Final Compromise Solution Research Articles

Li-ion battery state of health prediction through metaheuristic algorithms and genetic programming

Predicting the State of Health (SOH) of the Lithium-ion battery with higher accuracy and reduced cost is a challenging and crucial task for ensuring its reliability and safety. To achieve this, a two-stage prediction framework is proposed to find a concise expression of SOH using the health features of the battery through metaheuristic algorithms and genetic programming (GP).In Stage-I, three conflicting objectives are considered concurrently: the root-mean-square error (RMSE) of SOH prediction, the health features selected, and the expressional complexity of the battery capacity. The wrapper structure is utilized for SOH prediction, where a binary multi-objective grey wolf optimization (Binary MOGWO) algorithm is employed to select features and generate the Pareto set. Genetic programming is used to calculate the SOH value using symbolic regression models. In Stage-II, the final compromise solution is filtered from the Pareto set through decision-making approaches. The relationships between selected features and the capacity of the battery are investigated. The NASA Prognostics Center of Excellence battery dataset is chosen to verify the effectiveness of the proposed framework. The simulation results show that the features found through the framework can provide SOH predictions in the form of symbolic equations with higher accuracy, lower cost, and reduced complexity.

Crushing Response and Optimization of a Modified 3D Re-Entrant Honeycomb.

A modified 3D re-entrant honeycomb is designed and fabricated utilizing Laser Cladding Deposition (LCD) technology, the mechanical properties of which are systematically investigated by experimental and finite element (FE) methods. Firstly, the influences of honeycomb angle on localized deformation and the response of force are studied by an experiment. Experimental results reveal that the honeycomb angles have a significant effect on deformation and force. Secondly, a series of numerical studies are conducted to analyze stress characteristics and energy absorption under different angles (α) and velocities (v). It is evident that two variables play an important role in stress and energy. Thirdly, response surface methodology (RSM) and the Non-Dominated Sorting Genetic Algorithm II (NSGA-II) are implemented with high precision to solve multi-objective optimization. Finally, the final compromise solution is determined based on the fitness function, with an angle of 49.23° and an impact velocity of 16.40 m/s. Through simulation verification, the errors of energy absorption (EA) and peak crush stress (PCS) are 9.26% and 0.4%, respectively. The findings of this study offer valuable design guidance for selecting the optimal design parameters under the same mass conditions to effectively enhance the performance of the honeycomb.

Bandgap properties and multi-objective optimization of double-cone pentamode metamaterials with curved side

Pentamode metamaterials (PM) have a promising application in noise reduction fields. In this paper, in order to improve the acoustic modulation capability of PMs, several novel curve PMs are proposed by replacing the straight sides of conventional PMs with curves. At first, the elliptic PMs (EPMs) with various unit cell arrangements (i.e., triangular, square, and hexagonal) are designed, respectively, and their bandgap properties are studied numerically in detail. The EPM with hexagonal unit cell arrangement (EPMH) presents better comprehensive bandgap properties in the EPMs. Subsequently, sinusoidal and power curves are introduced into the EPMH respectively to explore the influences of curve types on bandgap properties. The results show that the bandgap properties improvement of EPMH is higher in comparison with introducing other curves, and the reasons behind these improvements are carefully disclosed in combination with the spring-mass system. Finally, to further improve the bandgap properties of EPMH, a high accuracy Kriging model is constructed according to both the Latin hypercube design and double-point infilling. The Pareto optimal solution sets are determined using a non-dominated sorting genetic algorithm (NSGA-II), and the final compromise solution is gained by employing a fitness function. The bandwidths of phononic bandgap and single mode bandgap, and the total bandwidth of optimized EPMH are increased respectively by about 114.5, 4.3, and 7.7 times than those of the conventional straight side PMs. This investigation provides a fresh strategy for designing PMs with excellent bandgap properties.

Parametric Analysis and Multi-Objective Optimization of Pentamode Metamaterial

Pentamode metamaterial (PM) has enormous application potential in the design of lightweight bodies with superior vibration and noise-reduction performance. To offer systematic insights into the investigation of PMs, this paper studies the various effects (i.e., unit cell arrangement, material, and geometry) on bandgap properties through the finite element method (FEM). With regards to the influences of unit cell arrangements on bandgap properties, the results show that the PM with triangular cell arrangement (PMT) possesses better bandgap properties than the others. The effects of material and geometry on bandgap properties are then explored thoroughly. In light of the spring-mass system theory, the regulation mechanism of bandgap properties is discussed. Multi-objective optimization is conducted to further enhance the bandgap properties of PMT. Based on the Latin hypercube design and double-points infilling, a high-accuracy Kriging model, which represents the relationship between the phononic bandgap (PBG), single mode phononic bandgap (SPBG), double-cone width, and node radius, is established to seek the Pareto optimal solution sets, using the non-dominated sorting genetic algorithm (NSGA-II). A fitness function is then employed to obtain the final compromise solution. The PBG and total bandgap of PMT are widened approximately 2.2 and 0.27 times, respectively, while the SPBG is narrowed by about 0.51 times. The research offers important understanding for the investigation of PM with superior acoustic regulation capacity.

Dynamic multiobjective optimization and multivariate analysis for power generation scheduling of the diesel generators in dynamically positioned vessels

Economic and environmental topics together with the higher performance of marine vessels have been becoming more demanding in recent years. This work aims to investigate the optimal operation of diesel generators in the dynamically positioned vessels. Due to the continuous external power demand, the dynamic multiobjective optimization model for optimal scheduling of the diesel generators is generated, taking the fuel consumption and greenhouse gas emission into consideration simultaneously. The present study proposes a 2-phase analysis framework for each time step. A newly developed meta-heuristic optimization algorithm, multi-objective ant lion optimizer (MOALO) is adopted to find the Pareto set in Phase-I. A necessary decision-making procedure based on a simple additive weighting (SAW) approach is utilized to find the final compromise solution in Phase-II. Furthermore, multivariate analysis (MVA) methods are employed to mine the historical features of economic and environmental performances as well as the loadings of all generators. Self-organizing mapping (SOM) together with cluster analysis is utilized to study the relationships among data samples. Multidimensional scaling (MDS) is adopted to examine the relationships among these attributes. An oil rig platform equipped with 8 diesel generators is selected as an illustrative example. The dynamic Pareto fronts and corresponding final compromise solutions obtained from SAW are provided. The effects of various weights upon the history of fuel consumption and emission are examined. The hidden information about the performances in history is studied through SOM and MDS. Results from the numerical example demonstrate that dynamic multiobjective optimization and multivariate analysis extend the application of optimization and data mining in the field of power scheduling for diesel generators in dynamically positioned vessels. The findings of this study add to the understanding of relationships among loads of the generators and corresponding economic and environmental features.

In-plane dynamic response and multi-objective optimization of negative Poisson's ratio (NPR) honeycomb structures with sinusoidal curve

In order to efficiently evaluate and design honeycomb structures with excellent energy-absorbing ability, in-plane dynamic response and multi-objective optimization of negative Poisson's ratio (NPR) honeycomb structures with sinusoidal curve are performed in this work. By establishing the in-plane impact finite element model, the deformation modes and in-plane dynamic responses of the sinusoidal NPR honeycomb structures under different impact velocities are detailed studied. And the geometric parameters (e.g., the amplitude and period) of the sinusoidal curve that affect the energy absorption performance of the structure are analyzed. Combining the optimal latin hypercube design method with the double-points infilling criterion, the high-precision adaptive Kriging models of the peak crush force (PCF) and the specific energy absorption (SEA) with respect to the amplitude and period are constructed. And then, a multi-objective crashworthiness optimization is carried out by non-dominated sorting genetic algorithm (NSGA-II). The Pareto optimal solution set is gained and the final compromise solution is then obtained based on the fitness function. The optimized results show the PCF of the sinusoidal NPR honeycomb structure decreases by 30.53%, while the SEA increases by 38.55%. It indicates that the optimized sinusoidal honeycomb structure has better energy absorption performance than the conventional concave hexagonal honeycomb. The results can provide some important design guidance for other honeycomb energy-absorbing structures.

Dynamic multiobjective optimization for thrust allocation in ship application

Thrust allocation is a key procedure in the dynamic position system (DPS) of marine vessels. The present work aims to study the characteristics of dynamic optimization in thrust allocation. A two-phase analysis process is proposed. In phase-I, the model for thrust allocation is generated from the viewpoint of multiobjective optimization. Fuel consumption and tear-and-wear on the thrusters are chosen as objectives. Multiobjective feasibility enhanced particle swarm optimization algorithm (MOFEPSO) is applied to find the Pareto set of this problem. An additional decision-making procedure, the technique of order preference by similarity to ideal solution (TOPSIS) is utilized to choose the final compromise solution in phase-II. The self-organizing map (SOM) technique is undertaken to mine the Pareto data set. A Remote Operated Vehicle (ROV) example is provided for illustrating the above analysis process. The effects of relative importance between objectives upon characteristics of thrust allocation are studied. The trajectories of decision variables and objectives are examined through the SOM method. Results from numerical examples demonstrate that the multiobjective optimization method together with decision-making skills can extend the application of optimization in the thrust allocation field. The findings in this work add to the understanding of relationships among several aspects of DPS.

Three-objective optimization of aircraft secondary power system rotor dynamics

Secondary power system based on gas turbine engine is usually used for starting the aircraft main engine at ground and finds similar application in air during the emergency. The secondary power system comprises of an auxiliary power unit (APU) and an air starter. APU provides stand-alone power to the main engine subsystems and air to the air starter for starting main engine. The main rotor system of APU is to be designed for safe operation during the ground critical speed crossing and maneuver loading. The weight of such a rotor system is an important design criterion. In the current work, multi-objective optimization using hybrid genetic algorithm (HGA) is employed for simultaneously minimizing the response at critical speed, the response during maneuvering, and shaft weight of the APU rotor system used in secondary power system of an aircraft. The shaft considered is a stepped one and is modeled using Rayleigh beam elements with three disks. Effects due to gyroscopic effect are also included in the analysis. A Pareto front is generated, and subsequently, an optimal solution is selected for the problem. The comparison with typical two-objective optimization result, having response at critical speed and shaft weight as objectives and response during maneuvering as constraint, has shown that the novel three-objective optimization has provided the designer with improved design choices for the selection of final compromise solution.

Optimal Allocation of Hybrid Renewable Energy System by Multi-Objective Water Cycle Algorithm

This article offers a multi-objective framework for an optimal mix of different types of distributed energy resources (DERs) under different load models. Many renewable and non-renewable energy resources like photovoltaic system (PV), micro-turbine (MT), fuel cell (FC), and wind turbine system (WT) are incorporated in a grid-connected hybrid power system to supply energy demand. The main aim of this article is to maximize environmental, technical, and economic benefits by minimizing various objective functions such as the annual cost, power loss and greenhouse gas emission subject to different power system constraints and uncertainty of renewable energy sources. For each load model, optimum DER size and its corresponding location are calculated. To test the feasibility and validation of the multi-objective water cycle algorithm (MOWCA) is conducted on the IEEE-33 bus and IEEE-69 bus network. The concept of Pareto-optimality is applied to generate trilateral surface of non-dominant Pareto-optimal set followed by a fuzzy decision-making mechanism to obtain the final compromise solution. Multi-objective non-dominated sorting genetic (NSGA-III) algorithm is also implemented and the simulation results between two algorithms are compared with each other. The achieved simulation results evidence the better performance of MOWCA comparing with the NSGA-III algorithm and at different load models, the determined DER locations and size are always righteous for enhancement of the distribution power system performance parameters.

Hierarchical Group Compromise Ranking Methodology Based on Euclidean–Hausdorff Distance Measure Under Uncertainty: An Application to Facility Location Selection Problem

Proposing a hierarchical group compromise method can be regarded as a one of major multi-attributes decision-making tool that can be introduced to rank the possible alternatives among conflict criteria. Decision makers’ (DMs’) judgments are considered as imprecise or fuzzy in complex and hesitant situations. In the group decision making, an aggregation of DMs’ judgments and fuzzy group compromise ranking is more capable and powerful than the classical compromise ranking. This research extends a new hierarchical group compromise ranking methodology under a hesitant fuzzy (HF)environment to handle uncertainty, in which for the margin of error, the DMs could assign the opinions in several membership degrees for an element. The hesitant fuzzy set (HFS)is taken into account for the process of the proposed hierarchical group compromise ranking methodology, namely HFHG-CR, and for avoiding the data loss, the DMs’ opinions with risk preferences are considered for each step separately. Also, the Euclidean–Hausdorff distance measure is utilized in a new proposed index for calculating the average group score, worst group score and compromise measure regarding each DM. A new ranking index is presented for final compromise solution for the evaluation. Proposed HFHG-CR methodology is applied to a practical example for a facility location selection problem, i.e. cross-dock location problem, to show the validation and application.

Design optimization of multilayer perceptron neural network by ant colony optimization applied to engine emissions data

A multilayer perceptron (MLP) artificial neural network (ANN) model has been optimized by the multi-objective ant colony optimization (MOACO) algorithm, which uses three objective functions. A sensitivity analysis to choose MOACO parameter values is carried out by calculating hypervolume metric, and the proposed approach adopts the Vlsekriterijumska Optimizacija I Kompromisno Resenje (VIKOR) decision method to choose final compromised solution on the Pareto front obtained from MOACO. As a result, we used the MLP-MOACO developed model to estimate the value of engine emissions of NO x in a four stroke, spark ignition (SI) gasoline engine and observed acceptable correlation coefficient ( R 2) of 0.99978.

Pressure retarded osmosis: Operating in a compromise between power density and energy efficiency

Pressure retarded osmosis (PRO) is a promising technology for salinity gradient energy utilization. Here, based on previous literature, we proposed a simplified model to describe the PRO process, which was validated by a great accordance with the experimental data of water flux and power density. A sensitivity analysis of the PRO system indicated that there exist different optimal hydraulic pressure differences leading to the maximum power density and energy efficiency, respectively. The performance of the PRO system under the maximum power density and energy efficiency is systematically investigated based on the GA method. Furthermore, the Pareto front that indicates any arbitrary compromise between the maximum power density and energy efficiency based on NSGA-II was obtained. Factors determining the choice of the final compromise solution in the Pareto frontier remains are systematically discussed, which should be referred to the local energy policies and technical and economic conditions of the PRO systems. For demonstration, the final compromise solution selected by the abstract heuristic TOPSIS method is discussed and a desirable compromise between the power density and energy efficiency is presented.

Research on Optimal Planning of Access Location and Access Capacity of Large-Scale Integrated Wind Power Plants

This paper proposes a multi-objective optimal planning model of access location and access capacity for large-scale integrated wind power generation considering the mutual restriction between the planning of large-scale wind power plants and the planning of power system network. In this model, the power flow equilibrium degree, investment costs and active network loss are taken as the optimization goals. The improved differential evolution (IDE) algorithm is applied to calculate the Pareto optimal solution set of wind power’s access planning. With the solution results described by the Pareto pattern, all the alternative solutions are then ranked based on the entropy weight method and the final compromised solution is selected by the method of technique for order preference by similarity to ideal (TOPSIS). And the proposed optimal planning model is tested based on a practical planning need of large-scale integrated wind power generation in an actual power grid of China in 2020. The simulation results show that applied with the proposed optimization model and matching algorithm, the planning scheme of large-scale wind power’s access location and access capacity under complex and practical power system circumstances has been successfully optimized.

Multi-objective electric distribution network reconfiguration solution using runner-root algorithm

This paper presents a runner-root algorithm (RRA) for electric distribution network reconfiguration (NR) problem. The considered NR problem in this paper is to minimize real power loss, load balancing among the branches, load balancing among the feeders as well as number of switching operations and node voltage deviation using max-min method for selection of the final compromised solution. RRA is equipped with two explorative tools, which are random jumps with large steps and re-initialization strategy to escape from local optimal. Moreover, RRA is also equipped with an exploitative tool to search around the current best solution with large and small steps to ensure the obtained result of global optimization. The effectiveness of the applied RRA in both single- and multi-objective has been tested on 33-node and 70-node distribution network systems and the obtained test results have been compared to those from other methods in the literature. The simulation results show that the applied RRA can be an efficient method for network reconfiguration problems with single- and multi-objective.

Evaluation and selection of resilient suppliers in fuzzy environment

Purpose– Supply chains (SCs) have become increasingly vulnerable to catastrophic events/disruptions that may be natural or man-made. Hurricanes, tsunamis and floods are natural disasters, whereas man-made disasters may be strikes, terrorist attacks, etc. Failure at any point in the SC network has the potential to cause the entire network to fail. SCs must therefore be properly designed to survive well in the disruption scenario. The capability of successful survival (of the firm’s SC) against those adverse events/happenings is termed as resilience; and, the SC designed under resilience consideration is called a resilient SC. Effective supplier selection is considered as a key strategic consideration in SC management. It is felt that apart from considering traditional suppliers selection criterions, suppliers’ resiliency strategy must be incorporated while selecting a potential supplier which can provide best support to the firm even in the disaster/disruption scenario. The purpose of this paper is to focus aspects of evaluation and selection of resilience supplier by considering general as well as resiliency strategy, simultaneously.Design/methodology/approach– In this work, subjectivity associated with ill-defined (vague) evaluation information has been tackled through logical exploration of fuzzy numbers set theory. Application of VIKOR embedded with fuzzy mathematics has been utilized here. Sensitivity analysis has been performed to reflect the effect of decision-makers’ (DM) risk bearing attitude in selecting the best potential supplier in a resilient SC. A case empirical example has also been presented.Findings– The work attempts to focus on a decision-making procedural hierarchy towards effective supplier selection in a resilient SC. The work exhibits application potential of VIKOR method integrated with fuzzy set theory to select potential supplier based on general strategy as well as resiliency strategy. The final supplier selection score (obtained by considering general strategy) and that of obtained by analyzing resiliency strategy have been combined to get a final compromise solution. The decision-support framework thus reported here also considers DMs’ risk bearing attitude.Practical implications– The study bears significant impact to the industry managers who are trying to adapt resiliency strategy in their SC followed by potential supplier selection in the context of resilient SC.Originality/value– Exploration of VIKOR embedded with fuzzy set theory towards suppliers’ evaluation and selection by considering general and resiliency criteria both. The decision-support module(s) adapted in this paper considers DMs’ risk bearing attitude to arrive the best compromise solution.

Maintenance supplier selection considering life cycle costs and risks: a fuzzy goal programming approach

In this study, we address a new variant of supplier selection problem named maintenance supplier selection problem faced by a manufacturer. The production system consists of different multi-component equipments whose maintenance activities require several components (parts) each of which could be provided by multiple suppliers. A multi-objective mathematical model is developed to decide about the supply base of each part as well as the purchasing quantity of each part from each selected supplier. The model accounts for the total life cycle costs of purchased parts and various risks threatening the candidate suppliers. A fuzzy/soft lexicographic goal programming approach with soft priorities between objectives is proposed to enable the decision-maker to make preferred trade-offs between objectives by which the effects of various risks in each phase of life cycle of procured parts are investigated. The capability and effectiveness of the proposed model is validated through a case study. Some sensitivity analyses are also carried out for investigating the impact of cost, risk and objectives’ priorities on the final preferred compromise solution. Finally, some managerial insights and concluding remarks are provided.

A multi-criteria optimization and decision-making approach for improvement of food engineering processes

The objective of this study was to propose a multi-criteria optimization and decision-making technique to solve food engineering problems. This technique was demonstrated using experimental data obtained on osmotic dehydration of carrot cubes in a sodium chloride solution. The Aggregating Functions Approach, the Adaptive Random Search Algorithm, and the Penalty Functions Approach were used in this study to compute the initial set of non-dominated or Pareto-optimal solutions. Multiple non-linear regression analysis was performed on a set of experimental data in order to obtain particular multi-objective functions (responses), namely water loss, solute gain, rehydration ratio, three different colour criteria of rehydrated product, and sensory evaluation (organoleptic quality). Two multi-criteria decision-making approaches, the Analytic Hierarchy Process (AHP) and the Tabular Method (TM), were used simultaneously to choose the best alternative among the set of non-dominated solutions. The multi-criteria optimization and decision-making technique proposed in this study can facilitate the assessment of criteria weights, giving rise to a fairer, more consistent, and adequate final compromised solution or food process. This technique can be useful to food scientists in research and education, as well as to engineers involved in the improvement of a variety of food engineering processes.

A multi-criteria optimization and decision-making approach for improvement of food engineering processes

The objective of this study was to propose a multi-criteria optimization and decision-making technique to solve food engineering problems. This technique was demonstrated using experimental data obtained on osmotic dehydration of carrot cubes in a sodium chloride solution. The Aggregating Functions Approach, the Adaptive Random Search Algorithm, and the Penalty Functions Approach were used in this study to compute the initial set of non-dominated or Pareto-optimal solutions. Multiple non-linear regression analysis was performed on a set of experimental data in order to obtain particular multi-objective functions (responses), namely water loss, solute gain, rehydration ratio, three different colour criteria of rehydrated product, and sensory evaluation (organoleptic quality). Two multi-criteria decision-making approaches, the Analytic Hierarchy Process (AHP) and the Tabular Method (TM), were used simultaneously to choose the best alternative among the set of non-dominated solutions. The multi-criteria optimization and decision-making technique proposed in this study can facilitate the assessment of criteria weights, giving rise to a fairer, more consistent, and adequate final compromised solution or food process. This technique can be useful to food scientists in research and education, as well as to engineers involved in the improvement of a variety of food engineering processes.

Ant colony optimisation for tree-searching-based synthesis of monopulse array antenna

The design of simple feed networks is of great interest in synthesising monopulse radar array antennas in order to reduce the complexity of the antenna architecture, the costs as well as the occupied physical space (e.g. on aircraft). Sub-arraying techniques have been proposed to properly address such a task. Starting from the formulation of the sub-arraying problem in terms of a combinatorial one, the final compromise solution is obtained by looking for the minimum cost path inside a binary tree graph through an ant colony optimiser.

Optimizing Injection Molding Toward Multiple Quality and Cost Issues

Injection-molding part designers are frequently faced with multiple quality and cost issues. These issues are usually in conflict with each other; thus, a trade-off needs to be made to reach a final compromised solution. Because evaluation of part quality and cost via injection-molding simulation is very time-consuming, implementation of a conventional multicriteria optimization procedure for injection-molding problems is economically unfavorable. However, many injection-molding problems dealing with multiple quality and cost issues can be modeled as constrained problems, with the total cost as the objective function and quality quantities as the constraints. By introducing a concept of penalized total cost, such constrained problems are further simplified into bounded single-criterion problems. The bounded single-criterion problems are then optimized using a direct search-based optimization procedure. Strategies of modeling, transformation, and optimization for these problems are discussed in this article. A case study is provided.