A fast and scalable multidimensional multiple-choice knapsack heuristic

Abstract

Many combinatorial optimization problems in the embedded systems and design automation domains involve decision making in multi-dimensional spaces. The multi-dimensional multiple-choice knapsack problem (MMKP) is among the most challenging of the encountered optimization problems. MMKP problem instances appear for example in chip multiprocessor run-time resource management and in global routing of wiring in circuits. Chip multiprocessor resource management requires solving MMKP under real-time constraints, whereas global routing requires scalability of the solution approach to extremely large MMKP instances. This paper presents a novel MMKP heuristic, CPH (for Compositional Pareto-algebraic Heuristic), which is a parameterized compositional heuristic based on the principles of Pareto algebra. Compositionality allows incremental computation of solutions. The parameterization allows tuning of the heuristic to the problem at hand. These aspects make CPH a very versatile heuristic. When tuning CPH for computation time, MMKP instances can be solved in real time with better results than the fastest MMKP heuristic so far. When tuning CPH for solution quality, it finds several new solutions for standard benchmarks that are not found by any existing heuristic. CPH furthermore scales to extremely large problem instances. We illustrate and evaluate the use of CPH in both chip multiprocessor resource management and in global routing.

Invasive computing for timing-predictable stream processing on MPSoCs

“…The approaches from [23,27,30] deal with spatial isolation by assignment of exclusive budgets of the MPSoC's compute tiles, however, ignoring communication details. The approaches in [19,24] consider dedicated point-to-point communication between compute tiles via a circuit-switched interconnect.…”

Online Heuristic for the Multi-objective Generalized Traveling Salesman Problem

“…FOR MULTI-OBJECTIVE GENERALIZED TSP CPH has been successfully applied to MMKP [3], a multiobjective, multiple-choice problem like MO-GTSP. CPH is based on Pareto Algebra [10] and the idea that partial solutions can be computed incrementally; i.e.…”

“…The reduction mechanism in CPH is used to control the size of the search space, and therefore the execution time. As described in [3], this can be done in several ways. For two-objective problems, we use a selection mechanism that slices the 2-D space into equal parts and selects one solution per slice.…”

“…We can remove all dominated solutions from the solution set by applying Pareto minimization. This minimization process removes all dominated solutions and is typically implemented by the simple cull algorithm as described extensively in [3] and [11].…”

“…CPH has been applied successfully to the Multi-dimensional Multiple-choice Knapsack Problem (MMKP) [3]. Such problems are found in e.g.…”