A fuzzy goal programming approach to multi-objective optimization problem with priorities

In goal programming problem, the general equilibrium and optimization are often two conflicting factors. This paper proposes a generalized varying-domain optimization method for fuzzy goal programming (FGP) incorporating multiple priorities. According to the three possible styles of the objective function, the varying-domain optimization method and its generalization are proposed. This method can generate the results consistent with the decision-maker (DM)’s expectation, that the goal with higher priority may have higher level of satisfaction. Using this new method, it is a simple process to balance between the equilibrium and optimization, and the result is the consequence of a synthetic decision between them. In contrast to the previous method, the proposed method can make that the higher priority achieving the higher satisfactory degree. To get the global solution of the nonlinear nonconvex programming problem resulting from the original problem and the varying-domain optimization method, the co-evolutionary genetic algorithms (GAs), called GENOCOPIII, is used instead of the SQP method. In this way the DM can get the optimum of the optimization problem. We demonstrate the power of this proposed method by illustrative examples.     

利用遗传算法求一类非线性规划的最优解

针对一类非线性规则问题（Nonlinear Programming Problem)，采用遗传算法思想设计求解算法，实例表明，该遗传算法具有较高的计算效率。     

Nonlinear programming and genetic search application for production scheduling in coal mines

Efforts to eliminate unnecessary scheduling and inventory problems faced by the coal industry today initiated the development of a generalized, nonlinear programming model. Although no accepted methodology for developing such a model for this purpose currently exists, one was created and successfully tested. Production and transportation cost estimates were obtained from independent coal mines in Illinois, Virginia, and Pennsylvania, and based on these estimates, a hypothetical model was developed and tested using genetic search for nonlinear optimization. The results of our tests indicate that the model has potential for decision support in coal mines.     

A semistrong sufficiency condition for optimality in nonconvex programming and its connection to the perturbation problem

What happens when a nonconvex program, having a local solutionx ⁰ at which the gradients of the binding constraints are linearly independent, but without strict complementarity hypothesis, is perturbed? Under a relatively weak second-order assumption (some nonnegative second-order terms are supposed to be strictly positive), the perturbed problem has, in the neighborhood ofx ⁰, a finite number of local minima, situated on curves that are connected to some pseudo-solutions of the tangent quadratic problem.