Multi-Objective Optimization

In this paper, a Goal Programming (GP) model is converted into a multi-objective optimization problem (MOO) of minimizing deviations from fixed goals. To solve the resulting MOO problem, a hybrid metaheuristic with two steps is proposed to find the Pareto set's solutions. First, a Record-to-Record Travel with an adaptive memory is used to find first non-dominated Pareto frontier solutions preemptively. Second, a Variable Neighbour Search technique with three transformation types is used to intensify every non dominated solution found in the first Pareto frontier to produce the final Pareto frontier solutions. The efficiency of the proposed approach is demonstrated by solving two nonlinear GP test problems and three engineering design problems. In all problems, multiple solutions to the GP problem are found in one single simulation run. The results prove that the proposed algorithm is robust, fast and simply structured, and manages to find high-quality solutions in short computational times by efficiently alternating search diversification and intensification using very few user-defined parameters.

Genetic algorithm (GA) and differential evolution (DE) are metaheuristic algorithms that have shown a favorable performance in the optimization of complex problems. In recent years, only GA has been widely used for single-objective optimal design of reinforced concrete (RC) structures; however, it has been applied for multiobjective optimization of steel structures. In this article, the total structural cost and the roof displacement are considered as objective functions for the optimal design of the RC frames. Using the weighted sum method (WSM) approach, the two-objective optimization problem is converted to a single-objective optimization problem. The size of the beams and columns are considered as design variables, and the design requirements of the ACI-318 are employed as constraints. Five numerical models are studied to test the efficiency of the GA and DE algorithms. Pareto front curves are obtained for the building models using both algorithms. The detailed results show the accuracy and convergence speed of the algorithms.

Purpose -This is the first part of a two-part paper. The purpose of this paper is to report on methods that use the Response Surface Methodology (RSM) to investigate an Evolutionary Algorithm (EA) and memory-based approach referred to as McBAR -the Mapping of Task IDs for Centroid-Based Adaptation with Random Immigrants. Some of the methods are useful for investigating the performance (solution-search abilities) of techniques (comprised of McBAR and other selected EAbased techniques) for solving some multi-objective dynamic resource-constrained project scheduling problems with time-varying number of tasks. Design/methodology/approach -The RSM is applied to: determine some EA parameters of the techniques, develop models of the performance of each technique, legitimize some algorithmic components of McBAR, manifest the relative performance of McBAR over the other techniques and determine the resiliency of McBAR against changes in the environment. Findings -The results of applying the methods are explored in the second part of this work. Originality/value -The models are composite and characterize an EA memory-based technique. Further, the resiliency of techniques is determined by applying Lagrange optimization that involves the models.

This work presents the development of a proof-of-concept generative design tool for the AEC industry, named Aplysia. Aplysia has the capability to provide the designer with the ability to produce emergent design solutions from multiobjective criteria without the tradeoff between number of objectives and computational resources. The current inefficiencies with existing generative design tools are primarily due to the underlying algorithms, such as evolutionary algorithms which require significant computational resources due to large search spaces, and inconsistencies between industry requirements and provided features, such as requiring domain expert input to use these tools which make it inaccessible to many users. We present the novel use of a compositional pattern-producing network (CPPN) and the Neuro-Evolution of Augmenting Topologies (NEAT) algorithm for a building-scale structure. This paper details the software development methodology to build the tool, driven by a user-centric approach. Requirements gathering, which framed the scope of Aplysia, was completed through a use case study. The user and technical requirements were translated into a distributed system architecture and user-friendly GUI. Aplysia was experimentally tested for the design of a lightweight, freestanding canopy. Our initial findings show that Aplysia has the potential to improve the generative design workflow for the test case, which we argue is more adaptable to real-world AEC design problems and outline further improvements in the continual development of Aplysia.

MOFPA--Multi-objective flower pollination algorithm. This demo solves a bi-objective ZDT function of D=30 (dimensions), which can be extended to solve other multi-objective optimization problems. It is relatively straightforward to extend this code to solve other multi-objective functions and optimization problems. You can change the objective functions, dimensionality, various parameters, and simple lower and upper bounds (Lb, Ub).

X.-S. Yang, M. Karamanoglu, X.-S. He, Flower pollination algorithm: A novel approach for multiobjective optimization, Engineering Optimization, vol. 46, no. 9, 1222-1237 (2014).

[Notes: Though this demo should work well using either Matlab (preferred) or Octave (free), Matlab can run more smoothly, whereas Octave can be slower. In addition, for the multi-objective codes, Octave can be very slow for the test problem with 30 dimensions given in the demo codes, so please modify the relevant part of the codes to display results more frequently to show the progress. At the moment, the results are displayed every 100 iterations.]

Many problems having single or multiple objectives are routinely solved using GA methodologies. This paper is devoted to the simultaneous weight and deflection optimization of cantilever beam by using a modified Non-Dominated sorting Genetic Algorithm, subjected to maximum stress and maximum deflection constraints. The multi-objective optimization algorithm used in this paper has better sorting, incorporates elitism and no sharing parameter needs to be chosen a priori.

This paper presents an evolutionary based technique for solving the multi-objective based economic environmental dispatch by considering the stochastic behavior of renewable energy resources (RERs). The power system considered in this paper consists of wind and solar photovoltaic (PV) generators along with conventional thermal energy generators. The RERs are environmentally friendlier, but their intermittent nature affects the system operation. Therefore, the system operator should be aware of these operating conditions and schedule the power output from these resources accordingly. In this paper, the proposed EED problem is solved by considering the nonlinear characteristics of thermal generators, such as ramp rate, valve point loading (VPL), and prohibited operating zones (POZs) effects. The stochastic nature of RERs is handled by the probability distribution analysis. The aim of proposed optimization problem is to minimize operating cost and emission levels by satisfying various operational constraints. In this paper, the single objective optimization problems are solved by using particle swarm optimization (PSO) algorithm, and the multi-objective optimization problem is solved by using the multi-objective PSO algorithm. The feasibility of proposed approach is demonstrated on six generator power system.

In this paper, we focus on computing a consistent traffic signal configuration at each junction that optimizes multiple performance indices, i.e., multi-objective traffic signal control. The multi-objective function includes minimizing trip waiting time, total trip time, and junction waiting time. Moreover, the multi-objective function includes maximizing flow rate, satisfying green waves for platoons traveling in main roads, avoiding accidents especially in residential areas, and forcing vehicles to move within moderate speed range of minimum fuel consumption. In particular, we formulate our multi-objective traffic signal control as a Multi-Agent System (MAS). Traffic signal controllers have a distributed nature in which each traffic signal agent acts individually and possibly cooperatively in a MAS. In addition, agents act autonomously according to the current traffic situation without any human intervention. Thus, we develop a multi-agent multi-objective Reinforcement Learning (RL) traffic signal control framework that simulates the driver’s behavior (acceleration/deceleration) continuously in space and time dimensions. The proposed framework is based on a multi-objective sequential decision making process whose parameters are estimated based on the Bayesian interpretation of probability. Using this interpretation together with a novel adaptive cooperative exploration technique, the proposed traffic signal controller can make real-time adaptation in the sense that it responds effectively to the changing road dynamics. These road dynamics are simulated by the Green Light District (GLD) vehicle traffic simulator that is the testbed of our traffic signal control. We have implemented the Intelligent Driver Model (IDM) acceleration model in the GLD traffic simulator. The change in road conditions is modeled by varying the traffic demand probability distribution and adapting the IDM parameters to the adverse weather conditions. Under the congested and free traffic situations, the proposed multi-objective controller significantly outperforms the underlying single objective controller which only minimizes the trip waiting time (i.e., the total waiting time in the whole vehicle trip rather than at a specific junction). For instance, the average trip and waiting times are lower  8 and 6 times respectively when using the multi-objective controller.
Keywords:
adaptive optimization, multi-objective optimization, reinforcement learning, exploration, traffic signal control, cooperative multi-agent system

Environmentally conscious construction has become a subject of research during the last decades. Even though construction
literature involves plenty of studies that emphasize the importance of environmental impact during the construction phase, most of the
previous studies failed to combine environmental analysis with other project performance criteria in construction. To achieve environmentally
conscious construction and successfully manage a complex construction environment, multiple project objectives and their relationships need
to be considered. In this study, the authors propose a framework on the basis of the concept of control accounts to determine optimal construction
operations when project time, cost, and environment impact (TCEI) are considered as project objectives during project planning.
The framework also supports decision-making by using sensitivity analysis. Life cycle assessment is applied to the evaluation of environmental
impact in terms of global warming potential (GWP). The nondominated sorting genetic algorithm II, or NSGA-II, is selected for
implementation in MATLAB to determine optimal construction operations. A case study is used to illustrate the application of the framework.
It is shown by the case study that the application of the genetic algorithm to search problems, such as the case study, is promising in terms of
determining optimal solutions, but computation speed can be an issue, if it involves a large set of data. In addition, data collection and
processing is a major challenge, especially the processing of environmental impact data. Tools are needed to facilitate data collection
and processing. Currently, the proposed framework includes a critical path method, on the basis of fixed logical relationships among activities,
to determine the duration of a project. The effect of resource and other constraints on such logical relationships, and potentially the
duration of a project, is not addressed in this study. DOI: 10.1061/(ASCE)ME.1943-5479.0000098. © 2012 American Society of Civil
Engineers.

Production of marketed commodities and protection of biodiversity in natural systems often conflict and thus the continuously expanding human needs for more goods and benefits from global ecosystems urgently calls for strategies to resolve this conflict. In this paper, we addressed what is the potential of a forest landscape to simultaneously produce habitats for species and economic returns, and how the conflict between habitat availability and timber production varies among taxa. Secondly, we aimed at revealing an optimal combination of management regimes that maximizes habitat availability for given levels of economic returns. We used multi-objective optimization tools to analyze data from a boreal forest landscape consisting of about 30,000 forest stands simulated 50 years into future. We included seven alternative management regimes, spanning from the recommended intensive forest management regime to complete set-aside of stands (protection), and ten different taxa representing a wide variety of habitat associations and social values. Our results demonstrate it is possible to achieve large improvements in habitat availability with little loss in economic returns. In general, providing dead-wood associated species with more habitats tended to be more expensive than providing requirements for other species. No management regime alone maximized habitat availability for the species, and systematic use of any single management regime resulted in considerable reductions in economic returns. Compared with an optimal combination of management regimes, a consistent application of the recommended management regime would result in 5% reduction in economic returns and up to 270% reduction in habitat availability. Thus, for all taxa a combination of management regimes was required to achieve the optimum. Refraining from silvicultural thinnings on a proportion of stands should be considered as a cost-effective management in commercial forests to reconcile the conflict between economic returns and habitat required by species associated with dead-wood. In general, a viable
strategy to maintain biodiversity in production landscapes would be to diversify management regimes. Our results emphasize the importance of careful landscape level forest management planning because optimal combinations of management regimes were taxon-specific. For cost-efficiency, the results call for
balanced and correctly targeted strategies among habitat types.

Nowadays, considering the importance of the energy issue, it has become a major concern of economic topic. According to the energy balance sheet data, more than one third of the total energy consumption in Iran is consumed in the building sector. With regard to the massive waste of energy in the existing buildings, as well as the low efficiency of heating and cooling systems, seeking the right solution to reduce energy consumption in this sector is of utmost important. In this study, based on mathematical modeling, a solution has been presented to help us choose a proper combination of primary building materials and active or inactive air conditioning systems for residential buildings. It aimed to minimize both costs and thermal energy consumption of building materials. The proposed model has been utilized for a residential building in Tehran. Then, the optimal combinations of materials have been determined based on national building regulations (code 19).

The central nervous system uses stereotypical combinations of the three wrist/forearm joint angles to point in a given (2D) direction in space. In this paper, we first confirm and analyze this Donders’ law for the wrist as well as the distributions of the joint angles. We find that the quadratic surfaces fitting the experimental wrist configurations during pointing tasks are characterized by a subject-specific Koenderink shape index and by a bias due to the prono-supination angle distribution. We then introduce a simple postural model using only four parameters to explain these characteristics in a pointing task. The model specifies the redundancy of the pointing task by determining the one-dimensional task-equivalent manifold (TEM), parameterized via wrist torsion. For every pointing direction, the torsion is obtained by the concurrent minimization of an extrinsic cost, which guarantees minimal angle rotations (similar to Listing’s law for eye movements) and of an intrinsic cost, which penalizes wrist configurations away from comfortable postures. This allows simulating the sequence of wrist orientations to point at eight peripheral targets, from a central one, passing through intermediate points. The simulation first shows that in contrast to eye movements, which can be predicted by only considering the extrinsic cost (i.e., Listing’s law), both costs are necessary to account for the wrist/forearm experimental data. Second, fitting the synthetic Donders’ law from the simulated task with a quadratic surface yields similar fitting errors compared to experimental data.

In this paper, a metaheuristic optimizer, the multi-objective water cycle algorithm (MOWCA), is presented for solving constrained multi-objective problems. The MOWCA is based on emulation of the water cycle process in nature. In this study, a set of non-dominated solutions obtained by the proposed algorithm is kept in an archive to be used to display the exploratory capability of the MOWCA as compared to other efficient methods in the literature. Moreover, to make a comprehensive assessment about the robustness and efficiency of the proposed algorithm, the obtained optimization results are also compared with other widely used optimizers for constrained and engineering design problems. The comparisons are carried out using tabular, descriptive, and graphical presentations.

Paper regards a performance increase of an actual off-road (4x4) rally car (FIA–T1) through multiobjective optimization of damping characteristics of wheel suspensions in the car model with 7 degrees of freedom. Focus is put to find the dampers setup enabling for fast and comfortable passing over road unevennesses of a bump (“hopa”) and a wave type. The optimization problem is defined with up to 8 design variables, describing damping characteristics, and two contradictory objectives regarding car performance and driver comfort. Tuning possibilities of damper valve systems enabling changes of 1 to 4 settings are compared. The formulated optimization algorithm aids finding the best setup of rally car for a given road type and it reduces expensive road tests and trial&error methods.

with any form of information storage and retrieval, electronic adaptation, computer software, or by similar 10013, USA), except for brief excerpts in connection with reviews or scholarly analysis. Use in connection or dissimilar methodology now known or hereafter developed is forbidden. The use in this publication of trade names, trademarks, service marks, and similar terms, even if they are proprietary rights.

Paper presents an innovative method for finding the best setup of: race driver actions, vehicle motion trajectory, and vehicle chassis parameters for a closed-loop maneuver. Formulated " miMa " simulation model of driver-vehicle-road system with 26 generalized coordinates and more than 400 parameters is implemented for optimization with genetic algorithms. Numerical example considers Ford Focus ST170 (FWD) prepared for a track racing, which is negotiating a selected track part with RH corner. The combined optimization includes 28 decision variables. Two criteria, i.e. section time and exit velocity, are defined as optimization goals. Different strategies for improving performance of FWD car are found by using optimization.

This paper provides an in-depth review of the optimal design of type-1 and type-2 fuzzy inference systems (FIS) using five well known computational frameworks: genetic-fuzzy systems (GFS), neuro-fuzzy systems (NFS), hierarchical fuzzy systems (HFS), evolving fuzzy systems (EFS), and multiobjective fuzzy systems (MFS), which is in view that some of them are linked to each other. The heuristic design of GFS uses evolutionary algorithms for optimizing both Mamdani-type and Takagi-Sugano-Kang-type fuzzy systems; whereas, the NFS combines the FIS with neural network learning method to improve the approximation ability. HFS combines two or more low-dimensional fuzzy logic units in a hierarchical design to overcome the curse of dimensionality. EFS solves the data streaming issues by refining (evolving) the system incrementally, and MFS solves the multi-objective trade-offs like the simultaneous maximization of both interpretability and accuracy. The overall synthesis of these dimensions explores the FIS's potential challenges and opportunities ; the complex relations among the dimension; and the FIS's potential to combining one or more computational frameworks adding another dimension: deep fuzzy systems.

This work presents the development of a proof-of-concept generative design tool for the AEC industry, named Aplysia. Aplysia has the capability to provide the designer with the ability to produce emergent design solutions from multi-objective criteria without the tradeoff between number of objectives and computational resources. easily and rapidly produce varied, performanceoriented geometries suited for concept design. The current inefficiencies with existing generative design tools are primarily due to the underlying algorithms, such as evolutionary algorithms which require significant computational resources due to large search spaces, and inconsistencies between industry requirements and provided features, such as requiring domain expert input to use these tools which make it inaccessible to many users. We present the novel use of a compositional pattern-producing network (CPPN) and the Neuro-Evolution of Augmenting Topologies (NEAT) algorithm for a building-scale structure. This paper details the software development methodology to build the tool, driven by a user-centric approach. Requirements gathering, which framed the scope of Aplysia, was completed through a use case study. The user and technical requirements were translated into a modular system architecture and user-friendly GUI. Aplysia was experimentally tested for the design of a lightweight, free-standing canopy. Our initial findings show that Aplysia improves the generative design workflow for the test case, which we argue is more adaptable to real-world AEC design problems and outline further improvements in the continual development of Aplysia.

The multi objective optimization problems can be found in various fields such as finance, automobile design, aircraft design, path optimization etc. This paper reviews some of the existing literature on multi objective optimization problems and some of the existing Swarm Intelligence (SI) based techniques to solve these problems. The objective of this paper is to provide a starting point to the multi objective optimization problems to the reader.

This paper explores the concepts of multi-criteria optimization in architecture and discusses two different methodological approaches: goal-oriented tech-niques and methods based on computational morphogenesis. The aim of the paper is to propose potential directions for the development of multi-criteria optimization tools for architects. The applicability of both approaches and the role of architect as Decision Maker (DM) in the optimization processes are discussed. The conclusion summarizes that goal-oriented techniques, such as Evolutionary Multi-objective Optimization (EMO) Algorithms and hybrid meth-ods, are more likely to be successfully implemented in design tools. Non-goal oriented techniques, like Compositional Pattern Producing Networks (CPPNs) and Novelty Search, although recognized as harder for direct implementation, show enormous research potential. They are promising for evolving aestheti-cally pleasant objects, however further work is necessary to determine wheth-er they can contribute to the field of multi-objective optimization in architecture.

The traffic of vehicles in urban areas has many problems that include the increase of traffic congestion and psychological stress of drivers leading to high rate of accidents, considerable time losses, and high rate of vehicle emissions. Accordingly, those problems have a considerable negative effect on the country economy. One possible solution for the traffic problem which has a great impact in tackling those negative effects is using traffic signal control. Hence, in this thesis, we focus on computing a consistent traffic signal con- figuration at each junction that optimizes multiple performance indices, i.e., multi-objective traffic signal control. The multi-objective function includes minimizing trip waiting time, total trip time, and junction waiting time. More- over, the multi-objective function includes maximizing flow rate, satisfying green waves for platoons traveling in main roads, avoiding accidents especially in residential areas, and forcing vehicles to move within moderate speed range of minimum fuel consumption. In particular, we formulate our multi-objective traffic signal control as a Multi- Agent System (MAS). Traffic signal controllers have a distributed nature in which each traffic signal agent acts individually and possibly cooperatively in a MAS. In addition, agents act autonomously according to the current traffic situation without any human intervention. Thus, we develop a multi-agent multi-objective Reinforcement Learning (RL) traffic signal control framework that simulates the driver’s behavior (acceleration/deceleration) continuously in space and time dimensions. This framework has two main challenges; the formulation of the learning task as a multi-objective function and the application of this multi-objective learn- ing framework on continuous space-time models. Particularly, the proposed framework is based on a multi-objective sequential decision making process whose parameters are estimated based on the Bayesian interpretation of prob- ability. Using this interpretation together with a novel adaptive cooperative exploration technique, the proposed traffic signal controller can make real- time adaptation in the sense that it responds effectively to the changing road dynamics. These road dynamics are simulated by the Green Light District (GLD) vehicle traffic simulator that is the testbed of our traffic signal control. GLD is an open-source traffic simulator that facilitates the traffic signal control research by using customizable road networks. We have implemented the Intelligent Driver Model (IDM) acceleration model in the GLD traffic simulator. The change in road conditions is modeled by varying the traffic demand proba- bility distribution and adapting the IDM parameters to the adverse weather conditions. For better performance evaluation, we added new performance indices based on collaborative learning to the GLD traffic simulator. These performance indices are based on estimating the remaining time of vehicles till arriving to their destinations rather than depending only on the elapsed time in the whole trip of the arrived vehicles. Moreover, we added new performance indices, i.e., Measures Of Effectiveness (MOEs) to evaluate the various system objectives, e.g., average number of trip stops, average speed, percentage of arrived vehicles, percentage of rejected vehicles, maximum and average queue lengths, etc. Under the congested and free traffic situations, the proposed multi-objective controller significantly outperforms the underlying single objective controller which only minimizes the trip waiting time (i.e., the total waiting time in the whole vehicle trip rather than at a specific junction). For instance, the average trip and waiting times are lower 8 and 6 times respectively when using the multi-objective controller.

Cognitive ability predicts mathematics performance. However, there are other factors like study habits and psycho-sociological characteristics which also influence students’ performance. With these factors, this study aspires to obtain a structural model that best fit college mathematics performance. The study was conducted using descriptive - correlational method. Employing convenience sampling, a total of 278 second year to fourth year BSED students of the selected state colleges and universities in the Davao region were subjected to study. Descriptive statistics was used to determine the respondents’ cognitive ability level, psycho-sociological level, level of study habits, and college mathematics performance. The structural equation modeling (SEM) was then employed to test the structural model fit of the variables. Results show that the respondents have very satisfactory cognitive ability level based on high school GPA and college admission test. Their psycho-sociological and study habits levels were both slightly high. Their college mathematics performances were also in very satisfactory level. A structural equation model that best fit mathematics performance was determined. The latent variables - cognitive ability, psycho-sociological factors, and study habits have direct effects to the mathematics performance. It confirmed that college mathematics performance is not only influenced by cognitive ability but also by psycho-sociological characteristics and study habits of the students. It concludes that enhancing psycho-sociological characteristics and study habits of the students will also improve their college mathematics performance. For further research on mathematics performance, inclusion of other non-cognitive factors in the structural model is recommended.

Strategies, models, and algorithms facilitating such models are explored to provide transportation network managers and planners with more flexibility under uncertainty. Network design problems with non-stationary stochastic OD demand are formulated as real option investment problems and dynamic programming solution methodologies are used to obtain the value of flexibility to defer and re-design a network. The design premium is shown to reflect the opportunity cost of committing to a “preferred alternative” in transportation planning. Both network option and link option design problems are proposed with solution algorithms and tested on the classical Sioux Falls, SD network. Results indicate that allowing individual links to be deferred can have significant option value. A resource relocation model using non-stationary stochastic variables as chance constraints is proposed. The model is applied to air tanker relocation for initial attack of wildfires in California, and results show that the flexibility to switch locations with non-stationary stochastic variables providing 3-day or 7-day forecasts is more cost-effective than relocations without forecasting. Due to the computational costs of these more complex network models, a faster converging heuristic based on radial basis functions is evaluated for continuous network design problems for the Anaheim, CA network with a 31-dimensional decision variable. The algorithm is further modified and then proven to converge for multi-objective problems. Compared to other popular multi-objective solution algorithms in the literature such as the genetic algorithm, the proposed multi-objective radial basis function algorithm is shown to be most effective. The algorithm is applied to a flexible robust toll pricing problem, where toll pricing is proposed as a strategy to manage network robustness over multiple regimes of link capacity uncertainty. A link degradation simulation model is proposed that uses multivariate Bernoulli random variables to simulate correlated link failures. The solution to a multi-objective mean-variance toll pricing problem is obtained for the Sioux Falls network under low and high probability seasons, showing that the flexibility to adapt the Pareto set of toll solutions to changes in regime – e.g. hurricane seasons, security threat levels, etc – can increase value in terms of an epsilon indicator.

Traditionally, gas turbine has attracted the attention of many engineers due to having aerial applications. These turbines have complex non-linear systems and particular restrictions that affect the flight quality and security. Accordingly, the feedback control system approach was always challenging. One of these engines known as turbofan engine is used in airplanes in a remarkable manner as a result of its higher efficiency and low consumption of special fuel in comparison to others. Herein, we aimed at analyzing the function of designing and optimizing Min-Max control algorithm in controlling turbofan engine. Therefore, at first the modeling process was analyzed in a dynamic state and with employment of system identification method, an efficient dynamic model was designed. Accordingly, different dynamic models such as Narx were analyzed in both uni-modal and multi-modal conditions based on Anfis and Hammerstein-Wiener systems. Also, the most efficient method was identified in each phase. In this research, the researcher analyzed the application of Min-Max algorithm in controlling turbofan engine and used genetic algorithm to identify Min-Max control parameters and reduce fuel consumption. The transient response, produced pollutants, and functional controller parameters were optimized in this research. The researcher has analyzed both uni-objective and multi-objective optimization models. The results indicate that the designed controller can not only reduce fuel consumption and other mentioned parameters but also it can identify the restrictions of turbofan engine. This controller inhibits turbine inlet temperature overshoot, surge, and burnout phenomena.

Since asset returns have been recognized as not normally distributed, the avenue of research regarding portfolio higher moments soon emerged. To account for uncertainty and vagueness of portfolio returns as well as of higher moment risks, we proposed a new portfolio selection model employing fuzzy sets in this paper. A fuzzy multi-objective linear programming (MOLP) for portfolio optimization is formulated using marginal impacts of assets on portfolio higher moments, which are modelled by trapezoidal fuzzy numbers. Through a consistent centroid-based ranking of fuzzy numbers, the fuzzy MOLP is transformed into an MOLP that is then solved by the maximin method. By taking portfolio higher moments into account, the approach enables investors to optimize not only the normal risk (variance) but also the asymmetric risk (skewness) and the risk of fat-tails (kurtosis). An illustrative example demonstrates the efficiency of the proposed methodology comparing to previous portfolio optimization models.

This presentation explains the fundamental ideas of the standard Flower Pollination Algorithm (FPA), which also contains the links to the free Matlab codes at Mathswork file exchanges and the animations of numerical simulations (video at Youtube). An example of multi-objective flower pollination algorithm (MOPFA) is also given with link to the Matlab code.

This paper considers a single machine scheduling problem, with the objective of minimizing a linear combination of total tardiness and waiting time variance in which the idle time is not allowed. Minimizing total tardiness is always regarded as one of the most significant performance criteria in practical systems to avoid penalty costs of tardiness, and waiting time variance is an important criterion in establishing quality of service (QoS) in many systems. Each of these criteria is known to be non-deterministic polynomial-time hard (NP-hard); therefore, the linear combination of them is NP-hard too. For this problem, we developed a genetic algorithm (GA) by applying its general structure that further improves the initial population, utilizing some of heuristic algorithms. The GA is shown experimentally to perform well by testing on various instances.

The multiobjective firefly algorithm (MOFA) is a nature-inspired optimization algorithm. This demo solves the bi-objective ZDT3 functions with D=30 (dimensions), and the obtained Pareto Front is displayed. It is relatively straightforward to extend this code to solve other multi-objective functions and optimization problems. You can change the objective functions, the dimensionality, and simple lower and upper bounds (Lb, Ub). Some parameter tuning to vary parameters slightly (such as theta, gamma, and number of iterations) may help improve the quality of the solutions.

Yang, Xin-She. “Multiobjective Firefly Algorithm for Continuous Optimization.” Engineering with Computers, vol. 29, no. 2, Springer Science and Business Media LLC, Jan. 2012, pp. 175–84, doi:10.1007/s00366-012-0254-1.


[Notes: Though this demo should work well using either Matlab (preferred) or Octave (free), Matlab can run more smoothly, whereas Octave can be slower. In addition, for the multi-objective codes, Octave can be very slow for the test problem with 30 dimensions given in the demo codes, so please modify the relevant part of the codes to display results more frequently to show the progress. At the moment, the results are displayed every 100 iterations.]

A two-stage optimization method is proposed for optimal distributed generation (DG) planning considering the integration of energy storage in this paper. The first stage determines the installation locations and the initial capacity of DGs using the well-known loss sensitivity factor (LSF) approach, and the second stage identifies the optimal installation capacities of DGs to maximize the investment benefits and system voltage stability and to minimize line losses. In the second stage, the multi-objective ant lion optimizer (MOALO) is first applied to obtain the Pareto-optimal solutions, and then the 'best' compromise solution is identified by calculating the priority memberships of each solution via grey relation projection (GRP) method, while finally, in order to address the uncertain outputs of DGs, energy storage devices are installed whose maximum outputs are determined with the use of chance-constrained programming. The test results on the PG&E 69-bus distribution system demonstrate that the proposed method is superior to other current state-of-the-art approaches, and that the integration of energy storage makes the DGs operate at their pre-designed rated capacities with the probability of at least 60% which is novel. Index Terms-active distribution network; distributed generation planning; two-stage optimization; energy storage; chance-constrained programming; multi-objective ant lion optimizer. Nomenclature αi loss sensitivity factor of real power loss at the ith bus PL total system active power losses; QL total system reactive power losses;

Combining simulation models and multi-objective optimization can help solving complex land use allocation problems by considering multiple, often competing demands on landscapes, such as agriculture, (drinking) water provision, or biodiversity conservation. The search for optimal land use allocations has to result in feasible solutions satisfying "real-world" constraints. We here introduce a generic and readily applicable tool to integrate user-specific spatial models (e.g. assessing different ecosystem services) for a Constrained Multi-objective Optimization of Land use Allocation (CoMOLA). The tool can handle basic land use conversion constraints by either a newly and specifically developed method to repair infeasible solutions or by penalizing constraint violation. CoMOLA was systematically tested for different levels of complexity using a virtual landscape and simple ecosystem service and biodiversity models. Our study shows that using repair mechanisms seems to be more effective in exploring the feasible solution space while penalizing constraint violation likely results in infeasible solutions.

The inclusion of expert knowledge in data-driven streamflow modeling is expected to yield better performances in modeling and more reliable estimates of river quantities. Modular techniques designed to work on different flow regimes and hydrological conditions are preferred ways to incorporate such hydrological knowledge in data-driven models. Previous studies have suggested that more accurate prediction of total streamflow could be achieved through modular Artificial Neural Networks (ANN) trained to perform an implicit baseflow separation. These models fit separately the baseflow (BF) and excess flow (EF) components as obtained by a digital filter, and reconstruct the total flow (TF) by adding these two signals at the output. The optimization of the filter parameters and ANN architectures is carried out through global search techniques that minimize a weighted function of the errors of the TF, BF, and EF components. Despite the favorable premises, the real effectiveness of these modular models (MM) has been tested only on a few case studies, and the quality of the baseflow separation performed by this technique has never been thoroughly assessed. In this study, we compare the performance of MM against global models (GM) for nine different gaging stations in the northern United States. Binary-coded swarm optimization is employed for the identification of filter parameters and model structure, while Extreme Learning Machines (ELM), instead of ANN, are used to drastically reduce the large computational times required to perform the experiments. The results show that there is no evidence that MMs outperform global GMs for predicting the TF. In addition, the baseflow produced by the MM largely underestimates the actual baseflow component expected for most of the considered gages. This occurs because the values of the filter parameters maximizing overall accuracy do not reflect the geological characteristics of the river basins. The results indeed show that setting the filter parameters according to expert knowledge results in accurate baseflow separation but lower accuracy of TF predictions, suggesting that these two objectives are intrinsically conflicting rather than compatible.

Keywords: rainfall-runoff; baseflow separation; extreme learning machine; multi-objective optimization; particle swarm optimization; modular neural network

Multi-objective optimization of power converters is a time-consuming task, especially when multiple operating points and multiple converter topologies must be considered. As a result, various steps are often taken to simplify the design problem and restrict the size of the design space prior to going through an optimization procedure. While this saves time, it produces potentially sub-optimal designs, and existing approaches must trade-off between running time and design optimality. This paper presents an optimization-oriented method for modeling power converters and their components as posynomial functions, allowing multi-objective optimization of converters to be formulated as a geometric program, a type of convex optimization problem. This allows the use of fast, powerful solvers that guarantee global optimality of solutions. The method is demonstrated using the example of low-power multi-level flying capacitor step-down converters. Results show that, using geometric programming, sets of globally Pareto-optimal designs of 2-, 3-, and 4-level converters with respect to efficiency and power density, for one design space and one operating point, can be generated in as little as 25 seconds, on an mid-to upper-range laptop computer. Thus optimal designs for three different converter topologies for hundreds of different operating points and/or design spaces can be generated in several hours-less than the time required to globally optimize one converter topology at one operating point for one design space using currently prevalent methods. The paper also demonstrates how geometric programming can be used to quickly perform sensitivity and trade-off analysis of optimal converter designs.

Planning requirements in terms of energy efficiency and daylighting strongly contribute to shaping the layout of cities. Direct solar access is the main requirement of the right to light in Estonia. Direct sunlight hours on building facades can be calculated by using environmental simulation software that also allows right-to-light analysis through the generation of the Solar Envelope. It is a method for calculating the maximum buildable volume that allows neighbors to receive the required amount of direct sunlight in a specific period of the year. The Solar Envelope can be determined on paper or more easily using simulations. The methods used by actual environmental software have significant limitations if used in complex urban environments. This paper discusses the potentialities of multi-objective optimization tools to generate Solar Envelopes for multiple facades with different orientations and specific amount of direct solar access requirements. The results show the superiority of the developed method that integrates parametric design, environmental simulations and multi-objective optimization, compared to existing methods.

Selecting an adequate set of inputs is a critical step for successful data-driven streamflow prediction. In this study, we present a novel approach for Input Variable Selection (IVS) that employs Binary-coded discrete Fully Informed Particle Swarm optimization (BFIPS) and Extreme Learning Machines (ELM) to develop fast and accurate IVS algorithms. A scheme is employed to encode the subset of selected inputs and ELM specifications into the binary particles, which are evolved using single objective and multi-objective BFIPS optimization (MBFIPS). The performances of these ELM-based methods are assessed using the evaluation criteria and the datasets included in the comprehensive IVS evaluation framework proposed by Galelli et al. (2014). From a comparison with 4 major IVS techniques used in their original study it emerges that the proposed methods compare very well in terms of selection accuracy. The best performers were found to be 1) a MBFIPS-ELM algorithm based on the concurrent minimization of an error function and the number of selected inputs, and 2) a BFIPS-ELM algorithm based on the minimization of a variant of the Akaike Information Criterion (AIC). The first technique is arguably the most accurate overall, and is able to reach an almost perfect specification of the optimal input subset for a partially synthetic rainfall-runoff experiment devised for the Kentucky River basin. In addition, MBFIPS-ELM allows for the determination of the relative importance of the selected inputs.  On the other hand, the BFIPS-ELM is found to consistently reach high accuracy scores while being considerably faster. By extrapolating the results obtained on the IVS test-bed, it can be concluded that the proposed techniques are particularly suited for rainfall-runoff modeling applications characterized by high nonlinearity in the catchment dynamics.

Keywords: input variable selection; streamflow prediction; rainfall-runoff; particle swarm optimization; multi-objective optimization; extreme learning machines

The project is a real-world case study where we advised our client in the selection of a viable and well-performing design from a set of computationally generated options. This process was undertaken while validating the algorithmic generative process and user-defined evaluation criteria through scrutinizing the other alternative options to ensure ample variability was considered. Optimisation algorithms were not ideal as low performing options were not visible to validate variability. We established variability by extracting the different groups of options, proving to the client that various operational behaviours were present and accounted for. In order to sieve through the noise and derive meaningful results, we employed methods to filter through thousands of options, including: k-means clustering, archetypal labelling and analysis, pareto front analysis and visualisation overlays. We present a sense-making and decision-making process that utilizes principles of genetic algorithms and analysis of multi-dimensional user-derived evaluation scores. To enable the client's confidence in the computational model, we proved the effectiveness of the generative model through communicating and visualizing the impact of different criterias. This ensured that operational needs were considered. The visualization methods we employed, including pareto front extraction and analysis eventually helped our clients to arrive at a decision.

I submit that epistemic progress in key areas of contemporary academic philosophy has been compromised by politically correct (" PC ") ideology. First, guided by an evolutionary account of ideology, results from social and cognitive psychology and formal philosophical methods, I expose evidence for political bias in contemporary Western academia and sketch a formalization for the contents of beliefs from the PC worldview taken to be of core importance, the theory of social oppression and the thesis of anthropological mental egalitarianism. Then, aided by discussions from contemporary epistemology on epistemic values, I model the problem of epistemic appraisal using the frameworks of multi-objective optimization theory and multi-criteria decision analysis and apply it to politically correct philosophy. I conclude that philosophy guided by politically correct values is bound to produce constructs that are less truth-conducive and that spurious values which are ideologically motivated should be abandoned. Objections to my framework stemming from contextual empiricism, the feminine voice in ethics and political philosophy are considered. I conclude by prescribing the epistemic value of empirical adequacy, the contextual value of political diversity and the moral virtue of moral courage to reverse unwarranted trends in academic philosophy due to PC ideology.

• The strength of linear programming is that it allows decision makers to allocate scarce resources to the organizations. A difficult task in employing linear programming is quantifying the trade-off between multiple incompatible and incommensurable objectives; however, more powerful techniques for dealing with this problem are evolving. The composite single-objective approach is useful if the decision maker has sufficient experience to be able to specify accurately a priori weights to each objective. The preemptive ordering approach is considered inferior to other methods because: 1. it ignores potential trade-offs between objectives and potential combination alternatives, and 2. it may result in satisficing rather than optimizing choices. When objective weights cannot be specified a priori, the efficient multiple objective solution approach should be used because it yields all possible efficient solutions given the objectives and the trade-offs between them. activities that optimize the benefits to their

Electric discharge machining (EDM) has verified to be an alternate approach for machining complex and critical shapes on
workpiece. In this work described EDM of AISI P20 tool steel in which best process environment (optimal) has been determined
to satisfy efficiency of graphite electrode material. Multi objective optimization of various EDM parameters for obtaining
favorable preference measures in surface integrity (surface crack density, white layer thickness and surface roughness) using
PCA based grey relational analysis has been selected.