucial in efficiently estimating the Pareto front (i.e., by finding more non-dominated points), relative to other sensible but ad-hoc approaches. Finally, the work serves to highlight possible synergy between deep learning and multi-objective optimisation. Given that deep learning is increasingly deployed in real-world decision making, the Pareto front can provide a formal way to reason about inherent conflicts.

This paper introduces an interactive framework to guide decision-makers in a multi-criteria supplier selection process. State-of-the-art multi-criteria methods for supplier selection elicit the decision-maker’s preferences among the criteria by processing pre-collected data from different stakeholders. We propose a different approach where the preferences are elicited through an active learning loop. At each step, the framework optimally solves a combinatorial problem multiple times with different weights assigned to the objectives. Afterwards, a pair of solutions among those computed is selected using a particular query selection strategy, and the decision-maker expresses a preference between them. These two steps are repeated until a specific stopping criterion is satisfied. We also introduce two novel fast query selection strategies, and we compare them with a myopically optimal query selection strategy. Computational experiments on a large set of randomly generated instances are used to examine the performance of our query selection strategies, showing a better computation time and similar performance in terms of the number of queries taken to achieve convergence. Our experimental results also show the usability of the framework for real-world problems with respect to the execution time and the number of loops needed to achieve convergence.

In recent years humanoid robots have been widely used in toy, performance, education and other service industries, but most biped robots walk slowly and have poor stability. The reason is that the driver parameters of the robot cannot properly match the walking gait algorithm, and the insufficient performance of the robot driver leads to the poor motion capability of the robot. In this paper, the optimization design process of biped robot parameters is studied and expounded, and its motion capability is improved by optimizing the driving parameters of the robot. Firstly, the contradiction between walking speed, stability and driver performance of biped robot is analysed. The performance evaluation functions of the three are further established, and the optimal parameter design to a certain extent is realized based on the multi-objective optimization method. Finally, combining with the physical simulation engine, the design parameters are simulated and checked, and the robot design process is completed through the guidance of simulation results.

Sustainable Supply Chain (SSC) management aims at integrating economic, environmental and social goals to assist in the long-term planning of a company and its supply chains. There is no consensus in the literature as to whether social and environmental responsibilities are profit-compatible. However, the conflicting nature of these goals is explicit when considering specific assessment measures and, in this scenario, multi-objective optimization is a way to represent problems that simultaneously optimize the goals. This paper proposes a Lagrangian matheuristic method, called $AugMathLagr$, to solve a hard and relevant multi-objective problem found in the literature. $AugMathLagr$ was extensively tested using artificial instances defined by a generator presented in this paper. The results show a competitive performance of $AugMathLagr$ when compared with an exact multi-objective method limited by time and a matheuristic recently proposed in the literature and adapted here to address the studied problem. In addition, computational results on a case study are presented and analyzed, and demonstrate the outstanding performance of $AugMathLagr$., 45 pages. Paper accepted to European Journal of Operational Research

Distributed flow shop scheduling of a camshaft machining is an important optimization problem in the automobile industry. The previous studies on distributed flow shop scheduling problem mainly emphasized homogeneous factories (shop types are identical from factory to factory) and economic criterion (e.g., makespan and tardiness). Nevertheless, heterogeneous factories (shop types are varied in different factories) and environment criterion (e.g., energy consumption and carbon emission) are inevitable because of the requirement of practical production and life. In this article, we address this energy-efficient scheduling of distributed flow shop with heterogeneous factories for the first time, where contains permutation and hybrid flow shops. First, a new mathematical model of this problem with objectives of minimization makespan and total energy consumption is formulated. Then, a hybrid multiobjective optimization algorithm, which integrates the iterated greedy (IG) and an efficient local search, is designed to provide a set of tradeoff solutions for this problem. Furthermore, the parameter setting of the proposed algorithm is calibrated by using a Taguchi approach of design-of-experiment. Finally, to verify the effectiveness of the proposed algorithm, it is compared against other well-known multiobjective optimization algorithms including MOEA/D, NSGA-II, MMOIG, SPEA2, AdaW, and MO-LR in an automobile plant of China. Experimental results demonstrate that the proposed algorithm outperforms these six state-of-the-art multiobjective optimization algorithms in this real-world instance.

In this paper, a hybrid algorithm was proposed for multi-objective optimization design with high efficiency and low computational cost based on the Gaussian process regression and particle swarm optimization algorithm. For the proposed method, the global performance indices, including regular workspace volume, global transmission index, global stiffness index, and global dynamic index were considered as objective functions. First, the multi-objective optimization problem considering the boundary conditions, objective, and constraint functions was constructed. Second, the Latin hypercube design was regarded as the design of experiment to obtain the computer sample points. Besides, the high-precision objective-function values were obtained by increasing the node density in the workspace at these sample points to provide sufficient information for the mapping model. Third, the Gaussian process regression was proposed to build the mapping model between the objective functions and the design parameters, thus reducing the computational cost of global performance indices. Cross-validation and external validation were adopted to verify the mapping model. Finally, the hybrid algorithm combined with the Gaussian process regression and particle swarm optimization algorithm was proposed for multi-objective optimization design. The 2PRU-UPR parallel manipulator was taken as a case to implement the proposed method (where P was a prismatic joint; R a revolute joint; U a universal joint). The comparison from the back propagation neural network, multivariate regression, and Gaussian process regression mapping models showed that the Gaussian process regression model had higher accuracy and robustness. The proposed hybrid algorithm saved 99.84% of computational cost compared to using the particle swarm optimization algorithm. The Pareto frontier of the multi-objective optimization problem of the 2PRU-UPR parallel manipulator was also obtained. After optimization, the performance indices were significantly improved.

A novel multiobjective adaptive surrogate model is employed for the prediction of full-film lubrication performance of surface texture profile for thrust bearings in axial piston pumps. At present, a surface texture optimization design of thrust bearing in axial piston pump has not been provided based on a unique design solutions. In this study, multi-objective adaptive surrogate-based optimization (MO-ASMO) algorithm was used for solving both the mechanical and volumetric losses performance design of surface texture. The non-dominated sorting genetic algorithm (NSGA-II) formed part of the developed multi-objective optimization model, having three competing design objectives which mainly include load capacity, friction torque and leakage rate. A comparative study of two models with accuracy analysis of each case was performed. The results show that the MO-ASMO has the best performance among the different surrogate models. Comparing with the NSGA-II model, the improvement of the leakage rate and the load carrying force made by MO-ASMO are higher about 16.12% and 3.67%, respectively. In other words, multi-objective optimization is capable of enhancing textured slipper bearing performance using MO-ASMO method. The optimal texture radius and texture depth are chosen to minimize the leakage rate and texture bearing capacity.

Dynamic multiobjective optimization problems (DMOPs) are characterized by optimization functions that change over time in varying environments. The DMOP is challenging because it requires the varying Pareto-optimal sets (POSs) to be tracked quickly and accurately during the optimization process. In recent years, transfer learning has been proven to be one of the effective means to solve dynamic multiobjective optimization. However, the negative transfer will lead the search of finding the POS to a wrong direction, which greatly reduces the efficiency of solving optimization problems. Minimizing the occurrence of negative transfer is thus critical for the use of transfer learning in solving DMOPs. In this article, we propose a new individual-based transfer learning method, called an individual transfer-based dynamic multiobjective evolutionary algorithm (IT-DMOEA), for solving DMOPs. Unlike existing approaches, it uses a presearch strategy to filter out some high-quality individuals with better diversity so that it can avoid negative transfer caused by individual aggregation. On this basis, an individual-based transfer learning technique is applied to accelerate the construction of an initial population. The merit of the IT-DMOEA method is that it combines different strategies in maintaining the advantages of transfer learning methods as well as avoiding the occurrence of negative transfer; thereby greatly improving the quality of solutions and convergence speed. The experimental results show that the proposed IT-DMOEA approach can considerably improve the quality of solutions and convergence speed compared to several state-of-the-art algorithms based on different benchmark problems.

Due to the widespread interest in dynamic multiobjective optimization in real-world applications, more and more approaches exploiting machine learning are deployed to tackle this type of problems. Unfortunately, recent works do not make full use of the data obtained during the optimization process, which could be benefit for model training thereby mining the dynamic characteristics of the underlying problem. To address this issue, this paper proposes a dynamic multiobjective evolutionary algorithm driven by inverse reinforcement learning to solve the dynamic multiobjective optimization problems. IRL is widely used to recover the unknown reward function, making it possible to perform at an expert level. The notable features of the proposed algorithm mainly consist of data-driven evolutionary technique, which uses inverse reinforcement learning as a surrogate-assisted model for model training. This design makes full use of the surrogate management strategy based on inverse reinforcement learning to optimize the reward function within a reinforcement learning framework. At the same time, the algorithm can generate a promising policy based on limited training data during the optimization process to achieve better algorithm evolution and guide the search. The experimental results on the benchmark problems validate that the proposed algorithm is effective in dealing with dynamic multiobjective optimization.

Counterpoising convergence and distribution becomes more intractable in many-objective optimization where the number of objectives exceeds three, evolutionary algorithms (EAs) via decomposition are prominent in convergence promotion yet suffer from diversity loss. The setting of direction vectors (DVs), scalarizing function (SF) and selection strategy can significantly affect the performance of this sort of algorithms. To remedy the issue, we develop a hyperplane driven and projection assisted EA, referred here as HPEA, using three-stage search. At the very beginning, search is performed only along the extreme objective-wise points to capture the corners of Pareto front (PF). After that, the convergence and diversity are coordinated, a set of DVs, adapted by the evolving population itself, is utilized to extend the search wideness, and two novel SFs are exploited to collect elites in each subregion for approaching a more complete PF. At last, diversity is emphasized, a projection distance aided elimination mechanism is employed to prune poorly diversified solutions one by one. Note that hyperplane utilized at second stage aims at identifying well-converged solutions, the rationale behind using two novel SFs is to take complementary effects of different criteria. The resultant HPEA is compared with several state-of-the-art multiobjective EAs on handling various types of many-objective problems. Extensive empirical studies demonstrate the effectiveness and competitiveness of the proposal in obtaining high quality solution set.

The hub motor significantly increases the unsprung mass of electric in-wheel vehicles, which deteriorates the ride comfort and safety of vehicles and which can be effectively improved by optimizing the main suspension parameters of vehicles reasonably, so a multi-objective optimization method of main suspension parameters based on adaptive particle swarm algorithm is proposed and the dynamic model of a half in-wheel electric vehicle is established. Taking the stiffness coefficient of the suspension damping spring and damping coefficient of the damper as independent variables, the vertical acceleration of the body, the pitch acceleration and the vertical impact force of the hub motor as optimization variables, and the dynamic deflection of the suspension and the dynamic load of the wheel as constraint variables, the multi-objective optimization function is constructed, and the parameters are simulated and optimized under the compound pavement. The simulation results show that the vertical acceleration and pitch acceleration are reduced by 20.2% and 18.4% respectively, the vertical impact force of the front hub motor is reduced by 3.7%, and the ride comfort and safety are significantly improved.