Solution-Guided Multi-Point Constructive Search (SGMPCS) is a novel constructive search technique that performs a series of resource-limited tree searches where each search begins either from an empty solution (as in randomized restart) or from a solution that has been encountered during the search. A small number of these "elite solutions is maintained during the search. We introduce the technique and perform three sets of experiments on the job shop scheduling problem. First, a systematic, fully crossed study of SGMPCS is carried out to evaluate the performance impact of various parameter settings. Second, we inquire into the diversity of the elite solution set, showing, contrary to expectations, that a less diverse set leads to stronger performance. Finally, we compare the best parameter setting of SGMPCS from the first two experiments to chronological backtracking, limited discrepancy search, randomized restart, and a sophisticated tabu search algorithm on a set of well-known benchmark problems. Results demonstrate that SGMPCS is significantly better than the other constructive techniques tested, though lags behind the tabu search.
Deep Dive into Solution-Guided Multi-Point Constructive Search for Job Shop Scheduling.
Solution-Guided Multi-Point Constructive Search (SGMPCS) is a novel constructive search technique that performs a series of resource-limited tree searches where each search begins either from an empty solution (as in randomized restart) or from a solution that has been encountered during the search. A small number of these “elite solutions is maintained during the search. We introduce the technique and perform three sets of experiments on the job shop scheduling problem. First, a systematic, fully crossed study of SGMPCS is carried out to evaluate the performance impact of various parameter settings. Second, we inquire into the diversity of the elite solution set, showing, contrary to expectations, that a less diverse set leads to stronger performance. Finally, we compare the best parameter setting of SGMPCS from the first two experiments to chronological backtracking, limited discrepancy search, randomized restart, and a sophisticated tabu search algorithm on a set of well-known bench
A number of metaheuristic and evolutionary approaches to optimization can be described as being "solution-guided, multi-point" searches. For example, in genetic and mimetic algorithms, a population of solutions is maintained and used as a basis for search. Each new generation is created by combining aspects of the current generation: search is therefore guided by existing solutions. As the population contains a number of individual solutions, the search makes use of multiple points in the search space. Traditional single-point metaheuristics, such as tabu search, have been augmented in a similar way. The TSAB tabu search (Nowicki & Smutnicki, 1996) maintains an elite pool consisting of a small number of the best solutions found so far during the search. Whenever the basic search reaches a threshold number of moves without finding a new best solution, search is restarted from one of the elite solutions. Again, the higher-level search is guided by multiple existing solutions, though the guidance is somewhat different than in genetic algorithms.
Solution-Guided Multi-Point Constructive Search (SGMPCS) 1 is a framework designed to allow constructive search to be guided by multiple existing (suboptimal) solutions to a problem instance. As with randomized restart techniques (Gomes, Selman, & Kautz, 1998), the framework consists of a series of tree searches restricted by some resource limit, 1. In previous conference and workshop publications, SGMPCS is referred to simply as Multi-Point Constructive Search (Beck, 2006;Heckman & Beck, 2006;Beck, 2005aBeck, , 2005b)). Empirical evidence of the importance of solution guidance motivated this change to a name more reflective of the important differences between this work and existing tree search techniques.
typically a maximum number of fails. When the resource limit is reached, search restarts. The difference with randomized restart is that SGMPCS keeps track of a small set of “elite solutions”: the best solutions it has found. When search is restarted, it starts from an empty solution, as in randomized restart, or from one of the elite solutions.
In this paper, we undertake the first fully crossed systematic empirical study of SGM-PCS. In particular, in Section 3 we investigate the different parameter settings and their impact on search performance for the makespan-minimization variant of the job shop scheduling problem. Results indicate that guidance with elite solutions contributes significantly to algorithm performance but, somewhat unexpectedly, that smaller elite set size results in better performance. Indeed, an elite set size of one showed the best performance. This result motivates subsequent experimentation on the diversity of the elite set in Section 4. We show, again contrary to expectation but consistent with an elite set size of one, that the less diverse the elite set, the stronger the performance. As discussed in-depth in Section 6, these two sets of experiments call into question the extent to which the exploitation of multiple points in the search space is important for the performance of SGMPCS. A final experiment (Section 5) compares the best parameter settings found in the first two experiments with chronological backtracking, limited discrepancy search (Harvey, 1995), randomized restart, and a state-of-the-art tabu search (Watson, Howe, & Whitley, 2006) on a set of well-known benchmarks. These results show that SGMPCS significantly outperforms the other constructive search methods but does not perform as well as the tabu search.
The contributions of this paper are as follows:
The introduction and systematic experimental evaluation of Solution-Guided Multi-Point Constructive Search (SGMPCS).
The investigation of the importance of the diversity of the elite set to the performance of SGMPCS.
The demonstration that SGMPCS significantly out-performs chronological backtracking, limited discrepancy search, and randomized restart on a benchmark set of job shop scheduling problems.
Pseudocode for the basic Solution-Guided Multi-Point Constructive Search algorithm is shown in Algorithm 1. The algorithm initializes a set, e, of elite solutions and then enters a while-loop. In each iteration, with probability p, search is started from an empty solution (line 6) or from a randomly selected elite solution (line 12). In the former case, if the best solution found during the search, s, is better than the worst elite solution, s replaces the worst elite solution. In the latter case, s replaces the starting elite solution, r, if s is better than r. Each individual search is limited by a maximum number of fails that can be incurred. When an optimal solution is found and proved or when some overall bound on the computational resources (e.g., CPU time, number of fails) is reached, the best elite solution is returned.
The elite solutions can be initialized by any search technique. In this paper, we use 50 independent runs of the same randomized textu
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