Host: The Japan Society of Mechanical Engineers
Name : [in Japanese]
Date : March 06, 2023 - March 07, 2023
In this paper, a generalized version of the minimal switching graph (MSG) problem is revisited. Problem MSG is a combinatorial optimization model of via minimization in double-sided circuit boards, and it is defined on a directed bipartite graph with a finite set of items and a finite set of switches. An item and a switch correspond to a via candidate connecting the two faces of circuit board in the initial design and to a wiring cluster, respectively. A turned-on switch means the move of every wire segment of the wiring cluster from its initial face to the other face. In the generalized version, each item has two non-negative profits, and each switch has a positive cost which is paid when the switch is turned on. A solution is a set of turned-on switches, and it is feasible if the total cost of turned-on switches does not exceed a given budget. When a switch is turned on, it changes the direction of each arc incident with the switch from the initial to the opposite. If a feasible solution makes the directions of all the arcs incident with an item identical, then the solution can collect the item and get either profit according to the resulting direction of the arcs. The objective is to maximize the total profit of collected items (which intends to maximize the total weighted number of via candidates to be removed from the initial circuit board design). In this paper, numerical experiments are conducted to demonstrate the solutions based on a recently proposed integer programming formulation of the generalized version, and the results are reported.
