multiobjective optimization‎

This paper aims to study a broad class of multiobjective mathematical problems with switching constraints in which all emerging functions are assumed to be locally Lipschitz. First, we are interested in some Abadie, Guignard, and Cottle types qualification conditions for the problem. Then, these constraint qualifications are applied to obtain several stationarity conditions. The results are based on Clarke's subdifferential.

In this paper, first and second order optimality conditions using the concept of approximations are developed for an optimistic fractional multiobjective bilevel problem with non-convex lower level problem. Our idea is based on using the properties of approximations in nonsmooth analysis and a separation theorem in convex analysis. All over the article, the data is assumed to be continuous but not necessarily Lipschitz.

This paper addresses a non-smooth multi-objective semi-infinite programming problem that involves a feasible set defined by inequality constraints‎. ‎Our focus is on introducing a new weak Slater constraint qualification and deriving the necessary and sufficient conditions for (weakly‎, ‎properly) efficient solutions to the problem using (weak and strong) Karush-Kuhn-Tucker types‎. ‎Additionally‎, ‎we present two duals of the Mond-Weir type for the problem and provide (weak and strong) duality results for them‎. ‎All of the results are given in terms of Clarke subdifferential‎.

We consider the multiobjective semi-infinite programming problems with feasible sets defined by equality and inequality constraints, in which the objective and the constraints functions are locally Lipschitz. First, we introduce an Arrow-Hurwitcz-Uzawa type constraint qualification which is based on the Clarke subdifferential. Then, we derive the strong Karush-Kuhn-Tucker type necessary optimality condition for properly efficient solutions of the considered problems.

One of the effective method for solving the multi-objective optimization problems is the ε-constraint method which, unlike the weighted sum method is able to find non-dominated points in non-convex parts of the non-dominated frontier. The main disadvantages of this method are finding similar non-dominated points for choosing different parameters and thus increasing the computational complexity of the algorithm and reducing its overall performance, which is not cost-effective in terms of time and cost. In this paper, a modified is made to ε-constraint method, which, due to the intelligence of the algorithm, the unnecessary areas that lead to the production of the same non-dominated points are eliminated from the beginning. Therefore, additional computational efforts are eliminated to produce the same non-dominated points. Discussions and details of the proposed method, with its algorithm, are presented and in the numerical examples section, the efficiency of the proposed method is compared with the ε-constraint method.

In this paper, approximate efficient ( -efficient) solutions of multiobjective optimization problems are investigated. One of the most important methods for solving multiobjective optimization problems is to use scalarization techniques. In these methods, a single objective optimization problem corresponding to the multiobjective problem is solved, and the relationship between optimal solutions of the single objective problem and (weakly, properly) efficient solutions of the multiobjective problem is investigated. In this paper, a combination of the modified constrained and elastic constrained scalarization methods is considered, which will provide necessary and sufficient conditions for generating approximate (weakly, properly) efficient solutions. We compare the results with the necessary and sufficient conditions obtained from the modified constrained and the elastic constrained methods. The presented results can be applied for every multiobjective optimization problem without any convexity assumption for the objective functions. ‎Unlike many of the previous methods, the obtained results are also consistent with multiobjective problems with unbounded criterion space.

In this paper‎, ‎we introduce and study some new single-valued gap functions for non-differentiable semi-infinite multiobjective optimization problems with locally Lipschitz data‎. ‎Since one of the fundamental properties of gap function for optimization problems is its abilities in characterizing the solutions of the problem in question‎, ‎then the essential properties of the newly introduced gap functions are established‎. ‎All results are given in terms of the Clarke subdifferential.

This paper studies the convex multiobjective optimization problem with vanishing constraints‎. ‎We introduce a new constraint qualification for these problems‎, ‎and then a necessary optimality condition for properly efficient solutions is presented‎. ‎Finally by imposing some assumptions‎, ‎we show that our necessary condition is also sufficient for proper efficiency‎. ‎Our results are formulated in terms of convex subdifferential.

For a nonsmooth multiobjective mathematical programming problem governed by infinitely many constraints‎, ‎we define a new gap function that generalizes the definitions of this concept in other articles‎. ‎Then‎, ‎we characterize the efficient‎, ‎weakly efficient‎, ‎and properly efficient solutions of the problem utilizing this new gap function‎. ‎Our results are based on $(Phi,rho)-$invexity‎, ‎defined by Clarke subdifferential.

Optimization of the product portfolio has been recognized as a critical problem in industry, management, economy and so on. It aims at the selection of an optimal mix of the products to offer in the target market. As a probability function, reliability is an essential objective of the problem which linear models often fail to evaluate it. Here, we develop a multiobjective integer nonlinear constraint model for the problem. Our model provides opportunities to consider the knowledge transferring cost and the environmental effects, as nowadays important concerns of the world, in addition to the classical factors operational cost and reliability. Also, the model is designed in a way to simultaneously optimize the input materials and the products. Although being to some extent complicated, the model can be efficiently solved by the metaheuristic algorithms. Finally, we make some numerical experiments on a simulated test problem.

Nonlinear constrained programing problem (NCPP) has been arisen in diverse range of sciences such as portfolio, economic management etc.. In this paper, a multiobjective imperialist competitive evolutionary algorithm for solving NCPP is proposed. Firstly, we transform the NCPP into a biobjective optimization problem. Secondly, in order to improve the diversity of evolution country swarm, and help the evolution country swarm to approach or land in the feasible region of the problem, three kinds of different methods of colonies moving toward their relevant imperialist are given. Thirdly, the new operator for exchanging position of the imperialist and colony is given similar as a recombination operator in genetic algorithm to enrich the exploration and exploitation abilities of the proposed algorithm. At last, the new approach is tested on two well-known NP-hard nonlinear constrained optimization functions, and the empirical evidence suggests that the proposed method is robust, efficient, and generic.

ýThe wide variety of available interactive methods brings the need for creating generalý ýinteractive algorithms enabling the decision maker (DM) to apply freely several convenient methods which best fit his/her preferencesý. ýTo this endý, ýin this paperý, ýwe propose a general scalarizing problem for multiobjective programming problemsý.
ýThe relation between optimal solutions of the introduced scalarizing problem and (weakly) efficient as well as properly efficient solutions of the main multiobjective optimization problem (MOP) is discussedý. ýIt is shown that some of the scalarizing problems used in different interactive methods can be obtained from proposed formulation by selecting suitable transformationsý. ýBased on the suggested scalarizing problemý, ýwe propose a general interactive algorithm (GIA) that enables the DM to specify his/her preferences in six different ways with capability to change his/her preferences any time during the iterations of the algorithmý.
ýFinallyý, ýa numerical example demonstrating the applicability of the algorithm is providedý.

In this paper, a quasi-Newton type algorithm for non-smooth multiobjective optimization is presented. In this algorithm, in every iteration a quadratic subproblem solves until a critical point is reached. Moreover, the global convergence of the algorithm is established under suitable assumptions.