Abstract
Multi-objective AI planning suffers from a lack of benchmarks with known Pareto Fronts. A tunable benchmark generator is proposed, together with a specific solver that provably computes the true Pareto Front of the resulting instances. A wide range of Pareto Front shapes of various difficulty can be obtained by varying the parameters of the generator. The experimental performances of an actual implementation of the exact solver are demonstrated, and some large instances with remarkable Pareto Front shapes are proposed, that will hopefully become standard benchmarks of the AI planning domain.
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Notes
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This might look unrealistic in real-world logistic domain. However, we hypothesize that the proposition still holds with the weaker condition that for any cities \(C_i, C_j, C_k\) (if we state the cost of \(C_I\) and \(C_G\) are respectively \(C_0\) and \(C_{n+1}\)), \(d_{ik} \le d_{ij} + d_{jk}\) (triangle inequality).
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Most of them are probably not Pareto-optimal, but w.r.t the previous proposition, any schedule resulting from a larger tuple \(e\) or \(w\) would be Pareto-dominated.
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Planning Domain Definition Language, universally used now in AI Planning to describe domains and instances.
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In the context of discrete optimization, the word “concave” seems rather abusive. However, we will call here concave parts of a Pareto front where all points are above the segment made of the two extreme points, w.r.t. the direction of optimization.
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Quemy, A., Schoenauer, M. (2015). True Pareto Fronts for Multi-objective AI Planning Instances. In: Ochoa, G., Chicano, F. (eds) Evolutionary Computation in Combinatorial Optimization. EvoCOP 2015. Lecture Notes in Computer Science(), vol 9026. Springer, Cham. https://doi.org/10.1007/978-3-319-16468-7_17
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DOI: https://doi.org/10.1007/978-3-319-16468-7_17
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