Multi-objective Formulation Research Articles

Optimal Economic–Environmental Operation for AC-MTDC Grids by Improved Crow Search Algorithm

This article develops a nonlinear, multimodal, and multiobjective formulation of the combined economic environmental operation (CEEO) problem in hybrid AC-multiterminal (AC-MT) high-voltage direct current grids. In these grids, the technologies of voltage source converters support more active and reactive power control in AC grids. The aim of the CEEO issue is to minimize the overall cost of fuel and the pollutant emissions of generators. Also, transmission loss minimization is another target. An improved crow search algorithm (ICSA) is proposed for obtaining the solution of the formulated problem. The proposed ICSA combines the merits of CSA by randomly switching into local search around the best crows’ position. Pareto dominance is activated to improve the crow's memory and the external repository for multiobjective models. The ICSA is tested on modified IEEE 30-bus, the Egyptian West Delta Power Network, and the large-scale 118-bus system to solve the CEEO problem in AC-MTDC grids. The simulation results illustrate the proposed ICSA capability for finding diversified Pareto solutions with several possible operating points. Furthermore, the effectiveness of the proposed ICSA is demonstrated in terms of its solution robustness compared with previous techniques.

Nonlinear multiobjective and dynamic real‐time predictive optimization for optimal operation of baseload power plants under variable renewable energy

AbstractConsidering the increase of disruptive variable renewable energy penetration into the power grid, this article focuses on the investigation of a multiobjective and dynamic real‐time optimization framework to address the cycling of large‐scale power plants under renewable penetration. In this framework, a parallelized particle swarm optimization step is first performed to generate feasible initial points. Then, a multiobjective and dynamic real‐time optimization formulation generates optimal trajectories. The benefit of predictive capability is investigated for the dynamic component, which introduces the novel nonlinear multiobjective and dynamic real‐time predictive optimization approach. Two multiobjective formulations to obtain Pareto front optimal in real time are explored: the modified Tchebycheff‐based weighted metric and ‐constraint methods. Economic and environmental objectives are considered in this study. A novel topical discussion on the intersection of dynamic real‐time optimization with model predictive control is also presented. The developed framework is successfully applied to a baseload coal‐fired power plant with postcombustion CO2 capture. Results indicate that the approach can be deployed for a large‐scale system if automatic differentiation, model reduction, and parallelization are adopted to improve computational tractability, with computational improvement up to 120‐folds after performing these steps. Finally, market and carbon policies showed an impact on the optimal compromise between the objectives with an additional 63 ton of CO2 captured under favorable market conditions.

A multi-modal algorithm based on an NSGA-II scheme for phylogenetic tree inference

The analysis of evolutionary data allows uncovering information about the organisms and how they have adapted and evolved. This information could provide us with new insights about the specialisation of organisms (or part of them), how they adapt, how similar they are with other species, among others. Unfortunately, this evolutionary history can only be estimated, and for that, several computational methods exist. Among the methods, optimisation methods are one of the main approaches to deal with this problem, with multiobjective optimisation producing promising results. In this paper, we deal with multiobjective phylogenetic inference, using a multi-modal metaheuristic approach that exploits the decision space in the multiobjective formulation of the problem. In particular, we incorporate a new metric based on a topological tree distance. We compare the method with state of the art algorithms in terms of performance. Additionally, we perform a thorough analysis of a study case on a yeast Saccharomyces cerevisiae dataset. Results show that our proposal is able to improve the diversity of solutions while improving or keeping the quality of solutions in terms of hypervolume.

Application of hybrid TLBO-PSO algorithm for allocation of distributed generation and STATCOM

This paper proposes a hybrid teaching learning-based optimization- particle swarm optimization (TLBO-PSO) Algorithm for optimal distributed generation (DG) and STATCOM placement. A multi-objective formulation is developed that optimizes the DG and STATCOM placement in IEEE 33 and real-time 52 bus distribution system. The objective function formulated involves maximizing cost-benefit and voltage stability factors while minimizing network security index and power losses. Simulation is carried out in MATLAB/Simulink for different systems and different cases. The results for single and multiple STATCOM and DG are compared with TLBO and PSO algorithm and the results exhibit better convergence performance with the hybrid optimization algorithm.

Joint optimization of bunker fuel and vessel speed considering delay and carbon emission

Vessel speed optimization and optimal bunkering ports are two critical facets of the maritime industry. These two factors are the major contributors to determining the total vessel operational cost. A multi-objective formulation is proposed in this paper to study the effect of a delay on a pre-planned schedule of a vessel. Here, the delay is defined as the service levels of the vessel at the different ports of calls. The formulation also includes emission costs to consider the increasing damages done by the maritime industry to the environment. Furthermore, the Non-dominated sorting Algorithm II is employed to perform the multi-objective optimization.

Investigating the Use of Linear Programming and Evolutionary Algorithms for Multi-Objective Electric Vehicle Charging Problem

With the increasing uptake of electric vehicles (EVs), the need for efficient scheduling of EV charging is increasingly becoming important. A charging station operator needs to identify charging/discharging power of the client EVs over a time horizon while considering multiple objectives, such as operating costs and the peak power drawn from the grid. Evolutionary algorithms (EAs) are a popular choice when faced with problems involving multiple objectives. However, since the objectives and constraints of this problem can be expressed using linear functions, it is also possible to come up with improvised multi-objective formulations which can be solved with exact techniques such as mixed-integer linear programming (MILP). With both approaches having their potential strengths and pitfalls, it is worth investigating their use to inform the algorithmic choices, which the current study aims to address. In doing so, it makes a number of contributions to the topic, including extension of an existing EV charging problem to a multi-objective form; observing some interesting properties of the problem to improve both the MILP and EA solution approaches; and comparing the performance of MILP and EA. The study provides some useful insights into the problem, initial results and quantitative basis for selecting solution approaches, and highlights some areas of further development.

Predicting Carbon Residual in Biomass Wastes Using Soft Computing Techniques

In recent decades, the development of complex materials developed a class of biomass waste-derived porous carbons (BWDPCs), which are used for carbon capture and sustainable waste management. It is difficult in understanding the adsorption mechanism of CO2 in the air as it has a wide range of properties associated with its diverse textures, functional group existence, pressure, and temperature of varying range. These properties influence diversely the adsorption mechanism of CO2 and pose serious challenges in the process. To resolve this multiobjective formulation, we use a machine learning classifier that maps systematically the CO2 adsorption as a function of compositional and textural properties and adsorption parameters. The machine learning classifier helps in the classification of various porous carbon materials during the time of training and testing. The results of the simulation show that the proposed method is more efficient in classifying the porous nature of the CO2 adsorption materials than other methods.

Robust RGBD Visual Odometry Using Windowed Direct Bundle Adjustment and Slanted Support Plane

This letter presents a robust, real-time visual odometry that efficiently exploits the available visual and geometry cues from RGB-D frames for both tracking and mapping. Together with a hybrid tracking algorithm based on a joint multi-objective formulation, we additionally incorporate the point-to-plane metrics into the photometric bundle adjustment (PBA) to constrain the iteration direction especially for those weakly-textured points. The relative pose constraints derived from optimized poses via PBA is then leveraged in combination with reprojection constraints retrieved from maintained feature map, to refine keyframe poses and feature locations. Moreover, the slanted support plane commonly used in multi-view stereo matching, is utilized for the adjustment of the semi-dense points to further enhance mapping accuracy that in turn benefits the front-end tracking. We extensively evaluate our algorithm on benchmark datasets, and those experimental results validate the advantage of our method in terms of overall tracking performance over other representative approaches.

OTIMIZAÇÃO DO AGENDAMENTO DE ATIVIDADES SILVICULTURAIS: UM ESTUDO DE CASO DE FUNÇÕES E MÉTODOS

ABSTRACT Scheduling problems are tasks of the operational routine in companies, which demand an optimal solution to support the decision. However, these problems have not been frequently investigated in forestry science. Therefore, it was proposed to describe a mathematical formulation for silviculture optimization under scheduling restriction of the workforce /sequencing of tasks (SSRCMM). Seeking the most suitable method to solve this combinatorial problem, two strategies were compared: i) Integer Linear Programming (ILP) and ii) simulated annealing (SA). The main criteria to assess strategies’ performance were to provide feasible solutions at an acceptable processing time and final project cost. The instance approached is a real problem outlined in 32 stands and five silvicultural tasks scheduled within a 40-day deadline. Three objective functions were also tested, defining case studies (S) to attend to the recurring managers’ decisions by minimizing: S1 – project cost, S2 – makespan, and S3 – workforce usage. The results reveal a robust model to support the forest planner in operational-level tasks. The ILP achieved the optimal solution only for the minimization of the project cost (S1) due to the delay in processing time of the other case studies. Thus, the SA stands out as an efficient method to solve the SSRCMM by providing satisfactory solutions in a reduced time. All the objective functions fitted properly with their proposed goals. The makespan and workforce usage functions increased by US$1,820.29 (S2) and US$2,146.39 (S3) from the S1, respectively, to finish the project earlier and reduce the oscillation of workforce usage over the days. Facing these findings, it is suggested that future researchers incorporate other challenges in decision-making, involving a multi-objective formulation or methods to reveal new insights for forest management and planning.

Multi-objective sustainable capacitated location routing problem formulation in sustainable supply-chain management

Conflicting sustainability dimensions are considered in a multi-objective formulation, focusing on the capacitated location routing problem (CLRP). The proposed sustainable version (S-CLRP) addresses the location of facilities, the routing of vehicles, the balance of the working load among drivers, and the environmental impact of operations due to the emission of greenhouse gases. In this work, both a mixed integer linear programming model solved using the goal attainment method and an approximated method based on iterated local search (ILS) and decomposition (ILS/D) are proposed. The results show the generation of non-dominated fronts with adequate dispersion and convergence characteristics with which supply-chain decision-makers can evaluate the impact of their decisions on the financial, environmental and social dimensions of their operations.

Multi-Objective Collaborative Flexibility Optimization Design of the Strengthening Layer of a Flexible Riser

Abstract Marine flexible risers are widely used in ocean oil and gas extraction, and need to withstand environment loads (wave and current) and the large offset of the floater. Therefore, the flexible riser is subjected to tension, bending, and torsion loads, which are mainly resisted by the key strengthening layer. Small bending stiffness of a cross section of the strengthening layer with larger tension and torsion stiffness are required to be compliant with the ocean environment. The traditional design of the key strengthening layer is partially rigid with larger cross-sectional stiffnesses. Therefore, the innovative configurations of the strengthening layer are imperative to make sure that the flexible riser is reliable and safe during the installation and operation. The strengthening layer of the flexible riser is treated as the cylindrical shell composed of periodic unit-cell beam structures, which is a hypothetical model. The optimization design is conducted through the novel implementation of the asymptotic homogenization (NIAH) method. The multi-objective collaborative flexibility optimization formulation of cylindrical shell structure is proposed, considering the ratio of cross-sectional tensile torsion stiffness to bending stiffness of the strengthening layer as the objectives. The optimal configuration results, the helically wound structures, are obtained, which are the alternative strengthening components of flexible risers. Finally, the optimal structures are compared with the commonly used marine flexible riser, which gives a great verification of the methodology feasibility and explains why the strengthening layer is designed as the type of helically wound structure.

Resource aware wind farm and D-STATCOM optimal sizing and placement in a distribution power system

<span lang="EN-US">Doubly fed induction generators (DFIG) based wind farms are capable of providing reactive power compensation. Compensation capability enhancement using reactors such as distributed static synchronous compensator (D-STATCOM) while connecting distribution generation (DG) systems to grid is imperative. This paper presents an optimal placement and sizing of offshore wind farms in a coastal distribution system that is emulated on an IEEE 33 bus system. A multi-objective formulation for optimal placement and sizing of the offshore wind farms with both the location and size constraints is developed. Teaching learning algorithm is used to optimize the multi-objective function constraining on the capacity and location of the offshore wind farms. The proposed formulation is a multi-objective problem for placement of the wind generator in the power system with dynamic wind supply to the power system. The random wind speed is generated as the input and the wind farm output generated to perform the optimal sizing and placement in the distributed system. MATLAB based simulation developed is found to be efficient and robust.</span>

Pearson coefficient matrix for studying the correlation of community detection scores in multi-objective evolutionary algorithm

Assessing a community detection algorithm is a difficult task due to the absence of finding a standard definition for objective functions to accurately identify the structure of communities in complex networks. Traditional methods generally consider the detecting of community structure as a single objective issue while its optimization generally leads to restrict the solution to a specific property in the community structure. In the last decade, new community detection models have been developed. These are based on multi-objective formulation for the problem, while ensuring that more than one objective (normally two) can be simultaneously optimized to generate a set of non-dominated solutions. However the issue of which objectives should be co-optimized to enhance the efficiency of the algorithm is still an open area of research. In this paper, first we generate a candidate set of partitions by saving the last population that has been generated using single objective evolutionary algorithm (SOEA) and random partitions based on the true partition for a given complex network. We investigate the features of the structure of communities which found by fifteen existing objectives that have been used in literature for discovering communities. Then, we found the correlation between any two objectives using the pearson coefficient matrix. Extensive experiments on four real networks show that some objective functions have a strong correlation and others either neutral or weak correlations.

Support Vector Machine Applied to the Optimal Design of Composite Wing Panels

One of the core technologies in lightweight structures is the optimal design of laminated composite stiffened panels. The increasing tailoring potential of new materials added to the simultaneous optimization of various design regions, leading to design spaces that are vast and non-convex. In order to find an optimal design using limited information, this paper proposes a workflow consisting of design of experiments, metamodeling and optimization phases. A machine learning strategy based on support vector machine (SVM) is used for data classification and interpolation. The combination of mass minimization and buckling evaluation under combined load is handled by a multi-objective formulation. The choice of a deterministic algorithm for the optimization cycle accelerates the convergence towards an optimal design. The analysis of the Pareto frontier illustrates the compromise between conflicting objectives. As a result, a balance is found between the exploration of new design regions and the optimal design refinement. Numerical experiments evaluating the design of a representative upper skin wing panel are used to show the viability of the proposed methodology.

A multi-objective formulation of maximal covering location problem with customers’ preferences: Exploring Pareto optimality-based solutions

The maximal covering location problem (MCLP) is a well-known combinatorial optimization problem with several applications in emergency and military services as well as in public services. Traditionally, MCLP is a single objective problem where the objective is to maximize the sum of the demands of customers which are served by a fixed number of open facilities. In this article, a multi-objective MCLP is proposed where each customer has a preference for each facility. The multi-objective MCLP with customers’ preferences (MOMCLPCP) deals with the opening of a fixed number of facilities from a given set of potential facility locations and then customers are assigned to these opened facilities such that both (i) the sum of the demands of customers and (ii) the sum of the preferences of the customers covered by these opened facilities are maximized. A Pareto-based multi-objective harmony search algorithm (MOHSA), which utilizes a harmony refinement strategy for faster convergence, is proposed to solve MOMCLPCP. The proposed MOHSA is terminated based on the stabilization of the density of non-dominated solutions. For experimental purposes, 82 new test instances of MOMCLPCP are generated from the existing single objective MCLP benchmark data sets. The performance of the proposed MOHSA is compared with the well-known non-dominated sorting genetic algorithm II (NSGA-II), and it has been observed that the proposed MOHSA always outperforms NSGA-II in terms of computation time. Moreover, statistical tests show that the objective values obtained from both algorithms are comparable.

Designing a disruption-aware supply chain network considering precautionary and contingency strategies: a real-life case study

Due to the high risk in the business environment, supply chains must adopt a tailored mechanism to deal with disruptions. This research proposes a multi-objective formulation to design a robust and resilient forward supply chain under multiple disruptions and uncertainty. The mentioned objective functions include minimizing the total cost, environmental impacts, and the network non-resiliency associated with the supply chain simultaneously countered using an augmented ε-constraint method. A Mulvey robust optimization approach is also utilized to deal with uncertainty. Ultimately, the developed model is validated based on three datasets associated with a case study of the steel industry. The results indicate that preventive and mitigation resilience strategies have significantly promoted the supply chain’s capabilities to deal with disruptions. Controlling network resiliency via non-resiliency measures has also created a risk-aware and robust structure in the incidence of disturbances. Numerical results reveal that multiple sourcing, lateral transshipment, and fortification of facilities will lead to the greatest cost-efficiency in the case study. Observations also indicate that the fortified supply chain will be highly economically viable in the long run due to the reduction of costs resulting from lost sales, unnecessary inventory holding, and the company’s credit risk.

Multi-objective design optimization of hydrodynamic journal bearings using a hybrid approach

PurposeIn this work, the design problem of hydrodynamic plain journal bearings is formulated as a multi-objective optimization problem to improve bearing performance under different operating conditions.Design/methodology/approachThe problem is solved using a hybrid approach combining genetic algorithm and sequential quadratic programming. The selected state variables are oil leakage flow rate, power loss and minimum oil film thickness. The selected design variables are the radial clearance, length-to-diameter ratio, oil viscosity, oil supply pressure and oil supply groove angular position. A validated empirical model is adopted to provide relatively accurate estimation of the bearing state variables with reduced computations. Pareto optimal solution sets are obtained for different operating conditions, and secondary selection criteria are proposed to choose a final optimum design.FindingsThe adopted hybrid optimization approach is a random search algorithm that generates a different solution set for each run, thus a different bearing design. For a number of runs, it is found that the key design variables that significantly affect the optimum state variables are the bearing radial clearance, oil viscosity and oil supply pressure. Additionally, oil viscosity is found to represent the significant factor that distinguishes the optimum designs obtained using the implemented secondary selection criteria. Finally, the results of the proposed optimum design framework at different operating conditions are presented and compared.Originality/valueThe proposed multi-objective formulation of the bearing design problem can provide engineers with a systematic approach and an important degree of flexibility to choose the optimum design that best fits the application requirements.

Simultaneous optimization of even flow and land and timber value in forest planning: a continuous approach

BackgroundForest management planning involves deciding which silvicultural treatment should be applied to each stand and at what time to best meet the objectives established for the forest. For this, many mathematical formulations have been proposed, both within the linear and non-linear programming frameworks, in the latter case generally considering integer variables in a combinatorial manner. We present a novel approach for planning the management of forests comprising single-species, even-aged stands, using a continuous, multi-objective formulation (considering economic and even flow) which can be solved with gradient-type methods.ResultsThe continuous formulation has proved robust in forest with different structures and different number of stands. The results obtained show a clear advantage of the gradient-type methods over heuristics to solve the problems, both in terms of computational time (efficiency) and in the solution obtained (effectiveness). Their improvement increases drastically with the dimension of the problem (number of stands).ConclusionsIt is advisable to rigorously analyze the mathematical properties of the objective functions involved in forest management planning models. The continuous bi-objective model proposed in this paper works with smooth enough functions and can be efficiently solved by using gradient-type techniques. The advantages of the new methodology are summarized as: it does not require to set management prescriptions in advance, it avoids the division of the planning horizon into periods, and it provides better solutions than the traditional combinatorial formulations. Additionally, the graphical display of trade-off information allows an a posteriori articulation of preferences in an intuitive way, therefore being a very interesting tool for the decision-making process in forest planning.

Eco-Friendly Feed Formulation and On-Farm Feed Production as Ways to Reduce the Environmental Impacts of Pig Production Without Consequences on Animal Performance.

Animal feeding has a major contribution to the environmental impacts of pig production. One potential way to mitigate such effects is to incorporate an assessment of these impacts in the feed formulation process. The objective of this study was to test the ability of innovative formulation methodologies to reduce the impacts of pig production while also taking into account possible effects on growth performance. We compared three different formulation methodologies: least-cost formulation, in accordance with standard practices on commercial farms; multiobjective (MO) formulation, which considered feed cost and environmental impacts as calculated by life cycle assessment (LCA); and MO formulation, which prioritized locally produced feed ingredients to reduce the impact of transport. Ninety-six pigs were distributed between three experimental groups, with pigs individually weighted and fed using an automatic feeding system from 40 to 115 kg body weight. Based on the experimental results, six categories of impacts were evaluated: climate change (CC), demand in non-renewable energy (NRE), acidification (AC), eutrophication (EU), land occupation (LO), and phosphorus demand (PD), at both feed plant gate and farm gate, with 1 kg of feed and 1 kg of live pig as functional units, respectively. At feed level, MO formulations reduced CC, NRE, AC, and PD impacts but sometimes increased LO and EU impacts. These formulations reduced the proportion of cereals and oil meals into feeds (feed ingredients with high impacts), while the proportion of alternative protein sources, like peas, faba beans, or high-protein agricultural coproducts increased (feed ingredients with low impacts). Overall, animal performance was not affected by the dietary treatment; because of this, the general pattern of results obtained with either MO formulation at farm gate was similar to that obtained at feed level. Thus, MO diet formulation represents an efficient way to reduce the environmental impacts of pig production without compromising animal performance.

Multi-objective topology optimization of pin-fin heat exchangers using spectral and finite-element methods

Forced convective pin-fin heat exchangers, due to the high wet surface area per volume and the hindered thermal boundary layers, feature low thermal resistances. However, the considerable coolant pressure drop, particularly for densely packed fin arrays, imposes operational costs for pumping power supply. This paper develops a multi-objective topology optimization approach to optimize sink geometries in order to minimize thermal resistance and pressure loss, concurrently. In accordance to the pin-fin geometrical characteristics, a dedicated pseudo-3D conjugate heat transfer model is utilized, by assuming periodic flow and fin design pattern, to reasonably reduce the high cost of full-3D model optimization. For the solution of flow part, a pseudo-spectral scheme is used, which is intrinsically periodic and features a high spectral accuracy, and the finite element method for the non-periodic conjugate heat transfer model. Exact partial derivatives of the discrete solutions are obtained analytically by hand-differentiation. This task is rather convenient for the flow part, due to the simplicity of the pseudo-spectral implementation; however, the MATLAB symbolic toolbox is selectively utilized for the finite element code to ensure an error-free implementation. Finally, the sensitivities are computed directly or via a discrete adjoint method, for the flow and heat models, respectively. To examine the present approach, two approaches are used for optimization of a practical cooling task: constrained and unconstrained multi-objective formulations, where in all cases more emphasis is placed on thermal resistance minimization. A series of optimized heat sink geometries via constrained or unconstrained multi-objective optimizations are obtained to examine practical utility of the present approach. The optimized topologies demonstrated superior cooling performances at lower costs of pressure losses compared to conventional (circular) in-line and staggered fins, and confirmed the supremacy of topology over pure sizing optimization.