Statistical Analysis of Computational Intelligence Algorithms on a Multi-Objective Filter Design Problem

Nsga Ii ◽

Multi Objective ◽

Optimal Parameter Estimation

This chapter presents the application of a comprehensive statistical analysis for both algorithmic performance comparison and optimal parameter estimation on a multi-objective digital signal processing problem. The problem of designing optimum digital finite impulse response (FIR) filters with the simultaneous approximation of the filter magnitude and phase is posed as a multi- objective optimization problem. Several computational-intelligence-based algorithms for solving this particular optimization problem are presented: genetic algorithms (GA), particle swarm optimization (PSO) and simulated annealing (SA) with multi-objective scalarization methods. Algorithms with Pareto sampling methods, namely non-dominated sorting genetic algorithm II (NSGA-II) and multi-objective simulated annealing (MOSA) are also applied as a way of dealing with multi-objective optimization. Instead of using a process of trial and error, a statistical exploratory analysis is used to estimate optimal parameters. A comprehensive statistical comparison of the applied algorithms is addressed, which indicates a particularly strong performance of NSGA-II and pure GA with weighting scalarization.

Hybrid QPSO-NNIA2 Algorithm for Multi-Objective Optimization Problem

International Journal of Pattern Recognition and Artificial Intelligence ◽

10.1142/s0218001419590250 ◽

2019 ◽

Vol 33 (08) ◽

pp. 1959025

Author(s):

Lan Zhang

Keyword(s):

Optimization Algorithm ◽

Optimization Problem ◽

Nearest Neighbor ◽

Superior Performance ◽

Optimal Solutions ◽

Nsga Ii ◽

Multi Objective ◽

Evolution Algebra ◽

Neighbor List

To improve the convergence and distribution of a multi-objective optimization algorithm, a hybrid multi-objective optimization algorithm, based on the quantum particle swarm optimization (QPSO) algorithm and adaptive ranks clone and neighbor list-based immune algorithm (NNIA2), is proposed. The contribution of this work is threefold. First, the vicinity distance was used instead of the crowding distance to update the archived optimal solutions in the QPSO algorithm. The archived optimal solutions are updated and maintained by using the dynamic vicinity distance based m-nearest neighbor list in the QPSO algorithm. Secondly, an adaptive dynamic threshold of unfitness function for constraint handling is introduced in the process. It is related to the evolution algebra and the feasible solution. Thirdly, a new metric called the distribution metric is proposed to depict the diversity and distribution of the Pareto optimal. In order to verify the validity and feasibility of the QPSO-NNIA2 algorithm, we compare it with the QPSO, NNIA2, NSGA-II, MOEA/D, and SPEA2 algorithms in solving unconstrained and constrained multi-objective problems. The simulation results show that the QPSO-NNIA2 algorithm achieves superior convergence and superior performance by three metrics compared to other algorithms.

Multi-objective optimization of retaining wall using genetic algorithm

Environmental engineering ◽

10.37023/ee.8.1-2.8 ◽

2021 ◽

Vol 8 (1-2) ◽

pp. 58-65

Author(s):

Filip Dodigović ◽

Krešo Ivandić ◽

Jasmin Jug ◽

Krešimir Agnezović

Keyword(s):

Genetic Algorithm ◽

Optimization Problem ◽

Retaining Wall ◽

Silty Sand ◽

Embedment Depth ◽

Nsga Ii ◽

Multi Objective ◽

Definition Of ◽

The Cost

The paper investigates the possibility of applying the genetic algorithm NSGA-II to optimize a reinforced concrete retaining wall embedded in saturated silty sand. Multi-objective constrained optimization was performed to minimize the cost, while maximizing the overdesign factors (ODF) against sliding, overturning, and soil bearing resistance. For a given change in ground elevation of 5.0 m, the width of the foundation and the embedment depth were optimized. Comparing the algorithm's performance in the cases of two-objective and three objective optimizations showed that the number of objectives significantly affects its convergence rate. It was also found that the verification of the wall against the sliding yields a lower ODF value than verifications against overturning and soil bearing capacity. Because of that, it is possible to exclude them from the definition of optimization problem. The application of the NSGA-II algorithm has been demonstrated to be an effective tool for determining the set of optimal retaining wall designs.

Advances in Chemical and Materials Engineering - Computational Approaches to Materials Design ◽

Multi-Objective Evolutionary Algorithms

10.4018/978-1-5225-0290-6.ch011 ◽

2016 ◽

pp. 301-345

Author(s):

A. K. Nandi ◽

K. Deb

Keyword(s):

Genetic Algorithm ◽

Evolutionary Algorithms ◽

Optimization Problem ◽

Performance Metrics ◽

Research Work ◽

Primary Objective ◽

Nsga Ii ◽

Mould Material ◽

The primary objective in designing appropriate particle reinforced polyurethane composite which will be used as a mould material in soft tooling process is to minimize the cycle time of soft tooling process by providing faster cooling rate during solidification of wax/plastic component. This chapter exemplifies an effective approach to design particle reinforced mould materials by solving the inherent multi-objective optimization problem associated with soft tooling process using evolutionary algorithms. In this chapter, first a brief introduction of multi-objective optimization problem with the key issues is presented. Then, after a short overview on the working procedure of genetic algorithm, a well- established multi-objective evolutionary algorithm, namely NSGA-II along with various performance metrics are described. The inherent multi-objective problem in soft tooling process is demonstrated and subsequently solved using an elitist non-dominated sorting genetic algorithm, NSGA-II. Multi-objective optimization results obtained using NSGA-II are analyzed statistically and validated with real industrial application. Finally the fundamental results of this approach are summarized and various perspectives to the industries along with scopes for future research work are pointed out.

An Adaptive Evolutionary Multi-Objective Approach Based on Simulated Annealing

Evolutionary Computation ◽

10.1162/evco_a_00038 ◽

2011 ◽

Vol 19 (4) ◽

pp. 561-595 ◽

Cited By ~ 112

Author(s):

H. Li ◽

D. Landa-Silva

Keyword(s):

Simulated Annealing ◽

Optimization Problem ◽

Weight Vector ◽

Metaheuristic Algorithms ◽

Search Performance ◽

Search Technique ◽

Multi Objective ◽

Initial Setting ◽

Single Objective

A multi-objective optimization problem can be solved by decomposing it into one or more single objective subproblems in some multi-objective metaheuristic algorithms. Each subproblem corresponds to one weighted aggregation function. For example, MOEA/D is an evolutionary multi-objective optimization (EMO) algorithm that attempts to optimize multiple subproblems simultaneously by evolving a population of solutions. However, the performance of MOEA/D highly depends on the initial setting and diversity of the weight vectors. In this paper, we present an improved version of MOEA/D, called EMOSA, which incorporates an advanced local search technique (simulated annealing) and adapts the search directions (weight vectors) corresponding to various subproblems. In EMOSA, the weight vector of each subproblem is adaptively modified at the lowest temperature in order to diversify the search toward the unexplored parts of the Pareto-optimal front. Our computational results show that EMOSA outperforms six other well established multi-objective metaheuristic algorithms on both the (constrained) multi-objective knapsack problem and the (unconstrained) multi-objective traveling salesman problem. Moreover, the effects of the main algorithmic components and parameter sensitivities on the search performance of EMOSA are experimentally investigated.

Multi-Objective Optimization of Internal Combustion Engine Valve Springs Based on NSGA-II

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.945-949.473 ◽

2014 ◽

Vol 945-949 ◽

pp. 473-477

Author(s):

You Jian Wang ◽

Guang Zhang

Keyword(s):

Genetic Algorithm ◽

Internal Combustion Engine ◽

Optimization Problem ◽

Combustion Engine ◽

Graphical Methods ◽

Design Quality ◽

Nsga Ii ◽

Engine Valve ◽

The design of engine valve spring generally belongs to multi-objective optimum design. The traditional trying means and the graphical methods are difficult to solve the multi-objective optimization problem, and the traditional multi-objective algorithms have certain defects. The elitist non-dominated sorting genetic algorithm (NSGA-II) is an excellent multi-objective algorithm, which is widely used to solve problems of multi-objective optimization. This method can improve the design quality and efficiency, and it has much more engineering practical value.

Multi-Objective Evolutionary Algorithms

Materials Science and Engineering ◽

10.4018/978-1-5225-1798-6.ch008 ◽

2017 ◽

pp. 185-229

Author(s):

A. K. Nandi ◽

K. Deb

Keyword(s):

Genetic Algorithm ◽

Evolutionary Algorithms ◽

Optimization Problem ◽

Performance Metrics ◽

Research Work ◽

Primary Objective ◽

Nsga Ii ◽

Mould Material ◽

Utilizing Multiple Objectives for the Optimization of the Pultrusion Process Based on a Thermo-Chemical Simulation

Key Engineering Materials ◽

10.4028/www.scientific.net/kem.554-557.2165 ◽

2013 ◽

Vol 554-557 ◽

pp. 2165-2174 ◽

Cited By ~ 17

Author(s):

Cem C. Tutum ◽

Ismet Baran ◽

Jesper Hattel

Keyword(s):

Optimization Problem ◽

Operating Conditions ◽

Die Design ◽

Process Efficiency ◽

Optimum Process ◽

Pareto Optimal ◽

Nsga Ii ◽

Pultrusion Process ◽

Pultrusion is one of the most effective manufacturing processes for producing composites with constant cross-sectional profiles. This obviously makes it more attractive for both researchers and practitioners to investigate the optimum process parameters, i.e. pulling speed, power and dimensions of the heating platens, length and width of the heating die, design of the resin injection chamber, etc., to provide better understanding of the process, consequently to improve the efficiency of the process as well the product quality. Numerous simulation approaches have been presented until now. However, optimization studies had been limited with either experimental cases or determining only one objective to improve one aspect of the performance of the process. This objective is either augmented by other process related criteria or subjected to constraints which might have had the same importance of being treated as objectives. In essence, these approaches convert a true multi-objective optimization problem (MOP) into a single-objective optimization problem (SOP). This transformation obviously results in only one optimum solution and it does not support the efforts to get more out of an optimization study, such as relations between variables and objectives or constraints. In this study, an MOP considering thermo-chemical aspects of the pultrusion process (e.g. cure degree, temperatures), in which the pulling speed is maximized and the heating power is minimized simultaneously (without defining any preference between them), has been formulated. An evolutionary multi-objective optimization (EMO) algorithm, non-dominated sorting genetic algorithm (NSGA-II [Deb et al., 2002]), has been used to solve this MOP in an ideal way where the outcome is the set of multiple solutions (i.e. Pareto-optimal solutions) and each solution is theoretically an optimal solution corresponding to a particular trade-off among objectives. Following the solution process, in other words obtaining the Pareto-optimal front, a further postprocessing study has been performed to unveil some common principles existing between the variables, the objectives and the constraints either along the whole front or in some portion of it. These relationships will reveal a design philosophy not only for the improvement of the process efficiency, but also a methodology to design a pultrusion die for different operating conditions.

An Entropy-Based Multiobjective Evolutionary Algorithm with an Enhanced Elite Mechanism

Applied Computational Intelligence and Soft Computing ◽

10.1155/2012/682372 ◽

2012 ◽

Vol 2012 ◽

pp. 1-11 ◽

Cited By ~ 5

Author(s):

Yufang Qin ◽

Junzhong Ji ◽

Chunnian Liu

Keyword(s):

Evolutionary Algorithm ◽

Pareto Front ◽

Optimization Problem ◽

State Of The Art ◽

Early Stage ◽

Test Problems ◽

Multiobjective Optimization Problem ◽

Nsga Ii ◽

Multiobjective optimization problem (MOP) is an important and challenging topic in the fields of industrial design and scientific research. Multi-objective evolutionary algorithm (MOEA) has proved to be one of the most efficient algorithms solving the multi-objective optimization. In this paper, we propose an entropy-based multi-objective evolutionary algorithm with an enhanced elite mechanism (E-MOEA), which improves the convergence and diversity of solution set in MOPs effectively. In this algorithm, an enhanced elite mechanism is applied to guide the direction of the evolution of the population. Specifically, it accelerates the population to approach the true Pareto front at the early stage of the evolution process. A strategy based on entropy is used to maintain the diversity of population when the population is near to the Pareto front. The proposed algorithm is executed on widely used test problems, and the simulated results show that the algorithm has better or comparative performances in convergence and diversity of solutions compared with two state-of-the-art evolutionary algorithms: NSGA-II, SPEA2 and the MOSADE.

Multi-Objective Optimization of Piezoelectric Actuator Placement for Shape Control of Plate Using Genetic Algorithms

Smart Materials, Adaptive Structures and Intelligent Systems, Volume 1 ◽

10.1115/smasis2008-343 ◽

2008 ◽

Author(s):

Rajesh Kudikala ◽

Deb Kalyanmoy ◽

Bishakh Bhattacharya

Keyword(s):

Shape Control ◽

Optimization Problem ◽

Piezoelectric Actuators ◽

Nsga Ii ◽

Multi Objective ◽

Input Control ◽

Wide Range ◽

Conflicting Objectives ◽

Lag Model

Shape control of adaptive structures using piezoelectric actuators has found a wide range of applications in recent years. In this paper, the problem of finding optimal distribution of piezoelectric actuators and corresponding actuation voltages for static shape control of a plate is formulated as a multi objective optimization problem. Two conflicting objectives: minimization of input control energy and minimization of mean square deviation between the desired and actuated shapes are considered with constraints on maximum number of actuators and maximum induced stresses. A shear lag model of the smart plate structure is created and the optimization problem is solved using an evolutionary multi-objective optimization (EMO) algorithm NSGA-II. Pareto-optimal solutions are obtained for different case studies. Further, the obtained solutions are verified by comparing with single-objective optimization solutions.

IDENTIFYING OCCUPANTS' APPROPRIATE SEATING POSITION AND VIEW DIRECTION IN OFFICE BUILDINGS: A STOCHASTIC SHADE CONTROL BASED MULTIOBJECTIVE VISUAL COMFORT OPTIMIZATION

Journal of Green Building ◽

10.3992/1943-4618.15.1.15 ◽

2020 ◽

Vol 15 (1) ◽

pp. 15-36

Author(s):

Jian Yao

Keyword(s):

Genetic Algorithm ◽

Statistical Analysis ◽

Behavior Model ◽

Visual Comfort ◽

Optimal Solutions ◽

Nsga Ii ◽

Multi Objective ◽

Office Rooms ◽

Seating Position

ABSTRACT Manually operated solar shades have a significant impact on indoor visual comfort. This research investigates occupants' appropriate seating position and view direction in a west-facing office cell using a previously developed shade behavior model. The non-dominant sorting genetic algorithm (NSGA-II) based Multi-objective optimization was adopted to identify the optimal and near optimal solutions. Daylight and glare index were used as two visual comfort objectives for optimization and robustness of optimization results against shade behavior uncertainty that was analyzed using statistical analysis. Results show that near optimal solutions can be used instead of the optimal one since they provide more flexibility in seating positions while maintaining almost the same visual comfort performance. And thus, the appropriate seating position considering occupants' preference is 1.5m away from the external window with two view directions near parallel to the window for west-facing office rooms.