Multi-objective Optimization Solution Research Articles

Voltage, var and watt optimization for a distribution system with high PV penetration: A probabilistic study

High penetration of rooftop photovoltaic (PV) panels in the distribution grid can affect the node voltages, and under light loading conditions, may even result in reverse power flow and localized overvoltage instances. While voltage control at the distribution grid level has been traditionally addressed using voltage and var control (VVC) techniques, with the introduction of PV resource as well as active demand, the problem needs to be reformulated as voltage, var and watt optimization (VVWO). A mixed-integer nonlinear multi-objective optimization solution has been proposed in this paper for the control of active and reactive power resources in an unbalanced distribution grid with high PV penetration. The goal of the proposed methodology is to simultaneously minimize line losses, active power curtailment of PVs, demand curtailment, and operation instances of voltage regulating transformers and shunt capacitors. Due to the stochastic nature of load and solar irradiance, at each PV penetration level the problem is solved probabilistically by using random samples for network loading levels and cloud coverage in the sky. A case study is presented using a modified version of the IEEE 123-bus test distribution feeder. Simulation results indicate that if voltages and reactive powers are optimally controlled, high PV penetration levels can be achieved at the distribution grid without any complications. It is also observed that allowing PVs to exchange reactive power with the grid can significantly affect the operation of voltage regulators and shunt capacitors.

Resilience-Oriented Optimal Operation Strategy of Active Distribution Network

The ability to withstand extreme disasters has a profound impact on the distribution network operation. This paper proposes a novel optimal operation strategy for an active distribution network to enhance system resilience.. The objectives in the proposed optimal strategy include, the resilience, operation cost, and its pollutant emissions. According to the existence of uncontrollable distributed energy resources in the active distribution network, the problem which takes the uncertainty most into account, is this multi-objective optimization problem. Thus, it can be treated as a min-max dual robust optimization problem. Benders decomposition is employed to decouple the problem, then non-dominated sorting genetic algorithm II is applied to search the multi-objective optimal solution which has an extremely low CPU time. The modified standard IEEE 34-node system, with different distributed energy resources types, is employed, as a studied case, to demonstrate the effectiveness of the proposed optimal operation strategy. The simulation results illustrate that, compared to other economic-oriented robust optimal operation models, the proposed strategy can enhance system resilience without a significant increase in the operation cost and pollutant emissions.

Targeting solutions in Bayesian multi-objective optimization: sequential and batch versions

Multi-objective optimization aims at finding trade-off solutions to conflicting objectives. These constitute the Pareto optimal set. In the context of expensive-to-evaluate functions, it is impossible and often non-informative to look for the entire set. As an end-user would typically prefer a certain part of the objective space, we modify the Bayesian multi-objective optimization algorithm which uses Gaussian Processes to maximize the Expected Hypervolume Improvement, to focus the search in the preferred region. The cumulated effects of the Gaussian Processes and the targeting strategy lead to a particularly efficient convergence to the desired part of the Pareto set. To take advantage of parallel computing, a multi-point extension of the targeting criterion is proposed and analyzed.

Multi-objective techno-economic optimization of a solar based integrated energy system using various optimization methods

In this research paper, a novel combined, cooling, heating and, power (CCHP) system is proposed consisting of Parabolic trough solar collectors (PTSC) field, a dual-tank molten salt heat storage, a Proton exchange membrane electrolyzer (PEME), an Organic Rankine Cycle (ORC) and a single effect Li/Br water absorption chiller. The first law of thermodynamics was applied for analyzing the proposed CCHP system. A multi-objective optimization is conducted with respect to exergy efficiency and total cost rate as two objective functions. In order to determine the optimal point in multi-objective optimization, NSGA-II algorithm was applied for the optimization purpose. Matlab software and python are employed to determine the system optimum operating conditions. The optimum solutions for the NSGA-II multi-objective optimization are 79% and 0.058 ($/s) for exergy efficiency and total cost rate, respectively. The results of single objective optimization are 0.0447 ($/s) for the economic objective function and 87.53% for the exergy efficiency objective function. The sensitivity of the Pareto frontier for different interest rates is also investigated and the results show that at the lower system exergy efficiency, the influence of the interest rate is more significant. In addition, Generalized Differential Evaluation (GDE3), Indicator-based evolutionary algorithm (IBEA), speed-constrained Multi-objective (SMPSO), and strength Pareto Evolutionary algorithm (SPEA) algorithms are also applied for the optimization of the proposed CCHP and the results of the algorithm are compared with each other. The IBEA algorithm was found the best approach to obtain the Pareto optimum solution. The comparison between NSGA-II and IBEA shows that the IBEA exergy efficiency of the optimum solution increase by 2.5% in comparison with NSGA-II and the IBEA cost rates decrease by 7% in comparison with NSGA-II.

Multi-objective optimal power flow solutions using a constraint handling technique of evolutionary algorithms

In power systems, optimal power flow (OPF) is a complex and constrained optimization problem in which quite often multiple and conflicting objectives are required to be optimized. The traditional way of dealing with multi-objective OPF (MOOPF) is the weighted sum method which converts the multi-objective OPF into a single-objective problem and provides a single solution from the set of Pareto solutions. This paper presents MOOPF study applying multi-objective evolutionary algorithm based on decomposition (MOEA/D) where a set of non-dominated solutions (Pareto solutions) can be obtained in a single run of the algorithm. OPF is formulated with two or more objectives among fuel (generation) cost, emission, power loss and voltage deviation. The other important aspect in OPF problem is about satisfying power system constraints. As the search process adopted by evolutionary algorithms is unconstrained, for a constrained optimization problem like OPF, static penalty function approach has been extensively employed to discard infeasible solutions. This approach requires selection of a suitable penalty coefficient, largely done by trial-and-error, and an improper selection may often lead to violation of system constraints. In this paper, an effective constraint handling method, superiority of feasible solutions (SF), is used in conjunction with MOEA/D to handle network constraints in MOOPF study. The algorithm MOEA/D-SF is applied to standard IEEE 30-bus and IEEE 57-bus test systems. Simulation results are analyzed, especially for constraint violation and compared with recently reported results on OPF.

Theoretical analysis and crashworthiness optimization of hybrid multi-cell structures

Thin-walled structure is widely used in automobile, aviation and other industrial fields due to its lightweight, high energy absorption efficiency and low cost. Four thin-walled hybrid multi-cell structures with circular and square sections are proposed in this paper. The energy absorption characteristics and crushing deformation of the hybrid structures are investigated by experimental testing and numerical analysis. Meanwhile, the theoretical models of mean crushing force and specific energy absorption of the hybrid structures are developed by simplified super folding element (SSFE) theory. It is found from the sensitivity analysis of parameters that the dimension of the external tube (D) and the wall thickness (T) of the structure have significant effects on energy absorption. Furthermore, the multi-objective optimization including multiple surrogate models is performed to obtain optimal crashworthiness of the hybrid multi-cell structures. The results show that multiple surrogate models are more favorable and accurate for the crashworthiness design, and the hybrid multi-cell structure with the outer circle and inner square section (CS2) has the best crashworthiness performance. Finally, the multi-objective optimization solutions are analyzed and chosen by the normal boundary intersection (NBI) method to carry out the crashworthiness comparison with the typical multi-cell structures of the same mass, and the hybrid structure (CS2) outperforms multi-cell tubes with the single circular or square section.

RO-RO: Routing Optimality - Reconfiguration Overhead Balance in Software-Defined ISP Networks

Software-defined networking provides a promising solution for traffic engineering (TE) by utilizing a centralized controller to remotely configure programmable network switches. In order to achieve optimal traffic distribution and meet the Quality of Service (QoS) requirements, the SDN controller must frequently solve complex optimization models. Applying an optimization model in ISP (Internet Service Provider) networks implies abundant routing reconfigurations, which adversely impact the network stability and QoS parameters. Namely, since routing updates usually cannot be applied on all switches at the same time, transient congestion and loops often happen as a result. Here, in this paper, we propose a new control framework that strives to maximize the network throughput and provide QoS with minimal reconfiguration costs. In contrast to the conventional TE approaches, which perform the network optimizations periodically and control the side effects of reconfigurations by carefully choosing the period length between the optimization cycles, we propose a multi-objective optimization model which jointly minimizes the routing cost function and the reconfiguration overhead. The Pareto frontier of the optimization model is generated by the augmented ∈-constrained method, whereas a Lyapunov drift-plus-penalty function is used to select the best compromise solution from the Pareto set. Since the reconfiguration overhead is reduced, the network controller could be allowed to optimize resource allocation more frequently, in order to respond quickly and efficiently to the network changes. Considering that the proposed optimization model is computationally intractable in large-scale networks, we also propose a heuristic algorithm to efficiently solve large instances of the problem. In simulations and Mininet experiments, we show that our solution brings performance improvement over the conventional periodic TE techniques. Moreover, the proposed heuristic achieves better QoS request acceptance ratio than the state-of-the-art multi-objective optimization solution, despite the significantly reduced computational complexity.

Multi-Objective Pricing Optimization for a High-Speed Rail Network Under Competition

Multi-objective pricing of high-speed rail (HSR) passenger fares becomes a challenge when the HSR operator needs to deal with multiple conflicting objectives. Although many studies have tackled the challenge of calculating the optimal fares over railway networks, none of them focused on characterizing the trade-offs between multiple objectives under multi-modal competition. We formulate the multi-objective HSR fare optimization problem over a linear network by introducing the epsilon-constraint method within a bi-level programming model and develop an iterative algorithm to solve this model. This is the first HSR pricing study to use an epsilon-constraint methodology. We obtain two single-objective solutions and four multi-objective solutions and compare them on a variety of metrics. We also derive the Pareto frontier between the objectives of profit and passenger welfare to enable the operator to choose the best trade-off. Our results based on computational experiments with Beijing–Shanghai regional network provide several new insights. First, we find that small changes in fares can lead to a significant improvement in passenger welfare with no reduction in profitability under multi-objective optimization. Second, multi-objective optimization solutions show considerable improvements over the single-objective optimization solutions. Third, Pareto frontier enables decision-makers to make more informed decisions about choosing the best trade-offs. Overall, the explicit modeling of multiple objectives leads to better pricing solutions, which have the potential to guide pricing decisions for the HSR operators.

Neutrosophic Optimization Model and Computational Algorithm for Optimal Shale Gas Water Management under Uncertainty

Shale gas energy is the most prominent and dominating source of power across the globe. The processes for the extraction of shale gas from shale rocks are very complex. In this study, a multiobjective optimization framework is presented for an overall water management system that includes the allocation of freshwater for hydraulic fracturing and optimal management of the resulting wastewater with different techniques. The generated wastewater from the shale fracking process contains highly toxic chemicals. The optimal control of a massive amount of contaminated water is quite a challenging task. Therefore, an on-site treatment plant, underground disposal facility, and treatment plant with expansion capacity were designed to overcome environmental issues. A multiobjective trade-off between socio-economic and environmental concerns was established under a set of conflicting constraints. A solution method—the neutrosophic goal programming approach—is suggested, inspired by independent, neutral/indeterminacy thoughts of the decision-maker(s). A theoretical computational study is presented to show the validity and applicability of the proposed multiobjective shale gas water management optimization model and solution procedure. The obtained results and conclusions, along with the significant contributions, are discussed in the context of shale gas supply chain planning policies over different time horizons.

Shape optimization of preform tools in forging of aerofoil using a metamodel-assisted multi-island genetic algorithm

ABSTRACTPreform design plays an important role in improving the material flow, mechanical properties and reducing defects for forgings with complex shapes. In this paper, a study on shape optimization of preform tools in forging of an airfoil is carried out based on a multi-island genetic algorithm combined with a metamodel technique. An optimal Latin hypercube sampling technique is employed for sampling with the expected coverage of parameter space. Finite element (FE) simulations of multistep forging processes are implemented to obtain the objective function values for evaluating the forging qualities. For facilitating the optimization process, a radial basis function surrogate model is established to predict the responses of the hot forging process to the variation of the preform tool shape. In consideration of the compromise between different optimal objectives, a set of Pareto-optimal solutions are identified by the suggested genetic algorithm to provide more selections. Finally, according to the proposed fitness function, the best solution of multi-objective optimization on the Pareto front is confirmed and the corresponding preform tool shape proves optimal performances with substantially improved forging qualities via FE validation.

Multi-Objective Optimal Cloud Model Design of Vehicle-to-Grid Connected Systems Based on the Multiple Performance Characteristic Index Method

In this paper, a statistical cloud model was proposed for optimal design of the proportional integral derivative (PID) controllers used in current control of vehicle-to-grid connected inverter systems with PID parameters. By collecting the effective control factors and noise factors from a cloud data base, the cloud model can minimize both the reactive power and the total harmonic distortion for the single-phase full-bridge vehicle-to-grid connected system. The multi-objective optimal solution is obtained by using statistical fuzzy-based response surface methodology with multiple performance characteristics index. The testing results showed the validity of the proposed cloud model. It is verified that the statistical cloud model can increase the performance of the single-phase full-bridge vehicle-to-grid connected system in practical vehicle-to-grid applications in the Internet of Things.

Fast artificial bee colony algorithm with complex network and naive bayes classifier for supply chain network management

In supply chain network (SCN) management, multi-objective Pareto optimization means the network can meet the demand for both minimal cost and minimal lead-time in SCN. Due to the compromise between cost and lead-time, it is a non-trivial issue to search for multi-objective Pareto optimal solutions (POS) in SCN. Furthermore, with the wide application of the internet, an increasing number of SCN applications have been based on the internet. As a result, the complexity of SCN increases exponentially with the number of suppliers increasing. It is really a big challenge to find the global multi-objective POS within a limited time in SCN management. In order to solve this problem, first, this paper proposes an artificial bee colony (ABC) optimization algorithm with two improvements: (1) a novel solution framework designed to extend the application field of the SCN based on complex network; (2) the acceleration of search speed by adopting naive Bayes classifier. Second, the paper provides a case example of optimizing a three-echelon SCN with the objective of minimizing both cost and lead-time. After the simulation with this example, it turns out that the enhanced ABC algorithm can satisfy the requirements of: (1) finding the global multi-objective POS; (2) improving the speed of finding optimal solutions in SCN management.

An Efficient Multi-Objective Optimization Method for Use in the Design of Marine Protected Area Networks

An efficient connectivity-based method for multi-objective optimisation applicable to the design of marine protected area networks is described. Multi-objective network optimisation highlighted previously unreported step changes in the structure of optimal subnetworks for protection associated with minimal changes in cost or benefit functions. This emphasises the desirability of performing a full, unconstrained, multi-objective optimisation for marine spatial planning. Brute force methods, examining all possible combinations of protected and unprotected sites for a network of sites, are impractical for all but the smallest networks as the number of possible networks grows as 2^m, where m is the number of sites within the network. A metaheuristic method based around Markov Chain Monte Carlo methods is described which searches for the set of Pareto optimal networks (or a good approximation thereto) given two separate objective functions, for example for network quality or effectiveness, population persistence, or cost of protection. The optimisation and search methods are independent of the choice of objective functions and can be easily extended to more than two functions. The speed, accuracy and convergence of the method under a range of network configurations are tested with model networks based on an extension of random geometric graphs. Examination of two real-world marine networks, one designated for the protection of the stony coral Lophelia pertusa, the other a hypothetical man-made network of oil and gas installations to protect hard substrate ecosystems, demonstrates the power of the method in finding multi-objective optimal solutions for networks of up to 100 sites. Results using network average shortest path as a proxy for population resilience and gene flow within the network supports the use of a conservation strategy based around highly connected clusters of sites.

Optimality conditions in convex optimization with locally Lipschitz constraints

In this paper, we consider a convex optimization problem with locally Lipschitz inequality constraints. The KKT optimality conditions (both necessary and sufficient) for quasi $$\epsilon $$ -solutions are established under Slater’s constraint qualification and a non-degeneracy condition. Moreover, we explore the optimality condition for weakly efficient solutions in multiobjective convex optimization involving locally Lipschitz constraints. Some examples are given to illustrate our results.

Based on Particle Swarm Optimization Algorithm for Finding Ideal and Effective Solution of Dynamic Batch Reactor Multi-objective Optimization

Chemical production process integration is higher and higher, the operation is more and more complex. Based on the dynamic simulation of the process, analysis automation engineering and obtain decision, is beneficial to improve the production efficiency, also ensure safety. The mathematical model is a multi-objective dynamic optimization problem, and it is difficult to solve the multi-objective and it involves the numerical solution of differential system. The particle swarm algorithm strategy is given in this paper for the problem of a numerical solution. Penalty term was added to the PSO algorithm is put forward, as well as the local extremum and global extremum was used to adjust further, so that PSO algorithm is suitable for finding the ideal efficient solutions for multi-objective optimization problem, at the same time in the process of evolution, embedded Runge-Kutta method, the algorithm could been used for dynamic multi-objective optimization problems.

Thermodynamic and economic analysis and multi-objective optimization of a novel transcritical CO2 Rankine cycle with an ejector driven by low grade heat source

Transcritical CO2 Rankine cycle (T-CO2) is a promising technology for the utilization of low temperature heat source. The low critical temperature of CO2 (about 31 °C) leads to a restriction in the practical application of the cycle, since CO2 could hardly be condensed into liquid using higher temperature heat sink under the environment conditions. In this paper, a novel transcritical CO2 Rankine cycle with an ejector is proposed to solve the condensation problem of CO2 under the higher temperature heat sink. By establishing the mathematical model, a parametric analysis is carried out to examine the effects of five key parameters on thermodynamic and economic performances of the system. A multi-objective optimization is also conducted to obtain the optimum performance of cycle. The results indicate that increasing turbine inlet temperature and ejector back pressure could increase the exergy efficiency. In addition, lower investment cost of the system could be achieved by increasing the turbine back pressure and the valve expansion pressure. Furthermore, according to the Pareto frontier solution of multi-objective optimization, the exergy efficiency could reach a maximum of 19.33% and the investment cost of the system could reach a minimum of 657.9 × 103 USD.

Dynamic design of grinding and polishing machine tool for blisk finishing

A virtual prototype was built in the dynamic design process of grinding and polishing machine tool for blisk. Through the analysis of multi-body dynamic of main structures changed to be flexible, column and beam had been found to be the weak link of the whole machine tool. Column and beam were optimized by changing the layout of plate to improve the low order natural frequency. The multi-objective optimization solutions of column were obtained through the genetic optimization algorithm in the FEA software. The sensitivity analysis was used to correct a set of optimized solution for the engineering. According to the optimization result, a new beam structure with inclined reinforcement plate is put forward. The first three order natural frequency of the optimized column increased by 11.9%, 18.2% and 2.8% respectively. The first three order natural frequency of the optimized beam increased by 45.3%, 8.23% and 17.8%. Analysis result of the whole machine tool show that the static and dynamic properties had improved significantly after optimization.

A Revised Pascoletti–Serafini Scalarization Method for Multiobjective Optimization Problems

The presented study deals with the scalarization techniques for solving multiobjective optimization problems. The Pascoletti–Serafini scalarization technique is considered, and it is attempted to sidestep two weaknesses of this method, namely the inflexibility of the constraints and the difficulties of checking proper efficiency. To this end, two modifications for the Pascoletti–Serafini scalarization technique are proposed. First, by including surplus variables in the constraints and penalizing the violations in the objective function, the inflexibility of the constraints is resolved. Moreover, by including slack variables in the constraints, easy-to-check statements on proper efficiency are obtained. Thereafter, the two proposed modifications are combined to obtain the revised Pascoletti–Serafini scalarization method. Theorems are provided on the relation of (weakly, properly) efficient solutions of the multiobjective optimization problem and optimal solutions of the proposed scalarized problems. All the provided results are established with no convexity assumption. Moreover, the capability of the proposed approaches is demonstrated through numerical examples.

Multi-objective process parameters optimization of hot-wire laser welding using ensemble of metamodels and NSGA-II

Abstract Hot-wire laser welding (HLW) can reduce the dispersion of laser energy and improve deposition efficiency by preheating filler wire during laser welding process. In order to obtain sound welding results, it is crucial to select appropriate process parameters. In this study, an optimization methodology based on ensemble metamodels (EM) which take the advantages of the prediction ability of stand-alone metamodels (Kriging, RBF and SVR), and Non-dominated sorting genetic algorithm (NSGA-II) are presented to obtain optimum process parameters during stainless steel 316L hot-wire laser welding. Firstly, EMs are developed through minimizing the generalized mean square Leave-one-out (LOO) errors to find the optimum weight factors of the used stand-alone Kriging, RBF and SVR metamodels. And then the EMs are applied to establish the relationships between process parameters (i,e., laser power (LP), welding speed (WS) and hot-wire current (I)) and welding results (i,e., welding depth-to-width ratio (DW), welding reinforcement (BR) and tensile strength (TS)). During optimization process, NSGA-II is employed to search for multi-objective Pareto optimal solutions based on EMs. In addition, the main effects of multiple process parameters on welding results are analyzed. The verification tests indicate that the obtained optimal process parameters are effective and reliable for producing expected welding results (maximized DW, maximized TS and desired BR value). In general, the proposed optimization method can provide a reliable guidance for HLW in engineering practice.

Simulation-based model for the optimization of machining parameters in a metal-cutting operation

To achieve a certain measurable performance in cutting machines, the machine parameters need to be optimized. Several constraints determine the possible values that these parameters can take. Although parameters are usually assumed to be deterministic, in practice, it is common to find variations on the characteristics of the products or the processes. Modeling machining parameters as stochastic factors provides a more realistic representation of cutting operations. Moreover, multiple operational objectives are of interest, in many real situations, these multiple objectives are conflicting. Consequently, the problem of setting the parameters becomes a trade-off situation. This paper presents a novel Simulation-based Multi-Objective Optimization (SimMOpt) solution procedure. The procedure is divided into two phases: (1) finding initial solutions and, (2) using a simulated annealing-based method for finding neighboring solutions. In the first phase, non-linear goal programming is used for finding high quality initial solutions. The second phase incorporates Pareto Archive Evolution Strategy (PAES) and hypotheses testing for searching near-optimal solutions for a set of stochastic parameters (i.e., cutting speed, feed rate, and depth of cut) in metal cutting operations. Three objectives are optimized (i.e., operation time, operation cost, and quality of the product). The results from implementing this procedure are analyzed and compared to a baseline methodology based on the Multi-Objective Simulated Annealing (MOSA) algorithm. The analysis demonstrates that the proposed method outperforms the Genetic Algorithm (GA), which was the benchmark algorithm, in terms of the solution quality of all the objectives. More importantly, the solutions from using the SimMOpt procedure outperform those obtained from using an enhanced MOSA-based approach (i.e., 4.71% improvement in the hypervolume approximation).