For more general cases when these optimality conditions do not hold, we use these expressions as heuristic solutions. Via computational studies, we demonstrate that these heuristics are extremely effective when the optimality conditions are not satisfied....
If such conditions are not satisfied this means that elements in the domain are irrelevant. BC can be inferred by moving such elements “out of the boundaries of the domain” which means pruning the bounds of the domain. The essential point is that a refinement of both bounds allows us to...
If all or as many constraints as possible are satisfied, we refer to the solution as exact; otherwise, it is approximate. (When referring to an optimization problem, an approximate solution is one in which all constraints are satisfied, but the optimal value of the objective function is not ...
aconditions-- the study presents the first ex ante analysis that extends the[translate] athat seller constraint, as well as the uncertainty of such a constraint, significantly depresses the expected selling price and increases risk. Our closed-form formulas provide a set of simple quantitative tool...
Optimality conditions are obtained in the general class of measurable control functions; The optimal controls are not unique, and a parameterization with one switching only can be used to achieve the optimality condition. The rest of this paper is organized as follows. A single-input nonlinear cont...
Whether the n has satisfied the restricted condition is dependent on the parameter p . 一个具体的n值是否达到了"充分大"这一要求,要视p值而定,并根据n,p间的关联性,给出了解析化的限制条件。 3. But because there are a few of restricted conditions, the process can t be finished in short ...
In this section, by constructing a Wirtinger-inequality-based Lyapunov functional, sufficient conditions are established to ensure the closed-loop active suspension system (10) possess asymptotical stability, desired\mathcal {H}_\inftyperformance and satisfy the constraints in the FF domain. ...
Except for functions g20 and g22, the algorithm successfully found the optimal solutions that satisfied the constraint conditions. This achievement was attributed to the introduction various innovative strategies in the basic WOA algorithm, including population initialization methods based on SPM chaotic ...
It can be seen that if the equality constraint is not satisfied (hi(x)≠ 0) or the inequality is violated (gi(x) > 0), then Eq. (11.60) gives a positive value for the function P, and the cost function is penalized, as seen in Eq. (11.59). The starting point for the method ...
This can create conditions favourable for the growth and development of other nearby crops (Kamel, and, A.S., S., S.T., I, 2004). Between-crop interactions can also enhance the fertility of the environment. For instance, legumes can provide nitrogen to benefit other crops grown in close...