Set In Multi-objective Optimization Research Articles

Decision support system (DSS) for selecting sustainable insulation material using Pareto search and novel fuzzy-modified technique for order of preference by similarity to ideal solution (TOPSIS) approach

Efforts to improve the sustainability of the building construction sector have tended to focus on reducing operational energy cost, whereas sustainability considerations in the material selection at the design and construction phase have received less attention due to construction budget constraints. The present study proposes a decision support system (DSS) to assist decision-makers in accounting for sustainability in their construction material selections. We demonstrate how the developed DSS can be used to identify the most sustainable insulation materials and thicknesses among commercially available alternatives. The DSS ranks available alternatives by incorporating individual project information, material information, and the decision maker’s preferences. Technique for order of preference by similarity to ideal solution (TOPSIS) and Pareto search technique are combined in the methodology. By limiting the alternatives to the ‘Pareto front’ of life cycle assessment (LCA) and life cycle cost in a multi-objective optimization setting, we seek to reduce subjectivity in the multi-criterion decision-making process. Moreover, product-specific environmental product declaration is used to calculate the embodied energy for the LCA. The framework recommends commercially available materials and thicknesses accordingly. The proposed method is programmed in Python to establish a user interface for data input and output of results.

Kinetics-informed neural networks

Chemical kinetics and reaction engineering consists of the phenomenological framework for the disentanglement of reaction mechanisms, optimization of reaction performance and the rational design of chemical processes. Here, we utilize feed-forward artificial neural networks as basis functions to solve ordinary differential equations (ODEs) constrained by differential algebraic equations (DAEs) that describe microkinetic models (MKMs). We present an algebraic framework for the mathematical description and classification of reaction networks, types of elementary reaction, and chemical species. Under this framework, we demonstrate that the simultaneous training of neural nets and kinetic model parameters in a regularized multi-objective optimization setting leads to the solution of the inverse problem through the estimation of kinetic parameters from synthetic experimental data. We analyze a set of scenarios to establish the extent to which kinetic parameters can be retrieved from transient kinetic data, and assess the robustness of the methodology with respect to statistical noise. This approach to inverse kinetic ODEs can assist in the elucidation of reaction mechanisms based on transient data.

Multi-objective optimization based algorithms for solving mixed integer linear minimum multiplicative programs

We present two new algorithms for a class of single-objective non-linear optimization problems, the so-called Mixed Integer Linear minimum Multiplicative Programs (MIL-mMPs). This class of optimization problems has a desirable characteristic: a MIL-mMP can be viewed as a special case of the problem of optimization over the efficient set in multi-objective optimization. The proposed algorithms exploit this characteristic and solve any MIL-mMP from the viewpoint of multi-objective optimization. A computational study on 960 instances demonstrates that the proposed algorithms outperform a generic-purpose solver, SCIP, by a factor of more than 10 on many instances. We numerically show that selecting the best algorithm among our proposed algorithms highly depends on the class of instances used. Specifically, since one of the proposed algorithms is a decision space search algorithm and the other one is a criterion space search algorithm, one can significantly outperform the other depending on the dimension of decision space and criterion space. Although it is possible to linearize some instances of MIL-mMPs, we show that a commercial solver, CPLEX, struggles to directly solve such linearized instances because linearization introduces additional constraints and binary decision variables.

An extension of the directed search domain algorithm to bilevel optimization

ABSTRACTA method is developed for generating a well-distributed Pareto set for the upper level in bilevel multiobjective optimization. The approach is based on the Directed Search Domain (DSD) algorithm, which is a classical approach for generation of a quasi-evenly distributed Pareto set in multiobjective optimization. The approach contains a double-layer optimizer designed in a specific way under the framework of the DSD method. The double-layer optimizer is based on bilevel single-objective optimization and aims to find a unique optimal Pareto solution rather than generate the whole Pareto frontier on the lower level in order to improve the optimization efficiency. The proposed bilevel DSD approach is verified on several test cases, and a relevant comparison against another classical approach is made. It is shown that the approach can generate a quasi-evenly distributed Pareto set for the upper level with relatively low time consumption.

Multiobjective optimization of expensive-to-evaluate deterministic computer simulator models

Many engineering design optimization problems contain multiple objective functions all of which are desired to be minimized, say. This paper proposes a method for identifying the Pareto Front and the Pareto Set of the objective functions when these functions are evaluated by expensive-to-evaluate deterministic computer simulators. The method replaces the expensive function evaluations by a rapidly computable approximator based on a Gaussian process (GP) interpolator. It sequentially selects new input sites guided by values of an “improvement function” given the current data. The method introduced in this paper provides two advances in the interpolator/improvement framework. First, it proposes an improvement function based on the “modified maximin fitness function” which is known to identify well-spaced non-dominated outputs when used in multiobjective evolutionary algorithms. Second, it uses a family of GP models that allows for dependence among output function values but which permits zero covariance should the data be consistent with this model. A closed-form expression is derived for the improvement function when there are two objective functions; simulation is used to evaluate it when there are three or more objectives. Examples from the multiobjective optimization literature are presented to show that the proposed procedure can improve substantially previously proposed statistical improvement criteria for the computationally intensive multiobjective optimization setting.

Solving the Pareto front for multiobjective Markov chains using the minimum Euclidean distance gradient-based optimization method

A novel method based on minimizing the Euclidean distance is proposed for generating a well-distributed Pareto set in multi-objective optimization for a class of ergodic controllable Markov chains. The proposed approach is based on the concept of strong Pareto policy. We consider the case where the search space is a non-strictly convex set. For solving the problem we introduce the Tikhonov’s regularization method and implement the Lagrange principle. We formulate the original problem introducing linear constraints over the nonlinear problem employing the c-variable method and constraining the cost-functions allowing points in the Pareto front to have a small distance from one another. As a result, the proposed method generates an even representation of the entire Pareto surface. Then, we propose an algorithm to compute the Pareto front and provide all the details needed to implement the method in an efficient and numerically stable way. As well, we prove the main Theorems for describing the dependence of the saddle point for the regularizing parameter and analyzes its asymptotic behavior. Moreover, we analyze the step size parameter of the Lagrange principle and also its asymptotic behavior. The suggested approach is validated theoretically and verified by a numerical example related to security patrolling that present a technique for visualizing the Pareto front.

Multi-objective optimization of distributed-order fractional damping

This paper investigates the multi-objective optimal design of distributed order fractional damper. A new hybrid method which takes advantages of both the evolutionary algorithms and the simple cell mapping method is used to obtain the Pareto solutions of the multi-objective optimal design. Three different cases of distributed damping coefficient c(α) are studied. The objective functions are taken from the time domain specifications of step response in the feedback control design, which include the overshoot, peak time and integrated tracking error. It is found that the multi-objective optimal designs of the damper can deliver much improved step responses in terms of the three objective functions, compared with the single-objective optimal design by minimizing the integrated tracking error alone. Numerical simulations of the three cases of c(α) demonstrate that better overall performance can be achieved with more design parameters in the multi-objective optimization setting.

A variable neighbourhood search algorithm with novel archive update strategies for redundancy allocation problems

This article proposes a variable neighbourhood search algorithm with novel archive update strategies (VNSAU) to solve redundancy allocation problems with the series–parallel system configuration. When solving single-objective optimization problems with different constraint levels, traditional approaches can only deal with one constraint level at a time. This usually leads to the waste of search information and extra computational effort. Different from traditional VNS algorithms, the proposed VNSAU algorithm employs an archive originally derived from the idea of Pareto optimal set in multi-objective optimization to keep track of the best solutions on different constraint levels. The performance of the proposed VNSAU algorithm is tested on a well-known benchmark suite with 33 instances. Computational results show that VNSAU outperforms seven other competing methods in the literature. The number of evaluations and the central processing unit (CPU) time needed by VNSAU also surpass other methods.

Efficient evolutionary approach to approximate the Pareto-optimal set in multiobjective optimization, UPS-EMOA

Solving real-life engineering problems requires often multiobjective, global, and efficient (in terms of objective function evaluations) treatment. In this study, we consider problems of this type by discussing some drawbacks of the current methods and then introduce a new population-based multiobjective optimization algorithm UPS-EMOA which produces a dense (not limited to the population size) approximation of the Pareto-optimal set in a computationally effective manner.

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.

Performance optimization of open zero-buffer multi-server queueing networks

Open zero-buffer multi-server general queueing networks occur throughout a number of physical systems in the semi-process and process industries. In this paper, we evaluate the performance of these systems in terms of throughput using the generalized expansion method (GEM) and compare our results with simulation. Secondly, we embed the performance evaluation in a multi-objective optimization setting. This multi-objective optimization approach results in the Pareto efficient curves showing the trade-off between the total number of servers used and the throughput. Experiments for a large number of settings and different network topologies are presented in detail.