We show that, for any c>0, the (1+1) evolutionary algorithm using an arbitrary mutation rate p_n = c/n finds the optimum of a linear objective function over bit strings of length n in expected time Theta(n log n). Previously, this was only known for c at most 1. Since previous work also shows that universal drift functions cannot exist for c larger than a certain constant, we instead define drift functions which depend crucially on the relevant objective functions (and also on c itself). Using these carefully-constructed drift functions, we prove that the expected optimisation time is Theta(n log n). By giving an alternative proof of the multiplicative drift theorem, we also show that our optimisation-time bound holds with high probability.
Monday, 16 July 2012
Tuesday, 7 February 2012
Brian O'Meara (hurler)
Career
O'Meara was a member of the county minor hurling panel in 2008 and won a Munster Under 21 Football medal with Tipperary in 2010, lining out at full-forward in the Munster Final against Kerry, to claim Tipperary's first ever title. On 27 May 2010, O'Meara was named to make his debut as full forward in the Tipperary Senior Hurling Team to play Cork in the Munster Senior Hurling Championship quarter-final in Páirc Uí Chaoimh on 30 May 2010. Tipperary ended up losing the game by 3–15 to 0–14, with O'Meara being substituted in the 43rd minute without scoring in the game. On 28 July 2010, O'Meara played at full-forward for Tipperary as they defeated Clare in the 2010 Munster Under-21 Hurling final at Semple Stadium, winning by 1–22 to 1–17.
On 5 September 2010, O'Meara was a non-playing substitute as Tipperary won their 26th All Ireland title, beating reigning champions Killkenny by 4–17 to 1–18 in the final, preventing Kilkenny from achieving an historic 5-in-a-row, it was O'Meara's first All-Ireland winners medal. Six day's later on 11 September 2010, Tipperary clinched the All Ireland Under-21 title by defeating Galway by 5–22 to 0–12 at Semple Stadium, with O'Meara starting at full forward and winning the man of the match award.
O'Meara was a member of the county minor hurling panel in 2008 and won a Munster Under 21 Football medal with Tipperary in 2010, lining out at full-forward in the Munster Final against Kerry, to claim Tipperary's first ever title. On 27 May 2010, O'Meara was named to make his debut as full forward in the Tipperary Senior Hurling Team to play Cork in the Munster Senior Hurling Championship quarter-final in Páirc Uí Chaoimh on 30 May 2010. Tipperary ended up losing the game by 3–15 to 0–14, with O'Meara being substituted in the 43rd minute without scoring in the game. On 28 July 2010, O'Meara played at full-forward for Tipperary as they defeated Clare in the 2010 Munster Under-21 Hurling final at Semple Stadium, winning by 1–22 to 1–17.
On 5 September 2010, O'Meara was a non-playing substitute as Tipperary won their 26th All Ireland title, beating reigning champions Killkenny by 4–17 to 1–18 in the final, preventing Kilkenny from achieving an historic 5-in-a-row, it was O'Meara's first All-Ireland winners medal. Six day's later on 11 September 2010, Tipperary clinched the All Ireland Under-21 title by defeating Galway by 5–22 to 0–12 at Semple Stadium, with O'Meara starting at full forward and winning the man of the match award.
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