Multiobjective Programming

1) studied the optimality conditions of invex functions for scalar programming problems. In this work, we generalize his results making them applicable to vectorial optimization problems. We prove that the equivalence between minima and stationary points or Kuhn-Tucker points (depending on the case) remains true if we optimize several objective functions instead of one objective function. To this end, we define accurately stationary points and Kuhn-Tucker optimality conditions for multiobjective programming problems. We see that the Martin results cannot be improved in mathematical programming, because the new types of generalized convexity that have appeared over the last few years do not yield any new optimality conditions for mathematical programming problems.

This paper introduces an interactive approach to support multi-criteria decision analysis of project portfolios. In high-scale strategic decision domains, scientific studies suggest that the Decision Maker (DM) can find help by using many-objective optimisation methods, which are supposed to provide values in the decision variables that generate highquality solutions. Even so, DMs usually wish to explore the possibility of reaching some levels of benefits in some objectives. Consequently, they should repeatedly run the optimisation method. However, this approach cannot perform well-in an interactive way-for large instances under the presence of many objective functions. We present a mathematical model that is based on compromise programming and fuzzy outranking to aid DMs in analysing multi-criteria project portfolios on the fly. This approach allows relaxing the problem of rapidly optimising portfolios while preserving the beneficial properties of the DM's preferences expressed by outranking relations. Our model supports the decision analysis on two instance benchmarks: for the first one, a better compromise solution was generated 84% of the runs; for the second one, this ranged from 93% to 97%. Our model was also applied to a real-world problem involving social projects, obtaining satisfactory results.

Multiobjective combinatorial optimization problems have received increasing attention in recent years. Nevertheless, many algorithms are still restricted to the bicriteria case. In this paper we propose a new algorithm for computing all Pareto optimal solutions. Our algorithm is based on the notion of level sets and level curves and contains as a subproblem the determination of K best solutions for a single objective combinatorial optimization problem. We apply the method to the Multiobjective Quadratic Assignment Problem (MOQAP). We present two algorithms for ranking QAP solutions and nally give computational results comparing the methods.

Different approaches besides the traditional Markowitz's model have been proposed in the literature to analyze portfolio selection problems. Among them, Compromise Programming (CP) is a suitable multiobjective programming technique which allows the handling of several objectives in those situations in which the existence of a high level of conflict between criteria does not permit the simultaneous optimization of all the considered objectives.

A class of second order (F, α, ρ, d)-convex functions and their generalizations is introduced. Using the assumptions on the functions involved, weak, strong and strict converse duality theorems are established for a second order Mond–Weir type multiobjective dual.

The potential conflict between protection of water quality and economic development by different uses of land within river basins is a common problem in regional planning. Many studies have applied multiobjective decision analysis under uncertainty to problems of this ...

In this paper, we introduce a new class of generalized (F,α,ρ,θ)–d–V(F,α,ρ,θ)–d–V-univex functions for a nonsmooth multiobjective programming problem. Sufficient optimality conditions under generalized (F,α,ρ,θ)–d–V(F,α,ρ,θ)–d–V-univex functions are established for a feasible solution to be an efficient solution. Appropriate duality theorems for a Mond–Weir-type dual are also presented under the aforesaid assumptions.

The estimate of the parameters which de®ne a conventional multiobjective decision making model is a dicult task. Normally they are either given by the Decision Maker who has imprecise information and/or expresses his considerations subjectively, or by statistical inference from the past data and their stability is doubtful. Therefore, it is reasonable to construct a model re¯ecting imprecise data or ambiguity in terms of fuzzy sets and several fuzzy approaches to multiobjective programming have been developed [1,9±11]. The fuzziness of the parameters gives rise to a problem whose solution will also be fuzzy, see , and which is de®ned by its possibility distribution. Once the possibility distribution of the solution has been obtained, if the decision maker wants more precise information with respect to the decision vector, then we can pose and solve a new problem. In this case we try to ®nd a decision vector, which approximates as much as possible the fuzzy objectives to the fuzzy solution previously obtained. In order to solve this problem we shall develop two dierent models from the initial solution and based on Goal Programming: an Interval Goal Programming Problem if we de®ne the relation``as accurate as possible'' based on the expected intervals of fuzzy numbers, as we showed in , and an ordinary Goal Programming based on the expected values of the fuzzy numbers that de®ned the goals. Finally, we construct algorithms that implement the above mentioned solution method. Our approach will be illustrated by means of a numerical example. Ó

MOPEN is a computational package designed as a global tool for Linear Multiobjective and Goal Programming problems with continuous and/or integer variables. The main existing techniques for these problems have been included in this package. That is, it is possible to generate or approximate the efficient set using Generating Methods, to obtain Compromise solutions or to use Goal Programming or reference Point approaches. As will be described, many advanced options have been implemented with every method. MOPEN has been implemented under a Windows environment; thus, it is easy to build and handle the data entry files and the result layout files. The behavior of MOPEN-in terms of CPU time used to solve large problems-can be considered as good; therefore, this package is a powerful tool to handle the previously mentioned problems.

Goal programming (GP) is perhaps one of the most widely used approaches in the field of multicriteria decision making. The major advantage of the GP model is its great flexibility which enables the decision maker to easily incorporate numerous variations on constraints and goals. Romero provides a general structure, extended lexicographic goal programming (ELGP) for GP and some multiobjective programming approaches. In this work, we propose the extension of this unifying framework to fuzzy multiobjective programming. Our extension is carried out by several methodologies developed by the authors in the fuzzy GP approach. An interval GP model has been constructed where the feasible set has been defined by means of a relationship between fuzzy numbers. We will apply this model to our fuzzy extended lexicographic goal programming (FELGP). The FELGP is a general primary structure with the same advantages as Romero’s ELGP and moreover it has the capacity of working with imprecise information. An example is given in order to illustrate the proposed method.

In this paper, we study the structural properties of DEA efficient surfaces of the production possibility set under the Generalized Data Envelopment Analysis (GDEA) model introduced by Yu, . The GDEA model contains the following well-known Data Envelopment Analysis (DEA) models as its special cases: the CCR model by Charnes, Cooper, and Rhodes (1978); the BCC model by Banker, Charnes and Cooper (1984); the FG model by F'fire and ; and the ST model by . The relationships among Decision Making Units (DMUs) can be found by solving the GDEA model with predilection cone description. Using these relations to identify relative positions of the DMUs on the DEA efficient surface, we devise an efficient algorithm for constructing all the DEA efficient surfaces. Through further analysis, we show properties of DEA-efficient surfaces under several important subclasses of DEA models. Analytical expressions for the DEA efficient surfaces are obtained, which are useful in analyzing the structure of DEA efficiencies and in strategic group classifications. Results from this paper suggest important applications in constructing Pareto solutions (or nondominated solutions) and in analyzing structural properties of Pareto solutions in multiobjective programming.

The objective of this paper is to apply one of the techniques of multiobjective programming (goal programming) in a brazilian forest problem, in a case study accomplished in the Santa Câ andida Farm, Paran a a, Brazil. The areas of this farm can be managed for timber (pine and native species), harvesting of erva-mate leaves, pasture, and tourism. There is also a concern of the farm managers with increasing the diversity of flora and fauna, increasing environmental protection conditions and maintaining employees in the farm. Goal programming was used to develop a project of land allocation, in which all the goals would be reached as closest as possible of the ideal, in a way to attend all the operational restrictions considered. In goal programming, the concept of optimum solution of LP problems is substituted by a satisfactory solution (nondominated). Several solutions can be obtained, and the best solution will depend on the priority associated to each goal. (N.M.P. Volpi). 0096-3003/02/$ -see front matter Ó 2002 Elsevier Science Inc. All rights reserved. PII: S 0 0 9 6 -3 0 0 3 ( 0 2 ) 0 0 2 2 0 -5

This paper is on the portfolio optimization problem for which two generic models are presented in the context of a proprietary solver called GENO:  the first is a pseudo-dynamic model with a single state variable that is meant for the single holding-period case; the second is a truly dynamic model with several state variables that applies to both single and multi-period scenarios. Both models can handle practical restrictions such as exposure, cardinality and round-lot constraints; both can accommodate non-traditional risk measures; and the usual two-element criterion set comprising ‘portfolio reward’ and ‘portfolio risk’ may be augmented by any number of sub-objectives deemed necessary. The paper also presents a ‘robust optimization’ model of the portfolio problem that explicitly accounts for data uncertainty; the robust model can also accommodate sophisticated risk measures, and one such function is presented in Appendix B. The compromise solution concept is used to compute portfolios that are Pareto-efficient; several numerical examples show that the portfolios thus found are not only optimal in the compromise sense, but they also have a competitive (and often the highest) reward-risk ratio—a proxy for the Sharpe ratio. A limited empirical analysis shows that the robust model is superior to its non-robust counterpart in terms of nominal performance and the potential for avoiding “opportunity costs” due to data uncertainty.

In this paper, we introduce new classes of vector functions which generalize the class of scalar invex functions. We prove that these new classes of vector functions are characterized in such a way that every vector critical point is an efficient solution of a Multiobjective Programming Problem. We establish relationships between these new classes of functions and others used in the study of efficient and weakly efficient solutions.

Effective planning of solid-waste recycling programs is a substantial challenge to the current solid-waste management systems in Taiwan. Due to the rapid depletion of landfill space and the continuing delay in construction programs of municipal incinerators, solid-waste management strategies have to be reorganized in light of the success of recycling, recovery, and reuse of secondary materials. One of these efforts is how to effectively allocate recycling drop-off stations of appropriate size and how to design efficient collection-vehicle routing and scheduling programs in the solid waste collection network. This management strategy is particularly important in the privatized system with recycling containers and material recovery facilities (MRFs) owned by one agency. This research seeks multiobjective evaluation of the trade-off between the number and size of drop-off stations, the population covered in the service network, the average walking distance to dropoff stations by the population, and the distance traveled by collection vehicles. It also illustrates the use of the multiobjective nonlinear mixed integer programming model to achieve such goals that are solved by the genetic algorithms (GA) in a geographical information system (GIS) platform. The case study shows the application potential of such a methodology in the city of Kaohsiung in Taiwan.

This work proposes a multiobjective approach for transmission expansion planning considering security constraints (N-1 criterion) and minimum cost. Elitist NSGA-II multiobjective algorithm is used and the operative problem is solved trhough high order interior point method. The methodology is tested on 24 and 6 bus IEEE systems.

Many practical optimization problems usually have several conflicting objectives. In those multiobjective optimization, no solution optimizing all the objective functions simultaneously exists in general. Instead, pareto -optimal solutions, which are efficient in terms of all objective functions, are introduced. In general we have many optimal solutions. Therefore we need to decide a final solutions among pareto -optimal solutions taking in to account the balance among objective functions. In this paper we find fuzzy efficient and pareto -optimal solution to the multiobjective linear plus linear fractional programming problem and show that, in the case that, when any goal is fully achieved, then fuzzy efficient solution may or may not be pareto -optimal solution and therefore we propose a procedure to obtain fuzzy efficient solution which is pareto -optimal also and review some results. In the proposed approach each objective function is transformed into linear functions by using Taylor's theorem. Then the MOLLFP is changed into equivalent multiobjective linear programming problem (MOLP) and then find fuzzy efficient and pareto -optimal solution in finite number of steps. Efficiency of proposed method is verified by numerical examples. To explore the potential use of the proposed method, three numerical examples are solved.

A pair of Wolfe type multiobjective second order symmetric dual programs with cone constraints is formulated and usual duality results are established under second order invexity assumptions. These results are then used to investigate symmetric duality for minimax version of multiobjective second order symmetric dual programs wherein some of the primal and dual variables are constrained to belong to some arbitrary sets, i.e., the sets of integers. This paper points out certain omissions and inconsistencies in the earlier work of Mishra [S.K. Mishra, Multiobjective second order symmetric duality with cone constraints, European Journal of Operational Research 126 (2000) 675–682] and Mishra and Wang [S.K. Mishra, S.Y. Wang, Second order symmetric duality for nonlinear multiobjective mixed integer programming, European Journal of Operational Research 161 (2005) 673–682].

This paper introduces a new class of non-convex vector functions strictly larger than that of P-quasiconvexity, with P⊆ m being the underlying ordering cone, called semistrictly ( m \ −int P)-quasiconvex functions. This notion allows us to unify various results on existence of weakly efficient (weakly Pareto) optima. By imposing a coercivity condition we establish also the compactness of the set of weakly Pareto solutions. In addition, we provide various characterizations for the non-emptiness, convexity and compactness of the solution set for a subclass of quasiconvex vector optimization problems on the real-line. Finally, it is also introduced the notion of explicit ( m \ −int P)-quasiconvexity (equivalently explicit (int P)-quasiconvexity) which plays the role of explicit quasiconvexity (quasiconvexity and semistrict quasiconvexity) of real-valued functions.

Data envelopment analysis (DEA) Multiple objective linear programming (MOLP) Min-ordering method Interactive multiobjective programming a b s t r a c t Data envelopment analysis (DEA) and multiple objective linear programming (MOLP) are tools that can be used in management control and planning. While these two types of model are similar in structure, DEA is a performance measurement tool that was initially without consideration of the decision maker (DM)'s preference structure and is directed to assessing past performances as part of management control function and MOLP to planning future performance targets. This paper will establish an equivalence model between DEA and MOLP and show how a DEA problem can be solved interactively by transforming it into MOLP formulation. We will use Zionts-Wallenius (Z-W) method to reflecting the DM's preferences in the process of assessing efficiency. A case study will conducted to illustrate how DEA-oriented efficiency analysis can be conducted using the MOLP method.

We introduce the use of systematic, combinatorial, multiobjective optimization models to analyse ecological-economic tradeoffs and to support complex decisionmaking associated with dam removal in a river system. The model's ecological objective enhances salmonid migration and spawning by maximizing drainage area reconnected to the sea. The economic objective minimizes loss of hydropower and storage capacity. We present a proof-of-concept demonstration for the Willamette River watershed (Oregon, USA). The case study shows a dramatic tradeoff in which removing twelve dams reconnects 52% of the basin while sacrificing only 1.6% of hydropower and waterstorage capacity. Additional ecological gains, however, come with increasingly steeper economic costs. A second model incorporates existing fish-passage systems. Because of data limitations and model simplifications, these results are intended solely for the purpose of illustrating a novel application of multiobjective programming to damremoval issues. Far more work would be needed to make policy-relevant recommendations. Nevertheless, this research suggests that the current practice of analysing dam-removal decisions on a dam-by-dam basis be supplemented by evaluation on a river-system basis, trading off economic and ecological goals.

In this paper, we revisit one of the most important scalarization techniques used in multiobjective programming, the ε-constraint method. We summarize the method and point out some weaknesses, namely the lack of easy-to-check conditions for properly efficient solutions and the inflexibility of the constraints. We present two modifications that address these weaknesses by first including slack variables in the formulation and second elasticizing the constraints and including surplus variables. We prove results on (weakly, properly) efficient solutions. The improved ε-constraint method that we propose combines both modifications.

Several sustainable production planning models are formulated and studied. One of them is a discrete multiobjective programming model that takes into account conflicting goals as return and financial risk and environmental costs. Starting from it two single objective models are formulated: a maximum expected return model and a minimum financial risk model. In order to control the pollution several pollution and monetary penalties for overcoming them levels are considered. Based on the production planning models, a software application was designed and realized as a decision support tool. A numerical example is given.

For multiobjective problems with inequality-type constraints the necessary conditions for efficient solutions are presented. These conditions are applied when the constraints do not necessarily satisfy any regularity assumptions, and they are based on the concept of 2-regularity introduced by Izmailov. In general, the necessary optimality conditions are not sufficient and the efficient solution set is not the same as the Karush-Kuhn-Tucker points set. So it is necessary to introduce generalized convexity notions. In the multiobjective nonregular case we give the notion of 2-KKT-pseudoinvex-II problems. This new concept of generalized convexity is both necessary and sufficient to guarantee the characterization of all efficient solutions based on the optimality conditions.

This paper uses the grey fuzzy multiobjective programming to aid in decision making for the allocation of waste load in a river system under versatile uncertainties and risks. It differs from previous studies by considering a multicriteria objective function with combined grey and fuzzy messages under a cost benefit analysis framework. Such analysis technically integrates the prior information of water

We present a proximal point method to solve multiobjective problems based on the scalarization for maps. We build a family of a convex scalar strict representation of a convex map F with respect to the lexicographic order on R m and we add a variant of the logarithmquadratic regularization of Auslender, where the unconstrained variables in the domain of F are introduced on the quadratic term and the constrained variables employed in the scalarization we put on the logarithmic term. We show that the central trajectory of the scalarized problem is bounded and converges to a weak Pareto of the multiobjective problem .

Methodology for minimization of risk in a river water quality management problem is presented. The risk minimization model is developed to minimize the fuzzy risk of low water quality along a river in the face of conflict among various stake holders.The model consists of three parts: a water quality simulation model, a risk evaluation model with uncertainty analysis and an optimization model. Fuzzy multiobjective programming is used to develop the multiobjective model. Probabilistic Global Search Laussane, a global search algorithm is used for the non-linear optimization. The result of the model is compared with the result of FWLAM, when the methodology is applied to the case study of Tunga-Bhadra River in southern India.

In recent years portfolio optimization models that consider more criteria than the standard expected return and variance objectives of the Markowitz model have become popular. For such models, two approaches to find a suitable portfolio for an individual investor are possible. In the multiattribute utility theory (MAUT) approach a utility function is constructed based on the investor's preferences and an optimization problem is solved to find a portfolio that maximizes the utility function. In the multiobjective programming (MOP) approach a set of efficient portfolios is computed by optimizing a scalarized objective function. The investor then chooses a portfolio from the efficient set. We outline these two approaches using the UTADIS method to construct a utility function and present numerical results for an example.

Maximum demand (MD) control is a well established tool by means of which eledricity end-users avoid the penalties of MD charges. in use under a great number of tariff schemes. This type of control is based on some means of measuring the power demand and automatically shedding and restoring loads in order that a pre-specified level of power is not surpassed. It may b e supported on large energy management systems or on dedicated controllers with specific firmware. In either case, there are several algorithms that may b e used to implement MD control. A few fundamental dasses of algorithms may b e identified. and a great number of modled versions are wrrenUy implemented. with daerent degrees of flexibili and eflediveness of control. The paper assesses some of the fundamental dasses referred and also some modified algorithms. A s o h a r e elmulation paokage (SIMCA -E2) has been used to pertom the tests, using some typical as well as some extreme load situations, seeking to assure oomparabllity beween the dMerent tested algorithms. The main oriterir used for evaluation have been: effeotlveness of MD oontrol. unavallabllity 01 loads and frequency of shedding adions. The results aro discussed both in a re& oontalned analysls lor ea& olass 01 algorlthms and In a OTOSG -comparative fashion. KaYsrds Demand-slde management M a x i m u d e m a n d control Load management Demand limiting T d s Load control algorithms Slmulatlon l " Maximum demand (MD) charges are widely used by utilities as one of the forms of implementing peak clipping. in the contaxl of deman&side management (DSM). They are typically one component of tariff schemes based on time-okday (TOD) rates. A MD meter installed in the consumer premises is necessary for determining the power demand value which is the basis for applyng the demand charge. This value is. in fad. a mean d u e of power. computed for a certain period of time of fixed duration. on an indefinitely repetitive fashion. The MD is the maximum of the values so obtained. usually monthly recorded.

A pair of Mond-Weir type second order symmetric nondifferentiable multiobjective programs is formulated. Weak, strong and converse duality theorems are established under g-pseudobonvexity assumptions. Special cases are discussed to show that this paper extends some work appeared in this area.

Strategic alliances Synergy effect Resource-based view Multiobjective programming model Objective synergies Resource allocations a b s t r a c t Strategic alliances are widely used in business to obtain the synergy effect and competitive advantage. On the basis of the resource-based view, it can be seen that the valuable resources of firms provide the motivation for entering into strategic alliances. Therefore, the issue of partner selection plays a critical role in the performance of strategic alliances. Although many mathematical programming models have been proposed to deal with the partner selection problems, two main issues such as objective synergies and resource allocations are seems to be ignored. In this paper, a new multiobjective programming model is proposed to determine the optimal partners in the alliance and the corresponding resource allocations. Furthermore, a numerical example is used to demonstrate the proposed method and compared with the conventional method. From the results, it can be concluded that objective synergies and resource allocations play a significant role in the problem of partner selection and should not be ignored in the realistic alliance's problems.

Dealing with the maritime transportation of crude oil and petroleum products has become a problem of major international concern due to the potential of environmental pollution created by oil spill incidents. This paper presents the development of a strategic multiobjective network flow model, allowing for risk analysis and routing, with multiple commodities, modalities and origin-destination pairs. The development of an interactive solution methodology is also presented followed by its implementation via a World Wide Web-based software package. Government agencies will find the model helpful in determining how regulations should be set to derive desirable routing schemes. Shippers will also find the model useful in optimizing their logistics costs.

In this paper, we revisit one of the most important scalarization techniques used in multiobjective programming, the ε-constraint method. We summarize the method and point out some weaknesses, namely the lack of easy-to-check conditions for properly efficient solutions and the inflexibility of the constraints. We present two modifications that address these weaknesses by first including slack variables in the formulation and second elasticizing the constraints and including surplus variables. We prove results on (weakly, properly) efficient solutions. The improved ε-constraint method that we propose combines both modifications.

In this paper we consider unitar concepts for some optimality and efficiency or approximate solutions in scalar optimization and vectorial optimization respectively. In this cases some necessary and/or sufficient conditions for these approximate solutions in the multiobjective case are derived via scalarization and an alternative theorem. Thus are generalized and refined some corresponding results in multiobjective optimization.

This paper presents four optimization models for solving over-specified or under-specified nonlinear equation systems. The presentation includes a 'variable endogenization' technique that patently enhances computational efficiency of the methods proffered; a basic comparative study attests to the effectiveness of the methods presented.

In the present paper, a pair of Wolfe type nondifferentiable multiobjective second-order symmetric dual programs involving two kernel functions is formulated. We established weak, strong and converse duality theorems for this pair under invexity assumptions.

In this work, we establish a strong duality theorem for Mond–Weir type multiobjective higher-order nondifferentiable symmetric dual programs. This fills some gaps in the work of Chen [X. Chen, Higher-order symmetric duality in nondifferentiable multiobjective programming problems, J. Math. Anal. Appl. 290 (2004) 423–435].

A nonlinear multiobjective programming problem is considered. Weak, strong and strict converse duality theorems are established under generalized second order (F, α, ρ, d)-convexity for second order Mangasarian type and general Mond-Weir type vector duals.

Convex multiobjective programming problems and multiplicative programming problems have important applications in areas such as finance, economics, bond portfolio optimization, engineering, and other fields. This paper presents a quite easy algorithm for generating a number of efficient outcome solutions for convex multiobjective programming problems. As an application, we propose an outer approximation algorithm in the outcome space for solving the multiplicative convex program. The computational results are provided on several test problems.

This paper introduces a new class of non-convex vector functions strictly larger than that of P-quasiconvexity, with P⊆ m being the underlying ordering cone, called semistrictly ( m \ −int P)-quasiconvex functions. This notion allows us to unify various results on existence of weakly efficient (weakly Pareto) optima. By imposing a coercivity condition we establish also the compactness of the set of weakly Pareto solutions. In addition, we provide various characterizations for the non-emptiness, convexity and compactness of the solution set for a subclass of quasiconvex vector optimization problems on the real-line. Finally, it is also introduced the notion of explicit ( m \ −int P)-quasiconvexity (equivalently explicit (int P)-quasiconvexity) which plays the role of explicit quasiconvexity (quasiconvexity and semistrict quasiconvexity) of real-valued functions.

Multiobjective approach is the common way of generalization single-criterion dynamic programming models. Another way is to consider partially ordered criteria structures. That approach is rather rare. The aim of the paper is to present such a model. Generalization of BellmanÕs principle of optimality is employed to create a forward procedure to find the set of all maximal elements. As this set is usual large, the second problem under consideration is to find its subsets. To reduce the number of solutions presented to decision maker we propose to apply a family of narrowing relations. That approach is similar to scalarization in multiobjective programming. Ordered structures of random variables based on mean-variance, stochastic dominance and inverse stochastic dominance are considered. Numerical illustration is given at the end of the paper.

In this paper,we characterize a vector-valued convex set function by its epigraph.The concepts of a vector-valued set function and a vector-valued concave set function are given respectively.The definitions of the conjugate functions for a vector-valued convex set function and a vector-valued concave set function are introduced.Then a Fenchel duality theorem in multiobjective programming problem with set functions is derived.

Recent works have shown how hybrid variants of gradientbased methods and evolutionary algorithms perform better than a pure evolutionary method both for single-objective and multiobjective optimization. This same idea has been used with Evolutionary Multiobjective Optimization (EMO), obtaining also very promising results. In most cases, gradient information is used as part of the mutation operator (and only for unconstrained MOPs), in order to move every generated point to the exact Pareto front. In our approach, we use the Karush-Kuhn-Tucker optimality condition for constrained optimization problems to combine the information provided by the gradient vector of each objective function and the gradient vectors of constraint functions to obtain a feasible movement direction in those points near the border. In our approach, gradients of the objective functions will be approximated using quadratic regressions, trying to avoid local optima. The proposed algorithm is able to converge on several nonlinear constrained multiobjective optimization problems obtained from a benchmark, consuming few objective function evaluations (between 150 and 1000). Our results indicate that our proposed scheme may produce a significant reduction in the computational cost, while producing results of good quality, when it is incorporated into a hybrid MOEA or when it is used to seed an EMO algorithm.