Each merit criterion has its own appealing feature. However, existing simplex algorithms cannot use multiple merits at the same time because each of these algorithms updates only one variable at a time. In a slightly different view, a merit criterion may be a good choice in most scenarios but may be a poor choice in some spacial case, such as the Klee-Minty cube. Therefore, randomized pivot rules [@ghz98; @kp06] that randomly select an entering variable from the set of possible entering variables that will improve the objective function have been proposed and proved to be able to find an optimizer in a polynomial time on average [@kp06]. This shows that using a combination of merits in the selection of pivot can be beneficial.

In this paper, we consider a novel simplex algorithm for linear programming problem. This algorithm is different from all existing simplex algorithms in that it updates two variables at one iteration. This strategy looks two pivots ahead instead of focus only on the next step. We believe that this strategy is better than all existing pivot rules because it looks longer term benefit instead of a short-sighted one-step achievement. Since the proposed algorithm updates two variables at 