Solution Of Multi-objective Optimization Problem Research Articles

Computational Solution for Multi-Objective Optimization Problem in CNC Milling Operation Using Particle Swarm Optimization Technique

Computational Solution for Multi-Objective Optimization Problem in CNC Milling Operation Using Particle Swarm Optimization Technique

Scalarization for characterization of approximate strong/weak/proper efficiency in multi-objective optimization

In this article, approximate solutions of multi-objective optimization problems are analysed. The notion of approximate solution suggested by Kutateladze is dealt with, and, utilizing different scalarization approaches, some necessary and sufficient conditions for ϵ-(strong, weak, proper) efficiency are provided. Almost all of the provided results are established without any convexity assumption.

Nonsmooth multiobjective optimization problems and weak vector quasi-variational inequalities

In this article, we investigate a nonsmooth multiobjective optimization problem (MOP) under generalized invexity. First, the Kuhn–Tucker type optimality conditions for MOP are obtained. Furthermore, the relationships between weakly efficient solutions of MOP and vector valued saddle points of its Lagrange function are established. Last but not the least, the relations between weakly efficient solutions of MOP and solutions of Hartman–Stampacchia weak vector quasi-variational inequalities and Hartman–Stampacchia nonlinear weak vector quasi-variational inequalities are also derived under some suitable assumptions. These results extend and improve some known results in the literature.

Multi-Objective Optimization of the Proposed Multi-Reservoir Operating Policy Using Improved NSPSO

Severe water shortage is unacceptable for water-supply reservoir operation. For avoiding single periods of catastrophic water shortage, this paper proposes a multi-reservoir operating policy for water supply by combining parametric rule with hedging rule. In this method, the roles of parametric rule and hedging rule can be played at the same time, which are reducing the number of decision variables and adopting an active reduction of water supply during droughts in advance. In order to maintain the diversity of the non-dominated solutions for multi-objective optimization problem and make them get closer to the optimal trade-off surfaces, the multi-population mechanism is incorporated into the non-dominated sorting particle swarm optimization (NSPSO) algorithm in this study to develop an improved NSPSO algorithm (I-NSPSO). The performance of the I-NSPSO on two benchmark test functions shows that it has a good ability in finding the Pareto optimal set. The water-supply multi-reservoir system located at Taize River basin in China is employed as a case study to verify the effect of the proposed operating policy and the efficiency of the I-NSPSO. The operation results indicate that the proposed operating policy is suitable to handle the multi-reservoir operation problem, especially for the periods of droughts. And the I-NSPSO also shows a good performance in multi-objective optimization of the proposed operating policy.

Pemodelan Sistem Interaksi Obat dengan Menggunakan Fuzzy Inference System dan Pareto Optimality

Drug interactions is the interaction occurs between drugs that consumption simultaneously. Drug interactions can produce a good effect on patients, but not rarely produce adverse effects. Patients with diabetes and hypertension expected to control blood pressure and blood glucose levels to remain in normal circumstances, it is necessary to consider the use of medications for both diseases in order to produce effective therapies.Pareto optimality is a popular concept in the determination optimal solution of multiobjective problems. In determining the optimal solution of multiobjective problem should pay attention for each objective function, frequently conflicting objective functions. The interaction of two drugs has two objective function that is maximizing the positive effects and minimize negative effects. So its use is necessary to find optimal solutions to achieve the expected therapeutic. This research using Fuzzy Inference Sistem (FIS) to determine the appropriate medication to keep blood pressure and blood glucose levels of patients with hypertension and diabetes under control in normal and Pareto optimality to determine drug optimal solution.Fuzzy Inference System generates output choice of drug classes based on fuzzy rules in accordance with the patient's disease condition. Pareto optimality produces a pair solution for diabetes and hypertension drug that satisfy thresholds the minimum effective level (Minimum Effective Concentration; MEC) and maximum toxic levels (Minimum Toxic Concentration; MTC) of each drug.

A novel particle swarm algorithm for multi-objective optimisation problem

To maintain the diversity and convergence of Pareto optimal solutions for multi-objective problem, an improved particle swarm optimisation algorithm based on dynamical changed inertia weight is proposed to improve algorithm’s ability of exploitation and exploration. By this method, if a particle finds a better solution then more energy is given onto the current velocity to speed up exploitation, and vice versa. The computer simulations for three well-known benchmark functions taken from the multi-objective optimisation literature are used to evaluate the performance of the proposed approach. Numerical experiments have been performed to evaluate the efficiency of the algorithm.

The review of multiple evolutionary searches and multi-objective evolutionary algorithms

Over the past decade, subdividing evolutionary search into multiple local evolutionary searches has been identified as an effective method to search for optimal solutions of multi-objective optimization problems (MOPs). The existing multi-objective evolutionary algorithms that benefit from the multiple local searches (multiple-MOEAs, or MMOEAs) use different dividing methods and/or collaborations (information sharing) strategies between the created divisions. Their local evolutionary searches are implicitly or explicitly guided toward a part of global optimal solutions instead of converging to local ones in some divisions. In this reviewed paper, the dividing methods and the collaborations strategies are reviewed, while their advantage and disadvantage are mentioned.

A Generic Branch-and-Cut Algorithm for Multiobjective Optimization Problems: Application to the Multilabel Traveling Salesman Problem

This paper describes a generic branch-and-cut algorithm applicable to the solution of multiobjective optimization problems for which a lower bound can be defined as a polynomially solvable multiobjective problem. The algorithm closely follows standard branch and cut except for the definition of the lower and upper bounds and some optional speed-up mechanisms. It is applied to a routing problem called the multilabel traveling salesman problem, a variant of the traveling salesman problem in which labels are attributed to the edges. The goal is to find a Hamiltonian cycle that minimizes the tour length and the number of labels in the tour. Implementations of the generic multiobjective branch-and-cut algorithm and speed-up mechanisms are described. Computational experiments are conducted, and the method is compared to the classical ϵ-constraint method.

Multiobjective Evolutionary Algorithms in Aeronautical and Aerospace Engineering

Nowadays, the solution of multiobjective optimization problems in aeronautical and aerospace engineering has become a standard practice. These two fields offer highly complex search spaces with different sources of difficulty, which are amenable to the use of alternative search techniques such as metaheuristics, since they require little domain information to operate. From the several metaheuristics available, multiobjective evolutionary algorithms (MOEAs) have become particularly popular, mainly because of their availability, ease of use, and flexibility. This paper presents a taxonomy and a comprehensive review of applications of MOEAs in aeronautical and aerospace design problems. The review includes both the characteristics of the specific MOEA adopted in each case, as well as the features of the problems being solved with them. The advantages and disadvantages of each type of approach are also briefly addressed. We also provide a set of general guidelines for using and designing MOEAs for aeronautical and aerospace engineering problems. In the final part of the paper, we provide some potential paths for future research, which we consider promising within this area.

Homotopy Continuous Method for Weak Efficient Solution of Multiobjective Optimization Problem with Feasible Set Unbounded Condition

In this paper, we propose a homotopy continuous method (HCM) for solving a weak efficient solution of multiobjective optimization problem (MOP) with feasible set unbounded condition, which is arising in Economical Distributions, Engineering Decisions, Resource Allocations and other field of mathematical economics and engineering problems. Under the suitable assumption, it is proved to globally converge to a weak efficient solution of (MOP), if its x-branch has no weak infinite solution.

Linear Complementarity Problem and Multiobjective Optimization

A new method is proposed for the linear complementarity problem (LCP). Firstly we formulate the LCP into a multiobjective optimization problem (MOP), and study the relations between the efficient solution of MOP and optimal solution of LCP. Based on the efficient solution of MOP, we define zero-efficient solution. Then we indicate that zero-efficient solution of the MOP is also the solution to the LCP. Finally some standard LCP examples are respectively transformed into MOP and solved by minimax method. Numerical results indicate that the proposed method is effective.

Distribution feeder reconfiguration considering fuel cell/wind/photovoltaic power plants

In this paper a new method based on multi-objective modified Honey Bee Mating Optimization (MHBMO) algorithm is presented to investigate the DFR problem with the consideration effect of the renewable energy sources (RESs). In the proposed algorithm, a new mating process is suggested to overcome the shortcomings which exist in the original HBMO. During the optimization process, the proposed algorithm finds a set of non-dominated (Pareto) optimal solutions which are stored in an external memory called repository. Also a fuzzy clustering technique is utilized to handle the size of the repository in the specified limits. Moreover, a fuzzy-based decision maker is adopted to select the ‘best compromised’ solution among the non-dominated optimal solutions of multi-objective optimization problem. In order to evaluate the feasibility and effectiveness of the proposed algorithm, two standard distribution systems are used as case studies.

Optimal operation management of fuel cell/wind/photovoltaic power sources connected to distribution networks

In this paper a new multiobjective modified honey bee mating optimization (MHBMO) algorithm is presented to investigate the distribution feeder reconfiguration (DFR) problem considering renewable energy sources (RESs) (photovoltaics, fuel cell and wind energy) connected to the distribution network. The objective functions of the problem to be minimized are the electrical active power losses, the voltage deviations, the total electrical energy costs and the total emissions of RESs and substations. During the optimization process, the proposed algorithm finds a set of non-dominated (Pareto) optimal solutions which are stored in an external memory called repository. Since the objective functions investigated are not the same, a fuzzy clustering algorithm is utilized to handle the size of the repository in the specified limits. Moreover, a fuzzy-based decision maker is adopted to select the ‘best’ compromised solution among the non-dominated optimal solutions of multiobjective optimization problem. In order to see the feasibility and effectiveness of the proposed algorithm, two standard distribution test systems are used as case studies.

On some multiobjective optimization problems arising in biology

In this paper, we discuss modelling and solving some multiobjective optimization problems arising in biology. A class of comparison problems for string selection in molecular biology and a relocation problem in conservation biology are modelled as multiobjective optimization programmes. Some discussions about applications, solvability and different variants of the obtained models are given, as well. A crucial part of the study is based upon the Pareto optimization which refers to the Pareto solutions of multiobjective optimization problems. For such solution, improvement of some objective function can only be obtained at the expense of the deterioration of at least one other objective function.

Conditional Distribution Inverse Method in Generating Uniform Random Vectors Over a Simplex

Motivated by numerous applications in Monte Carlo techniques and as of late, in deriving non dominated solutions in multi-objective optimization problems, this article addresses generating uniform random variables (λ i , λ i ≥ 0, i = 1,…, n) over a simplex in ℝ2 (n ≥ 2), i.e., . In this article, first, conditional distribution of λ i where is derived and then inverse method is applied to generate random variables.

Basic Study on Assembling of Objective Functions in Many-Objective Optimization Problems

Genetic Algorithms (GAs) have been widely applied to Multiobjective Optimization Problems (MOPs), called MOGA. A set of Pareto solutions in MOPs having plural fitness functions are searched, then GA is applied in a multipoint search. MOGA performance decreases with the increasing number of objective functions because solution space spreads exponentially. An effective MOGA search is an important issue in many objective optimization problems. One effective approach is assembling objective functions and reducing their number, but appropriate assembly and the number of objective functions to be assembled has not been studied sufficiently. Our purpose here is to determine the effects of assembling objective functions by studying assembly effects when MOGA is applied to a simplified Nurse Scheduling Problem (sNSP) in two types of assembly based on objective function meaning and correlation coefficients.

Generalized -quasi-solutions in multiobjective optimization problems: Existence results and optimality conditions

Abstract This paper is concerned with approximate solutions of multiobjective optimization problems whose order cone is not necessarily the nonnegative orthant. We introduce the concept of generalized e -quasi-solution, that extends other well-known approximate efficiency notions of the literature, and we study the limit behavior of these solutions as approximations to the efficient and weak efficient sets. Moreover, we prove several existence results and a bound for the generalized e -quasi-solution set under convexity assumptions and by using asymptotic analysis tools. Finally, we develop optimality conditions for a particular case of these kinds of e -quasi-solutions in nonsmooth convex and nonconvex problems.

Optimality Conditions for Approximate Solutions in Multiobjective Optimization Problems

We study first- and second-order necessary and sufficient optimality conditions for approximate (weakly, properly) efficient solutions of multiobjective optimization problems. Here, tangent cone, -normal cone, cones of feasible directions, second-order tangent set, asymptotic second-order cone, and Hadamard upper (lower) directional derivatives are used in the characterizations. The results are first presented in convex cases and then generalized to nonconvex cases by employing local concepts.

Structural analysis of Pareto-optimal solution sets for multi-objective optimization: An application to outer window design problems using Multiple Objective Genetic Algorithms

In single-objective optimization problems, with only one optimal design objective, the absolute optimal solution to maximize/minimize the objective function can be determined. However, in most real design problems, the optimization problems are multi-objective, where two or more independent design objectives must be optimized simultaneously, and no single absolute optimal solution necessarily exists. In these cases, it is helpful for designers to recognize the range of alternative solutions that exist in Pareto-optimal sets and choose an acceptable solution from among them. In this paper, the authors carried out multi-objective optimization using Multiple Objective Genetic Algorithms through a real case study involved in indoor environmental design – the design of outer windows. Then the authors analyzed structure of Pareto-optimal solution sets. Here we present the analysis process as well as the case study details, and show how the method proposed here is effective at finding an acceptable solution for multi-objective optimization problems.

METCO: A PARALLEL PLUGIN-BASED FRAMEWORK FOR MULTI-OBJECTIVE OPTIMIZATION

This paper presents a parallel framework for the solution of multi-objective optimization problems. The framework implements some of the best known multi-objective evolutionary algorithms. The plugin-based architecture of the framework minimizes the end user effort required to incorporate their own problems and evolutionary algorithms, and facilitates tool maintenance. A wide variety of configuration options can be specified to adapt the software behavior to many different parallel models. An innovation of the framework is that it provides a self-adaptive parallel model that is based on the cooperation of a set of evolutionary algorithms. The aim of the new model is to raise the level of generality at which most current evolutionary algorithms operate. This way, a wider range of problems can be tackled since the strengths of one algorithm can compensate for the weaknesses of another. The model proposed is a hybrid algorithm that combines a parallel island-based scheme with a hyperheuristic approach. The model grants more computational resources to those algorithms that show a more promising behavior. The flexibility and efficiency of the framework were tested and demonstrated by configuring standard and self-adaptive models for test problems and real-world applications.