Abstract
It has been shown that evolutionary algorithms are able to construct suitable search strategies for classes of Constraint Satisfaction Problems (CSPs) in Constraint Programming. This paper is an explanation of the use of multi-objective optimisation in contrast to simple additive weighting techniques with a view to develop search strategies to classes of CSPs. A hierarchical scheme is employed to select a candidate strategy from the Pareto frontier for final evaluation. The results demonstrate that multi-objective optimisation significantly outperforms the single objective scheme in the same number of objective evaluations. In situations where strategies developed for a class of problems fail to extend to unseen problem instances of the same class, it is found that the structure of the underlying CSPs do not resemble those employed in the training process.
Highlights
Constraint Programming (CP) is a declarative paradigm for defining discrete optimisation or satisfiability problems
The aim of this paper is to address a weakness of the simple additive weighting (SAW) metaheuristic scheme employed by Bennetto and Van Vuuren [3] and proposes a multi-objective formulation of the meta heuristic search for a suitable CP branching strategy to solve a class of Constraint Satisfaction Problems (CSPs)
The methodology employed reduces the specification of the strategy to an arithmetic function and adopts a classic ‘Koza’ style genetic pro gramming modelling approach in conjunction with the NSGA-II to search for candidate strategies
Summary
Constraint Programming (CP) is a declarative paradigm for defining discrete optimisation or satisfiability problems. While a heuristic strategy may be employed, the overall CP search remains a complete search, in that, given sufficient time, the search will terminate with either an optimality, feasibility or infeasibility proof It has been shown by several authors such as Minton [13], Epstein et al [7] and Bain et al [2] that heuristic approaches or metaheuristics can be used to develop search algorithms for solving classes of CSPs effectively. The metrics presented by Schuurmans and Southey [16] are not necessarily directly comparable to one another as the units of measurement for the metrics vary (mobility, coverage, depth, flips) If such metrics were used in a single objective scheme, a weighting for each of the metrics would be required in order to define an explicit trade-off between objective function components for use in single objective metaheuristics. Testing whether a tuple τ satisfies a constraint c is called a constraint check
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