Abstracthis p per t kles the di0 ult ut import nt t sk of o je tive lgorithm perE form n e ssessment for optimiz tionF ther th n reporting ver ge performE n e of lgorithms ross set of hosen inst n esD whi h m y i s on lusionsD we propose methodology to en le the strengths nd we knesses of di'erent optimiz tion lgorithms to e omp red ross ro der inst n e sp eF he results reported in re ent Computers and Operations Research p per omE p ring the perform n e of gr ph oloring heuristi s re revisited with this new methodology to demonstr te iA how po kets of the inst n e sp e n e found where lgorithm perform n e v ries signi( ntly from the ver ge perform n e of n lgorithmY iiA how the properties of the inst n es n e used to predi t lE gorithm perform n e on previously unseen inst n es with high ur yY nd iiiA how the rel tive strengths nd we knesses of e h lgorithm n e visu lized nd me sured o je tivelyF Keywords: omp r tive n lysisD heuristi sD gr ph oloringD lgorithm sele tionD perform n e predi tion B gorresponding uthorX k teFsmithEmilesdmon shFedu honeX CTI Q WWHSQIUH p xX CTI Q WWHSRRHQ

In this paper, we consider the problem of decomposing an integer matrix into a weighted sum of binary matrices that have the strict consecutive ones property. This problem is motivated by an application in cancer radiotherapy planning, namely the sequencing of multileaf collimators to realize a given intensity matrix. In addition, we also mention another application in the design of public transportation. We are interested in two versions of the problem, minimizing the sum of the coefficients in the decomposition (decomposition time) and minimizing the number of matrices used in the decomposition (decomposition cardinality). We present polynomial time algorithms for unconstrained and constrained versions of the decomposition time problem and prove that the (unconstrained) decomposition cardinality problem is strongly NP-hard. For the decomposition cardinality problem, some polynomially solvable special cases are considered and heuristics are proposed for the general case.

This paper tackles the issue of objective performance evaluation of machine learning classifiers, and the impact of the choice of test instances. Given that statistical properties or features of a dataset affect the difficulty of an instance for particular classification algorithms, we examine the diversity and quality of the UCI repository of test instances used by most machine learning researchers. We show how an instance space can be visualized, with each classification dataset represented as a point in the space. The instance space is constructed to reveal pockets of hard and easy instances, and enables the strengths and weaknesses of individual classifiers to be identified. Finally, we propose a methodology to generate new test instances with the aim of enriching the diversity of the instance space, enabling potentially greater insights than can be afforded by the current UCI repository.

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