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In this paper we evaluate how constructive heuristics degrade when a problemtransits from P to NP-hard. This is done by means of the linear orderingproblem. More specifically, for this problem we prove that the objectivefunction can be expressed as the sum of two objective functions, one of whichis associated with a P problem (an exact polynomial time algorithm is proposedto solve it), while the other is associated with an NP-hard problem. We studyhow different constructive algorithms whose behaviour only depends onunivariate information perform depending on the contribution of the P orNP-hard components of the problem. A number of experiments are conducted withreduced dimensions, where the global optimum of the problems is known, givingdifferent weights to the NP-hard component, while the weight of the P componentis fixed. It is observed how the performance of the constructive algorithmsgets worse as the weight given to the NP-hard component increases.

Transitions from P to NP-hardness: the case of the Linear Ordering Problem