Finding a tighter lower bound for optimization problems with capacity and/or precedence constraints
Abstract
Many optimization problems belong to the class of NP-complete problems whose optimal solution may not be obtained in polynomial time. Without loss of generality, we discuss minimization problems only. For NP-complete problems, a traditional approach is to develop a simple heuristic algorithm and find its worst-case performance ratio. Another approach is to find a tighter lower bound on the optimal solution. As the range between the lower bound and a heuristic solution approaches zero, the solution becomes closer to optimal. The emphasis of this research is on developing techniques for finding a tighter lower bound for optimization problems with capacity and/or precedence constraints. Three optimization problems are considered: (1) 1-D Bin Packing Problem: packing a set of objects into a minimum number of bins with fixed capacity. (2) Channel Routing Problem: assigning a set of connections to a minimum number of tracks in a two-layer channel such that no connections overlap on any layer. The detailed routing is one of the most important and time-consuming phases in VLSI design. (3) Superscalar Superpipeline Scheduling Problem: scheduling a set of instructions for a superscalar superpipelined processor such that the total execution time is minimized. In a superscalar superpipelined processor, there are multiple pipelined functional units with possibly non-uniform latencies. Multiple instructions may be issued per cycle if the capacity and precedence constraints are satisfied. We have developed efficient lower bound algorithms for each of these problems and a generic lower bound algorithm for problems with capacity and precedence constraints. To determine a tight lower bound for problems with multiple constraints requires careful consideration of the interaction between the constraints. The technique we have developed provides an efficient way of integrating the capacity constraints and precedence constraints, and is applicable to other problems impacted by these two constraints.
Degree
Ph.D.
Advisors
Harper, Purdue University.
Subject Area
Electrical engineering|Computer science|Operations research
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