Multi-objective Metaheuristics Research Articles

New techniques to improve neighborhood exploration in pareto local search

Pareto Local Search (PLS) is an extension of local search to multiobjective combinatorial optimization problems (MCOPs). It is widely used as a building block in many multiobjective metaheuristics. However, it suffers from poor anytime behavior and long convergence time. In this paper, we focus on improving the neighborhood exploration mechanism to accelerate PLS. In total, we propose three new search strategies, namely, Promising List, Don’t Look Bits and Continuing Search and implement them on the multiobjective Traveling Salesman Problem (mTSP) and the multiobjective Unconstrained Binary Quadratic Programming (mUBQP) problem. In Promising List, features of problem structure are utilized to guide the local search. In Don’t Look Bits, neighborhood moves that are less promising to produce improving solutions are skipped. In Continuing Search, the agent will start from where previous neighborhood exploration stops to avoid repetitive neighborhood moves. The experimental results verify the effectiveness of the three techniques both individually and collaboratively on most of the test instances. Besides, one proposed PLS variant outperforms two state-of-the-art PLS-based algorithms.

Radar placement optimization based on adaptive multi-objective meta-heuristics

Airspace surveillance is a significant issue for many countries to control and manage their airspace. The number of radars used and their coverage rate are the main issues to consider in this case. Therefore, this paper addresses the problem of finding the best radar locations to obtain the highest coverage rate with the least possible number of radars in a certain region. The radar placement problem is considered as a multi-objective optimization problem with two objectives: the number of radars and the coverage rate. To perfectly solve this optimization problem, a set of multi-objective meta-heuristic approaches based on simulated annealing, memory-based steady-state genetic algorithm, a decomposition-based multi-objective algorithm with differential evolution, and non-dominated sorting genetic algorithm (NSGA-II) are utilized. Algorithms are tested on a dataset created using DTED-1 map elevation data for two different selected regions. Based on the results, the NSGA-II algorithm achieves the best results and the highest coverage ratios among the tested algorithms. Two improved versions of the NSGA-II algorithm are also proposed to enhance its performance and make it more suitable for solving this optimization problem. The experimental results show that a coverage rate of 98% could be achieved with a small number of radars, and by increasing the number of radars, it exceeds 99%.

Multi-objective boxing match algorithm for multi-objective optimization problems

In the last two decades, due to having fast computation after inventing computers and also considering real-world optimization problems, research on developing new algorithms for problem having more than one objective have been one of the appealing and attractive topics both for academia and industrial practitioners. By this motivation, we introduce a Multi-Objective Boxing Match Algorithm (MOBMA) in this paper. The proposed algorithm studies the multi-objective version of the Boxing Match Algorithm (BMA) by incorporating a unique search strategy and new solutions-producing mechanism, enhancing the algorithm’s capability for exploration and exploitation phases. Besides, its performance is analyzed with famous and capable multi-objective metaheuristics. We consider ten multi-objective benchmarks and three classical engineering problems. Statistical analyses are also conducted on the benchmark test functions from three engineering design problems. This study shows the superior performance of the proposed algorithm, considering both quantitative and qualitative analyses.

Developing a numerical model for sediment transport in channel network by considering multigrade bed load sediment

ABSTRACT Predicting transport rates is difficult for the morphological features of marine, river, and coastal ecosystems. To design a model bed load sediment transport rate along with the surface layer, a mesh-based numerical method is used, and for the sediment transport the governing equations are employed and depth-averaged is used to create open channel flow and in three-dimensional horizontal space the evaluation is performed. By utilizing the governing equations, the open channel flow discretization and the numerical hydrodynamic model of sediment transport rate are calculated, and in the flow channel by using the solution method the settling velocity is determined. The complex issues involved nonlinear equations for the numerical modelling with solution methodology. The chicken swarm optimization algorithm is revealed by multi-objective metaheuristics optimization, and a better outcome is acquired by optimization. Finally, if polygonal mesh modelling is used in the diversion flow channel and curved bend channel, several experimental models were employed in the model experiments. A numerical measured and improved model is used to estimate the results in comparison, and the optimally developed model forecast rates with accuracy. In some open-channel flows such as reservoirs and rivers, the struggling flow and bed load sediment transport were dealt with in this model. Based on the results obtained, the proposed technique demonstrates significant improvements in both accuracy and prediction performance compared to the existing techniques. The proposed technique achieves an accuracy of 96.87%, outperforming the BCNN technique with an accuracy of 89.77% and the H-ANN-FA technique with an accuracy of 84.65%. Moreover, the proposed technique exhibits a lower RMSE value of 0.12, indicating a substantial reduction in the average deviation between predicted and observed values. Based on the NSE and R2 results, the proposed technique demonstrates remarkable improvements in prediction accuracy compared to the other techniques. The proposed technique achieves an NSE value of 0.998 and R2 value of 0.99, compared to the existing technique with an improvement of 46.47% and 11.24%.

Dynamic cyclic kitting part-feeding scheduling for mixed-model assembly line by a hybrid quantum-behaved particle swarm optimization

PurposeThe purpose of this paper is to cut down energy consumption and eliminate production waste on mixed-model assembly lines. Therefore, a supermarket integrated dynamic cyclic kitting system with the application of electric vehicles (EVs) is introduced. The system resorts to just-in-time (JIT) and segmented sub-line assignment strategies, with the objectives of minimizing line-side inventory and energy consumption.Design/methodology/approachHybrid opposition-based learning and variable neighborhood search (HOVMQPSO), a multi-objective meta-heuristics algorithm based on quantum particle swarm optimization is proposed, which hybridizes opposition-based learning methodology as well as a variable neighborhood search mechanism. Such algorithm extends the search space and is capable of obtaining more high-quality solutions.FindingsComputational experiments demonstrated the outstanding performance of HOVQMPSO in solving the proposed part-feeding problem over the two benchmark algorithms non-dominated sorting genetic algorithm-II and quantum-behaved multi-objective particle swarm optimization. Additionally, using modified real-life assembly data, case studies are carried out, which imply HOVQMPSO of having good stability and great competitiveness in scheduling problems.Research limitations/implicationsThe feeding problem is based on static settings in a stable manufacturing system with determined material requirements, without considering the occurrence of uncertain incidents. Current study contributes to assembly line feeding with EV assignment and could be modified to allow cooperation between EVs.Originality/valueThe dynamic cyclic kitting problem with sub-line assignment applying EVs and supermarkets is solved by an innovative HOVMQPSO, providing both novel part-feeding strategy and effective intelligent algorithm for industrial engineering.

MOCOVIDOA: a novel multi-objective coronavirus disease optimization algorithm for solving multi-objective optimization problems

A novel multi-objective Coronavirus disease optimization algorithm (MOCOVIDOA) is presented to solve global optimization problems with up to three objective functions. This algorithm used an archive to store non-dominated POSs during the optimization process. Then, a roulette wheel selection mechanism selects the effective archived solutions by simulating the frameshifting technique Coronavirus particles use for replication. We evaluated the efficiency by solving twenty-seven multi-objective (21 benchmarks & 6 real-world engineering design) problems, where the results are compared against five common multi-objective metaheuristics. The comparison uses six evaluation metrics, including IGD, GD, MS, SP, HV, and delta p (Delta mathrm{P}). The obtained results and the Wilcoxon rank-sum test show the superiority of this novel algorithm over the existing algorithms and reveal its applicability in solving multi-objective problems.

Simultaneous aerodynamic and structural optimisation of a low-speed horizontal-axis wind turbine blade using metaheuristic algorithms

AbstractThis work presents a concurrent design and multi-objective optimisation framework of horizontal axis wind turbine blades, made of composite material, for low wind speed. The optimisation model aims to minimise the structural mass of the blade whilst simultaneously maximising the turbine power output, subjected to three constraints viz. blade tip deflection, and Tsai-Hill and von Mises criteria. The design variables are blade shape and details of the internal blade structure. The control points and polynomial interpolation technique were adopted to determine the blade shape while the airfoil types at blade sections remained fixed. The internal blade structure design variables include the thickness of ribs and spars and the carbon fibre thickness and orientations. The blade element momentum approach is utilised to calculate turbine power and structural loads, whereas a finite element method is employed for structural analysis. Twelve multi-objective metaheuristics algorithms are used to solve the proposed multi-objective optimisation problem while their performance is investigated. The results obtained show that the multi-objective cuckoo search algorithm is the most efficient method. This study is said to be the baseline for a future study on multi-objective optimisation which combines two design stages of the composite low-speed wind turbine blades.

A New Multi-Heuristic Method to Optimize the Ammonia–Water Power/Cooling Cycle Combined with an HCCI Engine

Nowadays, sustainability is one of the key elements which should be considered in energy systems. Such systems are essential in any manufacturing system to supply the energy requirements of those systems. To optimize the energy consumption of any manufacturing system, various applications have been developed in the literature, with a number of pros and cons. In addition, in the majority of such applications, multi-objective optimization (MOO) plays an outstanding role. In related studies, the MOO strategy has been mainly used to maximize the performance and minimize the total cost of a trigeneration system with an HCCI (homogeneous charge compression ignition) engine as a prime mover based on the NSGA-II (non-dominated sorting genetic algorithm-II) algorithm. The current study introduces a novel multi-heuristic system (MHS) that serves as a metaheuristics cooperation platform for selecting the best design parameters. The MHS operates on a proposed strategy and prefers short runs of various metaheuristics to a single long run of a metaheuristic. The proposed MHS consists of four multi-objective metaheuristics collaborating to work on a common population of solutions. The optimization aims to maximize the exergy efficiency and minimize the total system cost. By utilizing four local archives and one global archive, the system optimizes these two objective functions. The idea behind the proposed MHS is that metaheuristics will be able to compensate for each other’s shortcomings in terms of extracting the most promising regions of the search space. Comparing the findings of the developed MHS shows that implementing the suggested strategy decreases the total unit costs of the system products to 25.85 USD/GJ, where the total unit cost of the base system was 28.89 USD/GJ, and the exergy efficiency of the system is increased up to 39.37%, while this efficiency was 22.81% in the base system. The finding illustrates significant improvements in system results and proves the high performance of the proposed method.

Single and Multi-objective Test Cases Prioritization for Self-driving Cars in Virtual Environments

Testing with simulation environments helps to identify critical failing scenarios for self-driving cars (SDCs). Simulation-based tests are safer than in-field operational tests and allow detecting software defects before deployment. However, these tests are very expensive and are too many to be run frequently within limited time constraints. In this article, we investigate test case prioritization techniques to increase the ability to detect SDC regression faults with virtual tests earlier. Our approach, called SDC-Prioritizer , prioritizes virtual tests for SDCs according to static features of the roads we designed to be used within the driving scenarios. These features can be collected without running the tests, which means that they do not require past execution results. We introduce two evolutionary approaches to prioritize the test cases using diversity metrics (black-box heuristics) computed on these static features. These two approaches, called SO-SDC-Prioritizer and MO-SDC-Prioritizer , use single-objective and multi-objective genetic algorithms ( GA ), respectively, to find trade-offs between executing the less expensive tests and the most diverse test cases earlier. Our empirical study conducted in the SDC domain shows that MO-SDC-Prioritizer significantly ( P - value <=0.1 e -10) improves the ability to detect safety-critical failures at the same level of execution time compared to baselines: random and greedy-based test case orderings. Besides, our study indicates that multi-objective meta-heuristics outperform single-objective approaches when prioritizing simulation-based tests for SDCs. MO-SDC-Prioritizer prioritizes test cases with a large improvement in fault detection while its overhead (up to 0.45% of the test execution cost) is negligible.

Parallel Multiobjective Multiverse Optimizer for Path Planning of Unmanned Aerial Vehicles in a Dynamic Environment with Moving Obstacles

Path planning with collision avoidance for unmanned aerial vehicles (UAVs) in environments with moving obstacles is a complex process of navigation, often considered a hard optimization problem. Ordinary resolution algorithms may fail to provide flyable and collision-free paths under the time-consumption constraints required by the dynamic 3D environment. In this paper, a new parallel multiobjective multiverse optimizer (PMOMVO) is proposed and successfully applied to deal with the increased computation time of the UAV path planning problem in dynamic 3D environments. Collision constraints with moving obstacles and narrow pass zones were established based on a mathematical characterization of any intersection with lines connecting two consecutive drones’ positions. For the implementation, a multicore central processing unit (CPU) architecture was proposed according to the concept of master–slave processing parallelization. Each subswarm of the entire PMOMVO population was granted to a corresponding slave, and representative solutions were selected and shared with the master core. Slaves sent their local Pareto fronts to the CPU core representing the master that merged the received set of nondominated solutions and built a global Pareto front. Demonstrative results and nonparametric ANOVA statistical analyses were carried out to show the effectiveness and superiority of the proposed PMOMVO algorithm compared to other homologous, multiobjective metaheuristics.

Multi-objective Metaheuristics with Intelligent Deep Learning Model for Pancreatic Tumor Diagnosis

Pancreatic tumor is the deadliest disease which needs earlier identification to reduce the mortality rate. With this motivation, this study introduces a Multi-Objective Metaheuristics with Intelligent Deep Learning Model for Pancreatic Tumor Diagnosis (MOM-IDL) model. The proposed MOM-IDL technique encompasses an adaptive Weiner filter based pre-processing technique to enhance the image quality and get rid of the noise. In addition, multi-level thresholding based segmentation using Kapur’s entropy is employed where the threshold values are optimally chosen by the barnacles mating optimizer (BMO). Besides, densely connected network (DenseNet-169) is employed as a feature extractor and fuzzy support vector machine (FSVM) is utilized as a classifier. For improving the classification performance, the BMO technique was implemented for fine-tuning the parameters of the FSVM model. The design of MOBMO algorithm for threshold selection and parameter optimization processes shows the novelty of the work. A wide range of simulations take place on the benchmark dataset and the experimental results highlighted the enhanced performance of the MOM-IDL technique over the recent state of art techniques.

Meta-Heuristics Optimization of Mirrors for Gravitational Wave Detectors: Cryogenic Case

In this paper, we explore the behavior of several optimization methods for reducing coating Brownian noise in the mirrors of gravitational wave detectors. We will refer to cryogenic operating temperatures, where the low refractive index material has mechanical losses higher than those of the high refractive index material. This situation is the exact opposite of that which occurs at room temperature, which is already widely known. The optimal design of the dielectric mirror (without a priori assumptions on thicknesses) can be obtained through the combined multi-objective optimization of transmittance and thermal noise. In the following, we apply several multi-objective meta-heuristics to compute the Pareto front related to the optimization problem of dielectric mirror thicknesses made of two materials (binary coatings). This approach gives us more certainty about the structure of the final result. We find strong evidence that all meta-heuristics converge to the same solution. The final result can be interpreted with simple physical considerations, providing useful rules to simplify the thicknesses of the optimization algorithm.

A multi-objective model for optimizing the redundancy allocation, component supplier selection, and reliable activities for multi-state systems

This paper presents a multi-objective availability-redundancy allocation optimization model for a hyper-system. The hyper-system consists of B systems with shared resources. The structure of the systems is series-parallel subsystems consisting of multi-failure and multi-state components. The components may be purchased from different suppliers based on their price and discounts. It is assumed that technical and organizational activities continuously affect the components' failure rates and the subsystems' working conditions before starting the system's mission horizon. The model aims to find the optimal number and the type of the subsystems' components for all systems from each supplier and the level of the technical and organizational activities. The problem is classified as an NP-hard class of problems; thus, four multi-objective meta-heuristics are adapted to solve the proposed model. These four meta-heuristics are non-dominated sorting genetic algorithm type II (NSGA-II) and type III (NSGA-III), non-dominated ranking genetic algorithm (NRGA), and multi-objective evolutionary algorithm based on decomposition (MOEA/D). The parameters of all algorithms are calibrated using response surface methodology. Moreover, a method based on a sequential combination of multi-objective evolutionary algorithms and data clustering is used on the Pareto solutions to yield a smaller and more manageable set of prospective solutions. The results showed the superiority of the NSGA-III and the MOEA/D algorithms to solve the presented model.

Exploring the Compositional Space of High-Entropy Alloys for Cost-Effective High-Temperature Applications

High-entropy alloys (HEAs) are nearly equimolar multi-principal element alloys, exhibiting exceptional thermal and mechanical properties at extreme conditions such as high-temperatures and stresses. Since the first discovery and early conceptualization of conventional HEAs nearly two decades ago, HEAs with far-from-equimolar compositions have attracted substantial interest to provide a broader range of material properties and to adjust price fluctuations and availability of commodities. Here, we present a first-principles investigation of non-equimolar chromium-manganese-iron-cobalt-nickel (CrMnFeCoNi) HEAs and effects of molybdenum (Mo) and niobium (Nb) substitutions on cost, phase stability and solubility, and mechanical and thermal performance up to 1000 K operational temperature. Virtual-crystal approximation is used to expediently approximate random solid solutions at the disordered mean-field limit. Using multi-objective metaheuristics built on a first-principles database, golden compositions are predicted for thermally well-insulated components and effective heat sinks. Replacing Co with Fe lowers commodity costs without hindering phase stability and solubility. Lower Ni concentration leads to lower thermal conductivity, indicating better thermal insulation, while reducing Mn concentration significantly increases the thermal conductivity, indicating better performing heat sinks. Moving away from equimolar ratios commonly increases the thermal expansion coefficient, which could generate higher thermal stresses. Nb and Mo substitution always lead to substantially higher commodity cost and density but with an increment in the mechanical performance due to solid-solution hardening. However, alloying with Mo and Nb is the only compositional space that reduces the thermal conductivity and thermal expansion coefficient.

Integrated optimization of transfer station selection and train timetables for road–rail intermodal transport network

In this study, we investigate the integrated optimization of container transfer station selection and train timetables for a road–rail intermodal transport network based on the transport organization mode of improved passenger-like container trains. The aim is to achieve a prompt response from train timetables for freight transportation needs to improve the quality of the timetable. The problem is formulated as a mixed-integer nonlinear programming problem, and a multiobjective bi-level optimization model is proposed with the objectives of increasing the average utilization ratio of the rail capacity and decreasing the number of road–rail transfer stations, transport costs, and transport delay penalty costs. To improve the quality of the Pareto solutions, a grid-based adaptive artificial bee colony (GBA-ABC) algorithm is designed to solve the model of a road–rail network with multicommodity flows. As a case study, the model is applied to the high-speed railway network in China and the China–Europe transcontinental railway network. The results show that the integrated optimization approach yields train timetables that can simultaneously reduce the transportation costs and the transportation delay penalty costs, with a rail capacity utilization rate of above 79.57%. Concurrently, it is beneficial for solving robust solutions under different case scales, demonstrating the effectiveness of the model and the algorithm. Finally, the proposed algorithm is experimentally compared with other multiobjective metaheuristics algorithms and is found to exhibit superior performance.

Trust Aware Multi-Objective Metaheuristic Optimization Based Secure Route Planning Technique for Cluster Based IIoT Environment

Industrial Internet of Things (IIoT) finds use in several industrial applications like robots, medical devices, and software-defined manufacturing processes. Apart from the promising benefits of the IIoT networks, several challenging issues need to be resolved, such as network connectivity, security, privacy, heterogeneity, scheduling, and energy efficiency. Due to the large-scale deployment and heterogeneity of the nodes in IIoT networks, some energy-limited nodes have existed in the IIoT networks, resulting in reduced network lifetime. At the same time, security and privacy are also considered as the major issues that exist in the design of IIoT, which can be addressed using secure routing techniques. In this view, this study develops a trust-aware multiobjective metaheuristic optimization-based secure clustering with route planning (TAMOMO-SCRP) technique for cluster-based IIoT environment. The presented TAMOMO-SCRP technique mainly focuses on the design of bald eagle search (BES) algorithm for clustering and routing processes. The proposed TAMOMO-SCRP model derives a fitness function for accomplishing maximum energy efficiency and security. For an effective clustering process, the TAMOMO-SCRP model designs an objective function involving four parameters such as trust level (TL), communication cost (CC), residual energy (RE), and node degree (ND). Besides, the route selection process is based on the fitness function with two variables, namely, queue length and link quality. For assessing the enhanced performance of the TAMOMO-SCRP model, a wide range of experiments were carried out to get the outcomes of network life time(NLT) as 39451,half network die (HND) as 25950 and Stability period (SP) 8000 time calculated no. of alive nodes. The achieved outcomes make sure the better performance of the TAMOMO-SCRP technique against the other recent approaches.

On the Sizing of CMOS Operational Amplifiers by Applying Many-Objective Optimization Algorithms

In CMOS integrated circuit (IC) design, operational amplifiers are one of the most useful active devices to enhance applications in analog signal processing, signal conditioning and so on. However, due to the CMOS technology downscaling, along the very large number of design variables and their trade-offs, it results difficult to reach target specifications without the application of optimization methods. For this reason, this work shows the advantages of performing many-objective optimization and this algorithm is compared to the well-known mono- and multi-objective metaheuristics, which have demonstrated their usefulness in sizing CMOS ICs. Three CMOS operational transconductance amplifiers are the case study in this work; they were sized by applying mono-, multi- and many-objective algorithms. The well-known non-dominated sorting genetic algorithm version 3 (NSGA-III) and the many-objective metaheuristic-based on the R2 indicator (MOMBI-II) were applied to size CMOS amplifiers and their sized solutions were compared to mono- and multi-objective algorithms. The CMOS amplifiers were optimized considering five targets, associated to a figure of merit (FoM), differential gain, power consumption, common-mode rejection ratio and total silicon area. The designs were performed using UMC 180 nm CMOS technology. To show the advantage of applying many-objective optimization algorithms to size CMOS amplifiers, the amplifier with the best performance was used to design a fractional-order integrator based on OTA-C filters. A variation analysis considering the process, the voltage and temperature (PVT) and a Monte Carlo analysis were performed to verify design robustness. Finally, the OTA-based fractional-order integrator was used to design a fractional-order chaotic oscillator, showing good agreement between numerical and SPICE simulations.

Outranking-based multi-objective PSO for scheduling unrelated parallel machines with a freight industry-oriented application

This paper presents Outranking-based Particle Swarm Optimisation (O-PSO) a novel metaheuristic to address the multi-objective Unrelated Parallel Machine Scheduling Problem. It is a particle swarm optimisation algorithm enriched with the preferences of the Decision Maker (DM), articulated in a fuzzy relational system based on ELECTRE III. Unlike other multi-objective metaheuristics, O-PSO searches for the Region of Interest (RoI) instead of approximating a sample of the complete Pareto frontier. The RoI is the subset consisting of those Pareto-efficient solutions that satisfy the outranking relations, that is, they are the best solutions in terms of the DM’s system of preferences. Therefore, O-PSO not only approximates the Pareto solutions but also supports multicriteria decision analysis of the schedules. The efficiency of O-PSO is validated on a benchmark of synthetic instances from the scientific literature, where the Wilcoxon rank-sum test provides statistical evidence that O-PSO offers high-quality solutions when compared with two state-of-the-art metaheuristics; specifically, O-PSO is capable of generating a greater proportion of solutions (on average, ranging from 7% to 14%) dominating those of the state-of-the-art algorithms, as well as finding more solutions (from 13% to 18%) that satisfy the DM’s preferences. O-PSO is also applied to a real-world case study in the transport industry to provide evidence for its applicability.

A Benchmark-Suite of real-World constrained multi-objective optimization problems and some baseline results

Generally, Synthetic Benchmark Problems (SBPs) are utilized to assess the performance of metaheuristics. However, these SBPs may include various unrealistic properties. As a consequence, performance assessment may lead to underestimation or overestimation. To address this issue, few benchmark suites containing real-world problems have been proposed for all kinds of metaheuristics except for Constrained Multi-objective Metaheuristics (CMOMs). To fill this gap, we develop a benchmark suite of Real-world Constrained Multi-objective Optimization Problems (RWCMOPs) for performance assessment of CMOMs. This benchmark suite includes 50 problems collected from various streams of research. We also present the baseline results of this benchmark suite by using state-of-the-art algorithms. Besides, for comparative analysis, a ranking scheme is also proposed.

Influence of the operating regimes of MOS transistors on the sizing and optimization of CMOS analog integrated Circuits

During the past few years the multi-objective metaheuristics have become the most skilled and fruitful algorithms that have gained a lot of popularity of analog designers. These algorithms have been implemented into an optimization-based design tool that can be used to size difficult and complex analog circuits. The optimization-based approach can be categorized into simulation-based, equation-based, or neural-network-based device sizing. In this paper, the simulation-based approach is used to generate the non-dominated set of points of the Pareto fronts. A particular interest is accorded to the multi-objective particle swarm optimization (MOPSO) algorithm as a priori the most adequate metaheuristic to apply in the field of analog circuit sizing. The performances of MOPSO compared to the non-dominated sorting genetic algorithm (NSGA-II) are evaluated for four analog circuits at different operating regimes of transistors such as weak inversion, linear and saturation region. Performance tests of the proposed method are conducted on these circuits in 0.18 μm CMOS technology. The results show that the proposed method can be useful for the optimal design of integrated circuits, to meet the challenge of automated design in the microelectronics domain.