This paper introduces simultaneous generalized hill-climbing (SGHC) algorithms as a framework for simultaneously addressing a set of related discrete optimization problems using heuristics. Many well-known heuristics can be embedded within the SGHC algorithm framework, including simulated annealing, pure local search, and threshold accepting (among others). SGHC algorithms probabilistically move between a set of related discrete optimization problems during their execution according to a problem probability mass function. When an SGHC algorithm moves between discrete optimization problems, information gained while optimizing the current problem is used to set the initial solution in the subsequent problem. The information used is determined by the practitioner for the particular set of problems under study. However, effective strategies are often apparent based on the problem description. SGHC algorithms are motivated by a discrete manufacturing process design optimization problem (that is used throughout the paper to illustrate the concepts needed to implement a SGHC algorithm). This paper discusses effective strategies for three examples of sets of related discrete optimization problems (a set of traveling salesman problems, a set of permutation flow shop problems, and a set of MAX 3-satisfiability problems). Computational results using the SGHC algorithm for randomly generated problems for two of these examples are presented. For comparison purposes, the associated generalized hill-climbing (GHC) algorithms are applied to the individual discrete optimization problems in the sets. These computational results suggest that near-optimal solutions can be reached more effectively and efficiently using SGHC algorithms.
Discrete manufacturing process design optimization can be difficult, due to the large number of manufacturing process design sequences and associated input parameter setting combinations that exist. Generalized hill climbing algorithms have been introduced to address such manufacturing design problems. Initial results with generalized hill climbing algorithms required the manufacturing process design sequence to be fixed, with the generalized hill climbing algorithm used to identify optimal input parameter settings. This paper introduces a new neighborhood function that allows generalized hill climbing algorithms to be used to also identify the optimal discrete manufacturing process design sequence among a set of valid design sequences. The neighborhood function uses a switch function for all the input parameters, hence allows the generalized hill climbing algorithm to simultaneously optimize over both the design sequences and the inputs parameters. Computational results are reported with an integrated blade rotor discrete manufacturing process design problem under study at the Materials Process Design Branch of the Air Force Research Laboratory, Wright Patterson Air Force Base (Dayton, Ohio, USA). [S1050-0472(00)01002-3]
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