Additional Objective Function Research Articles

A Multi‐Objective Evolutionary Algorithm Based on Bilayered Decomposition for Constrained Multi‐Objective Optimization

This paper proposes a multi‐objective evolutionary algorithm based on bilayered decomposition (MOEA/BLD) for solving constrained multi‐objective optimization problems. MOEA/D is an effective method for solving unconstrained multi‐objective optimization problems. It decomposes the objective space using weight vectors and simultaneously searches for solutions for the subproblems. However, real‐world applications impose many constraints, and these constraints must be handled appropriately when searching for good feasible solutions. The proposed MOEA/BLD treats such constraints as an additional objective function. Furthermore, in addition to the conventional weight vector, an augmented weight vector is introduced that decomposes the objective space and constraint violation space hierarchically. In the first stage, the objective space is decomposed by conventional weight vectors. In the next stage, the bi‐objective space consisting of the scalarizing function and constraint violation is decomposed by augmented weight vectors. The augmented weights are adjusted so that they decrease linearly in the search process as the search gradually moves from infeasible regions to feasible regions. The proposed algorithm is compared to several state‐of‐the‐art constrained MOEA/Ds using multi‐ and many‐objective problems. The results show that the proposed method outperforms existing methods, in terms of search performance, under various conditions. © 2024 Institute of Electrical Engineers of Japan and Wiley Periodicals LLC.

Multi-objective optimization of inerter-based building mass dampers

The building mass damper (BMD) is a design concept in which a structure is substructured in such a way that the upper substructure behaves as a large-mass tuned mass damper for the lower one. Its correct tuning usually requires softening (partial isolating) the upper substructure, which limits its application for retrofitting. The recently proposed inerter-based building mass damper (IBMD) solves, reasonably, the softening dynamically through the use of an inerter. This implies an in parallel intervention, which drastically simplifies the practicability of the BMD for retrofitting. The present paper involves comprehensive numerical simulations for multi-objective optimization of an IBMD, accounting for inherent structural damping. In particular, the deformation of the upper substructure is an additional objective function, besides the deformation of the lower substructure as considered in a previous work. Results demonstrate that the IBMD outperforms various benchmark interventions, including dampers, stiffeners, softening devices, and inerters without dampers. Additionally, it was found that the inherent structural damping partially replaces the need for additional damping. Finally, it was also shown that emphasizing the optimization of the lower substructure deformation enhances the overall structural safety in most cases. Nevertheless, the multi-objective optimization increases the versatility of the design concept in the case of substructures with different allowable deformations.

Revolutionizing E-Commerce Logistics

The traditional approach to logistics path planning is hindered by lengthy procedures. In this study, we explore the multi-objective optimization of logistics management, considering the conventional path and time efficiency indices alongside shelf safety and stability as additional objective functions. Based on particle swarm optimization (PSO), we optimize objective functions for internal path planning, scheduling timeliness, and shelf safety and stability. We then determine optimal routes under varying order demands using PSO and ultimately optimize the final path using dynamic programming and spline function restrictions to meet actual demand. Empirical results indicate that the proposed solution method outperforms other calculation methods, such as genetic algorithm (GA) and simulated annealing (SA), demonstrating over 10% improvement in time and total distance consumption. Further practical application tests demonstrate that the model in this study has a beneficial impact on all five distinct types of orders through efficient deployment optimization.

An Approach to Near-Optimal Continuous-Thrust Solution for Plane Constellation Deployment

Paving the way in satellite constellation deployment, this article presents the Comprehensive Program (GCP) for planning constellation deployment missions by introducing a near-optimal solution for continuous-thrust maneuvers. The GCP establishes time constraints, enabling appropriate time scheduling and eliminating reconfiguration phases. It considers various cases of satellite departure and arrival sequences, collision avoidance constraints, and time limitations. A near-optimal solution for the continuous-thrust trajectory of each satellite is introduced, relying on the Fourier series approximation of the thrust pointing angle. The Fourier series with constant coefficients replaces the thrust angle in the satellite’s orbital motion equations in polar coordinates. The primary advantage of this near-optimal approach lies in its simplicity in accommodating space perturbations, posing no challenges in problem-solving. Additionally, the approach is beneficial due to its straightforward implementation and simple mathematical computations. This approach does not require pre-determining the revolution number of the transfer trajectory, unlike shape-based methods. The proposed method’s flexibility allows it to adapt and optimize the trajectory without prior assumptions about the number of revolutions required for the mission. Analyses demonstrate the proposed algorithm’s versatility and precision across various scenarios involving different orbital eccentricities, thrust forces, and thrust pointing angles. The constant coefficients of the Fourier series are determined by defining a set of objective functions and minimizing them using the Multi-Objective Particle Swarm Optimization algorithm (MOPSO). The first and second objective functions ensure that the transfer orbit reaches the desired deployment point, while the third and fourth ones guarantee the tangential conditions between the transfer orbit and the final orbit. An additional objective function minimizes the trajectory time. As a perturbation of interest, the effect of Earth’s oblateness is considered.

Multi-level feature interaction for open knowledge base canonicalization

Open Information Extraction (OpenIE) aims to construct expansive open knowledge bases (OKBs) by extracting triples (noun phrase, relation phrase, noun phrase) from unstructured text. One critical problem in OKBs is the lack of canonicalization for noun phrases and relation phrases, leading to the storage of redundant and ambiguous facts. Consequently, open knowledge base canonicalization, which clusters synonymous phrases into the same group, has emerged as an active research area. Existing approaches either leverage fact triples or source context in isolation, or at best, interact them at the clustering level. However, these approaches lack explicit interaction or only loosely couple the two types of knowledge, resulting in the potential loss of valuable intermediate information. In this paper, we propose MuFIC, a novel unsupervised framework that interacts the fact triples and source context at the feature level to address these limitations. In order to capture and integrate fine-grained fact and context knowledge, we design three levels of feature interaction: low-level context-guided feature interaction, mid-level fact-guided feature interaction, and high-level gated fusion feature interaction. Furthermore, we introduce an additional objective function via contrastive learning to improve the quality of extracted features and reduce knowledge-specific noise. Finally, we design a bidirectional feedback mechanism to better guide the learning process of joint features by harnessing side information prototype learning, and to dynamically optimize side information based on the clustering results formed by joint features. Extensive experiments on three public benchmark datasets demonstrate the superiority of our proposed framework.

Two-stage coevolutionary constrained multi-objective optimization algorithm for solving optimal power flow problems with wind power and FACTS devices

As a large amount of wind energy is integrated into the grid, the randomness it brings poses a challenge to modern power systems. The application of Flexible AC Transmission Systems (FACTS) in the grid is becoming more and more common, and it is necessary to consider how to choose suitable equipment in the appropriate locations. In this paper, a multi-objective optimal power flow (MOOPF) model with wind farms and FACTS devices is established. The Weibull probability density function is used to establish the wind speed model, and the cost problem brought by wind power is considered. The locations and ratings of thyristor-controlled series compensators, thyristor-controlled phase shifters, and static VAR compensators are added to the system as control variables. In addition, the constraints on the prohibited operating areas of thermal power generators and the valve point effect are also considered. Coevolutionary constrained multi-objective optimization algorithm (CCMO) is an advanced technology, and this paper improves it and names it two-stage coevolutionary constrained multi-objective optimization algorithm (TSCCMO). The proposed algorithm uses the constraint violation value as an additional objective function in the sub-population environmental selection process, and integrates a neighborhood selection strategy into the mating selection process. The population evolution process is divided into two stages, in the first stage the two populations cooperate weakly, and in the second stage the two populations will have strong cooperation. TSCCMO is used to solve this complex constrained MOOPF problem, and its results are compared and analyzed with CCMO, NSGA–II–CDP, C3M, and PPS. The comprehensive performance of TSCCMO is the best among the 6 cases.

Coordinated torque control for enhanced steering and stability of independently driven mobile robots

PurposeMobile robots with independent wheel control face challenges in steering precision, motion stability and robustness across various wheel and steering system types. This paper aims to propose a coordinated torque distribution control approach that compensates for tracking deviations using the longitudinal moment generated by active steering.Design/methodology/approachBuilding upon a two-degree-of-freedom robot model, an adaptive robust controller is used to compute the total longitudinal moment, while the robot actuator is regulated based on the difference between autonomous steering and the longitudinal moment. An adaptive robust control scheme is developed to achieve accurate and stable generation of the desired total moment value. Furthermore, quadratic programming is used for torque allocation, optimizing maneuverability and tracking precision by considering the robot’s dynamic model, tire load rate and maximum motor torque output.FindingsComparative evaluations with autonomous steering Ackermann speed control and the average torque method validate the superior performance of the proposed control strategy, demonstrating improved tracking accuracy and robot stability under diverse driving conditions.Research limitations/implicationsWhen designing adaptive algorithms, using models with higher degrees of freedom can enhance accuracy. Furthermore, incorporating additional objective functions in moment distribution can be explored to enhance adaptability, particularly in extreme environments.Originality/valueBy combining this method with the path-tracking algorithm, the robot’s structural path-tracking capabilities and ability to navigate a variety of difficult terrains can be optimized and improved.

A conditioned Latin hypercube sampling design methodology for ground-truthing transient EM resistivity models

Translating 3D resistivity models of the subsurface to relevant hydrogeological parameters such as sediment texture requires applying a rock physics transform that is ideally calibrated using co-located 1D sediment texture logs. It is difficult to select optimal logging sites in the model that span the range of observed resistivity values using expert opinion alone. Instead, we demonstrate a methodology for selecting logging sites using conditioned Latin hypercube sampling (cLHS), a maximally stratified sampling design methodology. cLHS employs simulated annealing to select sampling sites that minimize an objective function by reproducing the statistics of the resistivity model. We implement numerous preprocessing steps to isolate desirable regions within the model for logging, and we use principal component analysis to reduce the dimensionality of the model to aid the convergence of the simulated annealing procedure while preserving the majority of the model variance. Additionally, we impose an additional objective function condition to penalize the selection of sites in the resistivity model that exhibit a high degree of lateral variance. This condition is used to increase the likelihood that the sediment texture logs acquired at the selected sites correlate well with the resistivity model. We tested our approach on a resistivity model obtained using a towed transient EM system in an almond orchard in California’s Central Valley, comparing our selected sets of logging sites against the five cone penetrometer testing logs originally acquired at the site, as well as randomly selected logging sites. The sample sets selected with cLHS were consistently able to reproduce the statistics of the resistivity model and did so more effectively than the true sampling locations or the random sampling locations.

Three-Dimensional Limited-Memory BFGS Inversion of Magnetic Data Based on a Multiplicative Objective Function

At present, the traditional magnetic three-dimensional inversion method has been fully developed and is widely used. Magnetic exploration is a kind of geophysical exploration method that uses the magnetic field changes (magnetic anomalies) caused by the magnetic differences between various rocks in the crust to find useful mineral resources and study the underground structure. Traditional magnetic three-dimensional inversion is relatively inefficient. Moreover, the traditional additive objective function (data fitting difference term plus regularization term and logarithmic obstacle term), which causes the regularization factor selection to be more complicated, is implemented in this method. Therefore, it is necessary to establish a new efficient three-dimensional magnetic inversion algorithm and optimize the selection of regularization factors. In this paper, based on the limited-memory BFGS (L-BFGS) method, the three-dimensional magnetic inversion of a multiplicative objective function is realized. The inversion test is conducted in this paper using both theoretical synthesis data and measured data. The results demonstrate that the limited-memory BFGS method significantly enhances the inversion efficiency and yields superior inversion outcomes compared to traditional magnetic three-dimensional inversion methods. Additionally, the multiplicative objective function-based three-dimensional magnetic inversion method simplifies the process of selecting weight factors for regularization terms.

Multiobjective-Based Constraint-Handling Technique for Evolutionary Constrained Multiobjective Optimization: A New Perspective

Multiobjective-based constraint-handling techniques are popular in evolutionary constrained single-objective optimization. However, most of these techniques run into troubles when dealing with constrained multiobjective optimization problems (CMOPs). That is, they have difficulty optimizing too many objective functions, are ineffective in maintaining population diversity, or are challenged in establishing appropriate additional objective functions. As a remedy to these limitations, we propose a novel technique called NRC for handling CMOPs. The novelty of NRC lies in its three sorting procedures: nondominated sorting, reversed nondominated sorting, and constrained crowding distance sorting, which are performed in sequence to provide driving forces toward the Pareto front (PF) of a transformed unconstrained multiobjective optimization problem (treating the overall constraint violation as an additional objective function), the boundary front, and the constrained PF, respectively. With the combination of these three different forces, NRC can conveniently approach the desired PF from diverse search directions. The effectiveness of NRC is experimentally verified. Also, we incorporate NRC into a two-archive mechanism and develop a novel constrained multiobjective evolutionary algorithm, called NRC2. Comprehensive experiments on 49 benchmark CMOPs and 21 real-world ones demonstrate that NRC2 is significantly superior or comparable to six state-of-the-art constrained evolutionary multiobjective optimizers on most test instances.

Extensions to traffic control modeling store-and-forward

The store-and-forward traffic model is widely used because of its simplicity and reasonable comprehension. Its results determine the duration of the green light according to a preset cycle. This paper builds further on the currently existing model: it expands the definitional domain of the optimization problem by adding additional probabilistic requirements regarding the number of vehicles in a street segment between intersections controlled by traffic lights. The defined optimization problem minimizes the probability of increasing the number of vehicles in the considered transport network. A further extension of the store-and-forward model allows the control domain to contain both green lights and cycle durations. Such optimal control allows the achievement of additional objective functions such as minimizing the number of vehicles in the network and minimizing the total time spent through the network. The definition of this control problem is done through a bi-level hierarchical formalization involving the store-and-forward model. The derived extended models are numerically tested and compared with real cases, giving preference to the derived extensions of the classical store-and-forward model.

VERBAL DESCRIPTION OF THE TECHNOLOGY FOR PLANNING THE QUALITY IMPROVEMENT OF A SUBSET OF THE PROCESSES OF THE SPICE MATURITY REFERENCE MODEL

It is noted that to solve the problem of developing information technology for planning the increase of maturity level of a subset of the processes of the SPICE reference maturity model, this issue must first be considered at the verbal level as a technology (sequence of stages) for the implementation of the given problem. At the first stage, the structure of the SPICE reference model, which consists of a number of separate processes, was formalized. This set is presented as a hierarchical structure: the first level is a set of processes and subprocesses; the second level is a set of process groups; the third level is a set of process categories. At the second stage, the method of assessing the level of possibility of a separate process/sub-process of the reference maturity model SPICE is considered. It is given from the point of view of two dimensions of the SPICE model: the purpose of the processes; the attributes of the processes (measurable characteristics necessary for managing the process and increasing the possibility of its execution). The third stage of the technology is focused on the synthesis of planning model of the subset development processes for the SPICE model, which determines the quality level of a separate component of the software development process (SDP), which in turn has a positive effect on the level of development of software systems. Assessment and planning of the possibility level of a subset of processes is implemented during a certain planning period under conditions of limited resources based on their optimal distribution, taking into account the importance of individual processes and their practices during the planning period. At the fourth stage of the technology, an algorithm for planning the development of a subset of processes of the reference maturity model SPICE is considered based on the method of sequential analysis of options. This is primarily due to the fact that the optimization model has an additive objective function. The method allows discarding those appropriate solutions that do not contain optimal solutions. In the future, when specifying the model, it is planned to choose an algorithm that belongs to this method and adapt it to the solution of the given problem. The fifth stage is devoted to information technology implementation of the developed model and algorithm. At this stage, the following set of problems is solved. Analysis of business processes of the technology of improving the quality of software development process. Definition of software requirements. Forming a diagram of use cases. Development of data models. Justification of the choice of tools for software development. Selection of reference system architecture. Next, software coding and testing. At the sixth stage, based on information technology, a number of variants of the plan for improving the quality of a subset of the processes of the SPICE maturity model are formed in order to support decision-making by the management of the IT company. For this, a set of effective solutions is preliminarily determined, which is proposed to determine the final option, which is implemented later.

Multi-objective optimization and evaluation of a water-saving scenario to produce hydrogen and freshwater in an innovative biomass-assisted plant

With global communities being susceptible to adverse impacts of greenhouse gases, hydrogen has substantially drawn the attention of scientists to investigate it as a promising fuel. Hence, the present investigation aims to conduct an exhaustive thermodynamic analysis of an innovative biomass-assisted system driven by the Brayton cycle through multi-objective optimization to detect the different optimal scenarios for generating and storing hydrogen. This system contains a Brayton cycle as a prime mover, steam gasification of biomass and three-stage compressors to generate and store hydrogen, and multi-effect distillation to produce freshwater. The ultimate goal of this study is to use the generated steam through the produced freshwater as a steam agent of the gasifier to conclude a water-efficient scenario in producing hydrogen. To discern the impact of the chosen design parameters on the performance of the system, an exhaustive parametric study has been carried out. Afterward, multi-objective optimization via the non-dominated sorting genetic algorithm has been undertaken to find the optimal values by regarding the financial constraints. Tri-objective optimization results demonstrated that optimum values of total cost rate, exergy efficiency, and hydrogen production rate are 1.43 $/s, 47.56%. , and 0.12 kg/s. Besides, by regarding the consumption of water as an additional objective function, the results demonstrate that by reducing consumed water up to 47.5%, the generated hydrogen only decreases by 8%.

Use of the entropy approach in water resource monitoring systems

Effective management of water resources is possible only with an effectively organized monitoring system. After the emergence and development of information theory, the concept of information entropy found its place in the field of the development of water monitoring systems. The purpose of this work is to review research related to the construction of water monitoring systems and networks that applied the entropy theory in the design process. Methodology. Entropy terms used in the construction of water monitoring systems are summarized. Recent applications of the entropy concept for water monitoring system designs classified by precipitation are reviewed; flow and water level; water quality; soil moisture and groundwater. The integrated method of designing multifactorial monitoring systems is also highlighted. Results. The review analyzes studies and their implementation in the design of water monitoring networks based on entropy. The use of various methods of information theory and their adaptation for use in the design of monitoring networks is demonstrated, with the goal of network design methods being the selection of stations that provide the most information for the monitoring network, while being independent of each other. Through extensive testing, information theory has proven to be a reliable tool for evaluating and designing an optimal water monitoring network. Scientific novelty. This review focuses on studies that have applied information theory or information entropy to construct monitoring networks and systems. Information theory was developed by Shannon in the middle of the last century to measure the information content of a data set and was subsequently applied to solving water resources problems. To date, there are no review studies regarding the design of water monitoring networks based on the concept that entropy will be able to characterize the information specific to the monitoring station or monitoring networks. The main goal is to have the maximum amount of information. Practical significance. The optimal design of the monitoring network can be built based on the specified design criteria; however, the practical application of a new optimal monitoring network is rarely evaluated in a hydrological or other model. It is also important to identify the benefits of entropy-based network design to convince decision-makers of the importance of entropy-based approaches. The optimal network can be subjective, based on the choices made during the entropy calculation and the design method chosen, especially when additional objective functions are considered in the design. This applies to the method chosen to construct the optimal monitoring network, whether it is found using an iterative method where one station is added at a time, or a collection of stations that are added simultaneously. Research has also shown that data length, catchment scale, and the order can affect optimal network design. when using discrete entropy, it was shown that the binning method affects the final network design. Therefore, when selecting options based on the intended application of the monitoring network, a clear understanding and further research is needed to provide recommendations specific to water monitoring networks. In particular, more work is needed on the spatial and temporal scaling of the entropy calculation data to provide robust recommendations for decision-makers.

Timing of hydrologic anomalies direct impacts on migration traits in a flood pulse fishery system

Abstract Understanding adaptive reservoir management strategies that balance ecological outcomes with other objectives necessitates properly articulated environmental objectives. Aside from flood pulse extent related metrics, residual‐based descriptors provide robust descriptions of fish assemblage structure and harvest. We proposed a model framework based on spectral analysis of hydrologic variation and the Multivariate AutoRegressive State Space (MARSS) model to statistically quantify the effect sizes of hydrologic variation impacts on total fish catch and functional group (migration types) fish harvest and applied it to 17 years of fish harvest data from the Lower Mekong River Basin (LMB). Our findings suggest that duration and timing of hydrologic anomalies matter as much as their magnitude. Anomaly droughts coupled with strong pulse can benefit species if timed correctly. Longitudinal migrators were more sensitive to anomalous floods and droughts than other migratory species. Fish catch projections using effect sizes derived from historical data revealed that a well‐timed and protracted drought followed by a powerful flood pulse would be advantageous to the fishery, but a flood delay could negate such benefits. Synthesis and applications: We designed a spectral analysis framework to quantify hydrological variation and linked it with fishery harvest records. Quantified effect sizes of hydrologic anomalous events demonstrated one designed hydrograph for fishery benefits: properly timed prolong drought followed by a strong flood pulse. Our results add to a growing body of research that suggests ecological flows can be engineered. For most dams, the rule curve describing reservoir releases and resulting downstream hydrograph are designed in an ecological vacuum in which the objectives are to maximize human services—power production, flood control or navigation. Our work demonstrates that hydrograph can be designed to manage aspects of functional biodiversity directly. Though the exact shape of our hydrograph may not apply to other engineered river systems, we suggest that the approach can be applied generally, and globally both to developed and developing river basins. Specifically, a functional biodiversity rule curve could be optimized as an additional objective function in a multi‐objective optimization framework. Our methodology provides a quantitative method for deriving an ecological flow for this larger tradeoff analysis.

Twin SVM for conditional probability estimation in binary and multiclass classification

In this paper, we estimate the conditional probability function by presenting a new twin SVM model (CPTWSVM) in binary and multiclass classification problems. The motivation of CPTWSVM is to implement the empirical risk minimization on training data, which is hard to realize in traditional twin SVMs. In each subproblem of CPTWSVM, it measures the empirical risk and outputs the corresponding probability estimate of each class, which eliminates the problems of inconsistent measurement in twin SVMs. Though an additional discriminant objective function is introduced, the optimization problem size of each subproblem is smaller than conditional probability SVM, and is solved by block decomposition algorithm efficiently. In addition, we extend CPTWSVM to multiclass classification by estimating the conditional probability of each class, and maintaining the above properties. Numerical experiments on benchmark and real application datasets demonstrate that CPTWSVM outputs the estimate of probability and the data projection well, resulting in better generalization ability than some leading TWSVMs communities, in terms of binary and multiclass classification.

A constrained multi-objective evolutionary algorithm assisted by an additional objective function

In constrained multi-objective optimization, the degree of constraint violation as an additional objective function has been optimized together with the original M objective functions for better diversity. However, it still faces the challenge of deeply exploring feasible regions while maintaining the diversity of the population. To this end, this paper proposes a novel constrained multi-objective evolutionary algorithm assisted by an additional objective function, called CMAOO. First, the main population is constructed to optimize an (M+1)-objective optimization problem consisting of the original M objective functions and the degree of constraint violation. Additionally, all the feasible solutions are saved in an external archive. Then, the main population and the external archive are evolved to search the whole space and the feasible regions, respectively. After that, their offspring are combined to separately update the external archive and the main population. Experimental studies are conducted to test the performance of CMAOO with four state-of-the-art algorithms on 34 test problems and a real-world problem. The results demonstrate that CMAOO is competitive to solve constrained multi-objective optimization problems.

Generalized pigeon-inspired optimization algorithm for balancing exploration and exploitation

<p indent="0mm">A generalized pigeon-inspired optimization (GPIO) algorithm for balancing the exploration and exploitation abilities is proposed herein. The traditional pigeon-inspired optimization algorithm includes two operators, namely the map and compass operator and the landmark operator. These two operators are implemented only for one round at a single run. In the GPIO algorithm, the search process is divided into multiple stages, and two operators are implemented in each stage. These two operators are implemented for multiple rounds at one single run. The map and compass operator focuses on the exploration ability, while the landmark operator focuses on the exploitation ability. The GPIO algorithm changes the execution order of the two operators without additional objective function evaluation. Moreover, the structure of the solutions and the parameter settings are extended in the GPIO algorithm, which is beneficial to search quality improvement. The simulation results show that the GPIO algorithm improves the search efficiency and the search results of the algorithm.

Optimizing a complex multi-objective personnel scheduling problem jointly complying with requests from customers and staff

This paper deals with a complex multi-objective personnel scheduling problem motivated by a real case. A multi-objective mixed integer linear programming formulation of the problem is proposed. Constraints are classified into mandatory and optional. The work introduces a solution approach, dubbed PRIMP (Prioritize & Improve), that enforces constraint satisfaction by adopting additional objective functions. All the (given and additional) objective functions are lexicographically ordered. The method sequentially solves single-objective problems, according to their priority. Each problem is first processed by an exact solver; if no optimal solution is found within a given time limit, the problem is then addressed heuristically. The proposed multi-stage method is efficient (it takes just a few minutes to produce a daily schedule) and effective, compared both to the manual approach followed by the company and to the method that optimally tackles each single-objective problem by means of a competitive mixed-integer linear programming solver. Experimental results indicate that PRIMP can produce high quality schedules, where a larger number of optional constraints are satisfied and both the global idle time of employees and the waiting time of customers is reduced. The approach is modular and easily adaptable to manage different objective functions and/or constraints.

A Novel Whale Optimization Algorithm for the Design of Tuned Mass Dampers under Earthquake Excitations

This paper introduces a novel methodology for the optimum design of linear tuned mass dampers (TMDs) to improve the seismic safety of structures through a novel Whale Optimization Algorithm (WOA). The algorithm is aimed to reduce the maximum horizontal peak displacement of the structure, and the root mean square (RMS) response of displacements as well. Furthermore, four additional objective functions, derived from multiple weighted linear combinations of the two previously mentioned parameters, are also studied in order to obtain the most efficient TMD design configuration. The differential evolution method (DEM), whose effectiveness has been previously demonstrated for TMD applications, and an exhaustive search (ES) process, with precision to two decimal positions, are used to compare and validate the results computed through WOA. Then, the proposed methodology is applied to a 32-story case-study derived from an actual building, and multiple ground acceleration time histories are considered to assess its seismic performance in the linear-elastic range. The numerical results show that the proposed methodology based on WOA is effective in finding the optimal TMD design configuration under earthquake loads. Finally, practical design recommendations are provided for TMDs, and the robustness of the optimization is demonstrated.