Single-objective Optimization Algorithms Research Articles

A multi-objective problem based on fuzzy inference with application to parametric design of an electrophotographic system

This paper proposes a systematic approach to conduct system-level optimal parametric design for a class of electrophotographic systems. A conventional monochrome laser printer serves as the platform for verification of the proposed optimal design approach. Besides performance, we incorporate two other practical indices, i.e., cost and energy consumption, into design objectives and formulate a multi-objective optimization problem. A fuzzy inference system is established to provide the nonlinear or linguistic mapping between the decision variables and the design objectives. For comparative purpose, the problem is solved using both single-objective and multi-objective optimization algorithms. Note that the proposed approach is also applicable to other complex systems.

Optimization of a solar powered absorption cycle under Abu Dhabi’s weather conditions

In order for the solar absorption air conditioners to become a real alternative to the conventional vapour compression systems, their performance has to be improved and their total cost has to be reduced. A solar powered absorption cycle is modeled using the Transient System Simulation (TRNSYS) program and Typical Meteorological Year 2 data of Abu Dhabi. It uses evacuated tube collectors to drive a 10 kW ammonia–water absorption chiller. Firstly, the system performance and its total cost are optimized separately using single objective optimization algorithms. The design variables considered are: the collector slope, the collector mass flow rate, the collector area and the storage tank volume. The single objective optimization results show that MATLAB global optimization methods agree with the TRNSYS optimizer. Secondly, MATLAB is used to solve a multi-objective optimization problem to improve the system’s performance and cost, simultaneously. The optimum designs are presented using Pareto curve and show the potential improvements of the baseline system.

A Fast Algorithm for Finding the non Dominated Set in Multiobjective Optimization

INTRODUCTION: The working of single objective optimization algorithm and multi objective optimization algorithm is quite different. This difference is due to number of optimal solution approached by both the algorithms. In single objective optimization problem there will be a single optimal solution, even though in multi model optimization there may be more than one solution but we are interested in only one optimal solution, where as in multi objective optimization problem, there will be many set of optimal solutions. These sets are called different non dominated front, and every non dominated front will contain a set of non dominated solutions thus there are two tasks of an ideal multi objective optimization algorithm (i) To find multiple non dominated fronts (or to identify different set of non dominated solutions). (ii) To seek for Pareto optimal solutions with a good diversity in objective and decision variable values. In this paper, we explain a new algorithm for finding non dominated set of a multi objective optimization problem. In literature many algorithms are used for this task like naive and slow method [2], fast and efficient method [3] and Kung et al method [7]. Recently two new algorithms are proposed by Ding [4] and Jun Du[1].The worst case time complexity of all algorithm(including recently proposed algorithm) is (OM(N)),Previously Kung’s algorithm was best in its average and best case time complexity but Jun du in 2007 proved that his algorithm is best in comparison of kung’s algorithm. While we were unable to reduce worst case time complexity, The best case time complexity of proposed algorithm is O(NLog(N))( for any number of objective functions )which is a improvement as compared to othere algorithms. Also it follows a simple approach, no hectic summation and production method. The paper is organized into four sections. Section 2 presents some background detail of Different Preexisting Algorithms and specifies the necessary definition related to non dominated set. Section 3 describes the proposed approach and stepwise algorithm also difference between Kung’s algorithm and proposed algorithm is presented; In Section 4, an experimental analysis and complexity of the proposed algorithm are presented. Finally, Section 5 concludes the paper.

A nature-inspired multi-objective optimisation strategy based on a new reduced space searching algorithm for the design of alloy steels

In this paper, a salient search and optimisation algorithm based on a new reduced space searching strategy, is presented. This algorithm originates from an idea which relates to a simple experience when humans search for an optimal solution to a ‘real-life’ problem, i.e. when humans search for a candidate solution given a certain objective, a large area tends to be scanned first; should one succeed in finding clues in relation to the predefined objective, then the search space is greatly reduced for a more detailed search. Furthermore, this new algorithm is extended to the multi-objective optimisation case. Simulation results of optimising some challenging benchmark problems suggest that both the proposed single-objective and multi-objective optimisation algorithms outperform some of the other well-known Evolutionary Algorithms (EAs). The proposed algorithms are further applied successfully to the optimal design problem of alloy steels, which aims at determining the optimal heat treatment regime and the required weight percentages for chemical composites to obtain the desired mechanical properties of steel hence minimising production costs and achieving the overarching aim of ‘right-first-time production’ of metals.

DESIGN OF TIME-MODULATED LINEAR ARRAYS WITH A MULTI-OBJECTIVE OPTIMIZATION APPROACH

This article proposes a Multi-objective Optimization (MO) framework for the design of time-modulated linear antenna arrays with ultra low maximum Side Lobe Level (SLL), maximum Side Band Level (SBL) and main lobe Beam Width between the First Nulls (BWFN). In contrast to the existing optimization-based methods that attempt to minimize a weighted sum of SLL, SBL, and BWFN, we treat these as three distinct objectives that are to be achieved simultaneously and use one of the best known Multi- Objective Evolutionary Algorithms (MOEAs) of current interest called MOEA/D-DE (Decomposition based MOEA with Difierential Evolution operator) to determine the best compromise among these three objectives. Unlike the single-objective approaches, the MO approach provides greater ∞exibility in the design by yielding a set of equivalent flnal solutions from which the user can choose one that attains a suitable trade-ofi margin as per requirements. We compared time-modulated antenna structures with other methods for linear array synthesis such as the excitation method and the phase-position synthesis method on the basis of the approximated Pareto Fronts (PFs) yielded by MOEA/D-DE and the best compromise solutions determined from the Pareto optimal set with a fuzzy membership- function based method. The flnal results obtained with MOEA/D-DE were compared with the results achieved by two state-of-the-art single objective optimization algorithms and flve other MO algorithms. Our simulation studies on three instantiations of the design problem re∞ect the superiority of the MOEA/D-DE based design of time-modulated linear arrays.

Find the 'Best' Solution from Multiple Analog Topologies via Pareto-Optimality

This paper presents a novel method using multi-objective optimization algorithm to automatically find the best solution from a topology library of analog circuits. Firstly this method abstracts the Pareto-front of each topology in the library by SPICE simulation. Then, the Pareto-front of the topology library is abstracted from the individual Pareto-fronts of topologies in the library followed by the theorem we proved. The best solution which is defined as the nearest point to specification on the Pareto-front of the topology library is then calculated by the equations derived from collinearity theorem. After the local searching using Nelder-Mead method maps the calculated best solution backs to design variable space, the non-dominated best solution is obtained. Comparing to the traditional optimization methods using single-objective optimization algorithms, this work can efficiently find the best non-dominated solution from multiple topologies for different specifications without additional time-consuming optimizing iterations. The experiments demonstrate that this method is feasible and practical in actual analog designs especially for uncertain or variant multi-dimensional specifications.

Covariance Matrix Adaptation for Multi-objective Optimization

The covariance matrix adaptation evolution strategy (CMA-ES) is one of the most powerful evolutionary algorithms for real-valued single-objective optimization. In this paper, we develop a variant of the CMA-ES for multi-objective optimization (MOO). We first introduce a single-objective, elitist CMA-ES using plus-selection and step size control based on a success rule. This algorithm is compared to the standard CMA-ES. The elitist CMA-ES turns out to be slightly faster on unimodal functions, but is more prone to getting stuck in sub-optimal local minima. In the new multi-objective CMAES (MO-CMA-ES) a population of individuals that adapt their search strategy as in the elitist CMA-ES is maintained. These are subject to multi-objective selection. The selection is based on non-dominated sorting using either the crowding-distance or the contributing hypervolume as second sorting criterion. Both the elitist single-objective CMA-ES and the MO-CMA-ES inherit important invariance properties, in particular invariance against rotation of the search space, from the original CMA-ES. The benefits of the new MO-CMA-ES in comparison to the well-known NSGA-II and to NSDE, a multi-objective differential evolution algorithm, are experimentally shown.

Multi-objective particle swarm optimization by fuzzy-pareto-dominance meta-heuristic

This paper introduces a new approach to multi-objective Particle Swarm Optimization (PSO). The approach is based on the recently proposed Fuzzy-Pareto-Dominance (FPD) relation. FPD is a generic ranking scheme, where ranking values are mapped to element vectors of a set. These ranking values are directly computed from the element vectors of the set and can be used to perform rank operations (e.g. selecting the largest) with the vectors within the given set. FPD can be seen as a paradigm or meta-heuristic to formally expand single-objective optimization algorithms to multi-objective optimization algorithms, as long as such vector-sets can be defined. This was already shown for the Standard Genetic Algorithm. Here, we explore the application of this concept to PSO, where a swarm of particles is maintained. The resulting PSO_{f2r} algorithm is studied on a fundamental optimization problem (so-called Pareto-Box-Problem) where a complete analysis is possible. The PSO_{f2r} algorithm is shown to handle the case of a larger number of objectives, and shows similar properties like the (single-objective) PSO.

ParEGO: a hybrid algorithm with on-line landscape approximation for expensive multiobjective optimization problems

This paper concerns multiobjective optimization in scenarios where each solution evaluation is financially and/or temporally expensive. We make use of nine relatively low-dimensional, nonpathological, real-valued functions, such as arise in many applications, and assess the performance of two algorithms after just 100 and 250 (or 260) function evaluations. The results show that NSGA-II, a popular multiobjective evolutionary algorithm, performs well compared with random search, even within the restricted number of evaluations used. A significantly better performance (particularly, in the worst case) is, however, achieved on our test set by an algorithm proposed herein-ParEGO-which is an extension of the single-objective efficient global optimization (EGO) algorithm of Jones et al. ParEGO uses a design-of-experiments inspired initialization procedure and learns a Gaussian processes model of the search landscape, which is updated after every function evaluation. Overall, ParEGO exhibits a promising performance for multiobjective optimization problems where evaluations are expensive or otherwise restricted in number.

Multiobjective anatomy-based dose optimization for HDR-brachytherapy with constraint free deterministic algorithms

In high dose rate (HDR) brachytherapy, conventional dose optimization algorithms consider multiple objectives in the form of an aggregate function that transforms the multiobjective problem into a single-objective problem. As a result, there is a loss of information on the available alternative possible solutions. This method assumes that the treatment planner exactly understands the correlation between competing objectives and knows the physical constraints. This knowledge is provided by the Pareto trade-off set obtained by single-objective optimization algorithms with a repeated optimization with different importance vectors. A mapping technique avoids non-feasible solutions with negative dwell weights and allows the use of constraint free gradient-based deterministic algorithms. We compare various such algorithms and methods which could improve their performance. This finally allows us to generate a large number of solutions in a few minutes.We use objectives expressed in terms of dose variances obtained from a few hundred sampling points in the planning target volume (PTV) and in organs at risk (OAR). We compare two- to four-dimensional Pareto fronts obtained with the deterministic algorithms and with a fast-simulated annealing algorithm. For PTV-based objectives, due to the convex objective functions, the obtained solutions are global optimal. If OARs are included, then the solutions found are also global optimal, although local minima may be present as suggested.

Multi-objective global optimization for hydrologic models

The development of automated (computer-based) calibration methods has focused mainly on the selection of a single-objective measure of the distance between the model-simulated output and the data and the selection of an automatic optimization algorithm to search for the parameter values which minimize that distance. However, practical experience with model calibration suggests that no single-objective function is adequate to measure the ways in which the model fails to match the important characteristics of the observed data. Given that some of the latest hydrologic models simulate several of the watershed output fluxes (e.g. water, energy, chemical constituents, etc.), there is a need for effective and efficient multi-objective calibration procedures capable of exploiting all of the useful information about the physical system contained in the measurement data time series. The MOCOM-UA algorithm, an effective and efficient methodology for solving the multiple-objective global optimization problem, is presented in this paper. The method is an extension of the successful SCE-UA single-objective global optimization algorithm. The features and capabilities of MOCOM-UA are illustrated by means of a simple hydrologic model calibration study.