Solving the Interval-Valued Linear Fractional Programming Problem

This paper introduces an interval valued linear fractional programming problem (IVLFP). An IVLFP is a linear frac-tional programming problem with interval coefficients in the objective function. It is proved that we can convert an IVLFP to an optimization problem with interval valued objective function which its bounds are linear fractional functions. Also there is a discussion for the solutions of this kind of optimization problem.

A KIND OF FUZZY LINEAR PROGRAMMING PROBLEMS BASED ON INTERVAL-VALUED FUZZY SETS

The objective of this paper is to deal with a kind of fuzzy linear programming problem based on interval\|valued fuzzy sets (IVFLP) through the medium of procedure that turns IVFLP into parametric linear programming via the mathematical programming.Some useful results for the benefit of solving IVFLP are expounded and proved,developed and discussed.Furthermore,that the proposed techniques in this paper allow the decision\|maker to assign a different degree of importance can provide a useful way to efficiently help the decision\|maker make their decisions.

An Exact l(1) Penalty Approach for Interval-Valued Programming Problem

The objective of this paper is to propose an exact l1 penalty method for constrained interval-valued programming problems which transform the constrained problem into an unconstrained interval-valued penalized optimization problem.Under some suitable conditions,we establish the equivalence between an optimal solution of interval-valued primal and penalized optimization problem.Moreover,saddle-point type optimality conditions are also established in order to find the relation between an optimal solution of penalized optimization problem and saddle-point of Lagrangian function.Numerical examples are given to illustrate the derived results.

Sufficiency and Duality for Nonsmooth Interval-Valued Optimization Problems via Generalized Invex-Infine Functions

In this paper,a new concept of generalized-affineness type of functions is introduced.This class of functions is more general than some of the corresponding ones discussed in Chuong(Nonlinear Anal Theory Methods Appl 75:5044–5052,2018),Sach et al.(J Global Optim 27:51–81,2003)and Nobakhtian(Comput Math Appl 51:1385–1394,2006).These concepts are used to discuss the sufficient optimality conditions for the interval-valued programming problem in terms of the limiting/Mordukhovich subdifferential of locally Lipschitz functions.Furthermore,two types of dual problems,namely Mond–Weir type and mixed type duals are formulated for an interval-valued programming problem and usual duality theorems are derived.Our results improve and generalize the results appeared in Kummari and Ahmad(UPB Sci Bull Ser A 82(1):45–54,2020).

A Line Search SQP-type Method with Bi-object Strategy for Nonlinear Semidefinite Programming

We propose a line search exact penalty method with bi-object strategy for nonlinear semidefinite programming.At each iteration,we solve a linear semidefinite programming to test whether the linearized constraints are consistent or not.The search direction is generated by a piecewise quadratic-linear model of the exact penalty function.The penalty parameter is only related to the information of the current iterate point.The line search strategy is a penalty-free one.Global and local convergence are analyzed under suitable conditions.We finally report some numerical experiments to illustrate the behavior of the algorithm on various degeneracy situations.

A KIND OF FUZZY MULTI-OBJECTIVE LINEAR PROGRAMMING PSOBLEMS BASED ON INTER VALVALUED FUZZY SETS

This paper presents a general solution procedure and an interactive fuzzy satisfying method for a kind of fuzzy multi-objective linear programming-problems based on interval valued fuzzy sets. Firstly, a fuzzy set of the fuzzy solutions, which can be focused on providing complete information for the final decision, can be obtained by the proposed tolerance analysis of a non-dominated set. Secondly, the satisfying solution for the decisionmaker can be derived from Pareto optimal solutions by updating the current reference membership levels on the basis of the current levels of the membership functions together with the trade-off rates between the membership functions.

Site selection of emergency material warehouse under fuzzy environment

The objective of this work was to determine the location of emergency material warehouses. For the site selection problem of emergency material warehouses, the triangular fuzzy numbers are respectively demand of the demand node, the distance between the warehouse and demand node and the cost of the warehouse, a bi-objective programming model was established with minimum total cost of the system and minimum distance between the selected emergency material warehouses and the demand node. Using the theories of fuzzy numbers, the fuzzy programming model was transformed into a determinate bi-objective mixed integer programming model and a heuristic algorithm for this model was designed. Then, the algorithm was proven to be feasible and effective through a numerical example. Analysis results show that the location of emergency material warehouse depends heavily on the values of degree a and weight wl. Accurate information of a certain emergency activity should be collected before making the decision.

Bi-objective mathematical model for choosing sugarcane varieties with harvest residual biomass in energy cogeneration

Sugarcane crop occupies an area of about 23.78 million hectares in 103 countries,and an estimated production of 1.66 billion tons,adding to this volume more than 6%to 17%concerning residual biomass resulting from harvest.The destination of this residual biomass is a major challenge to managers of mills.There are at least two alternatives which are reduction in residue production and increased output in electricity cogeneration.These two conflicting objectives are mathematically modeled as a bi-objective problem.This study developed a bi-objective mathematical model for choosing sugarcane varieties that result in maximum revenue from electricity sales and minimum gathering cost of sugarcane harvesting residual biomass.The approach used to solve the proposed model was based on theε-constraints method.Experiments were performed using real data from sugarcane varieties and costs and showed effectiveness of model and method proposed.These experiments showed the possibility of increasing net revenue from electricity sale,i.e.,already discounted the cost increase with residual biomass gathering,in up to 98.44%.

Compromising Solution of Geometric Programming Problem with Bounded Parameters

This paper addresses a geometric programming problem,where the objective function and constraints are interval-valued functions.The concept of acceptable feasible region is introduced,and a methodology is developed to transform this model to a general optimization problem,which is free from interval uncertainty.Relationship between the solution of the original problem and the transformed problem is established.The methodology is illustrated through numerical examples.Solutions by the proposed method and previous methods are analyzed.

Research on a stock-matching trading strategy based on bi-objective optimization

In recent years,with strict domestic financial supervision and other policy-oriented factors,some products are becoming increasingly restricted,including nonstandard products,bank-guaranteed wealth management products,and other products that can provide investors with a more stable income.Pairs trading,a type of stable strategy that has proved efficient in many financial markets worldwide,has become the focus of investors.Based on the traditional Gatev-Goetzmann-Rouwenhorst(GGR,Gatev et al.2006)strategy,this paper proposes a stock-matching strategy based on bi-objective quadratic programming with quadratic constraints(BQQ)model.Under the condition of ensuring a long-term equilibrium between pairedstock prices,the volatility of stock spreads is increased as much as possible,improving the profitability of the strategy.To verify the effectiveness of the strategy,we use the natural logs of the daily stock market indices in Shanghai.The GGR model and the BQQ model proposed in this paper are back-tested and compared.The results show that the BQQ model can achieve a higher rate of returns.