Selecting the option -xe in PAR will let PAR try extra effort.
Please see below for more details on the -xe option.
-xe (Extra Effort Level)
Use this option to set the extra effort level.
n (normal) tells PAR to use additional runtime intensive methods in an attempt to meet difficult timing constraints.
If PAR determines that the timing constraints cannot be met, then a message is issued explaining that the timing cannot be met and PAR exits.
c (continue) tells PAR to continue routing even if PAR determines the timing constraints cannot be met.
PAR continues to attempt to route and improve timing until little or no timing improvement can be made.
Note: Use of extra effort c can result in extremely long runtimes.
To use the -xe option, you must also set the -ol (Overall Effort Level) option to high or the -pl (Placer Effort Level) option and -rl (Router Effort Level) options to high.
par -ol high -xe n design.ncd output.ncd design.pcf
This example directs PAR to use extra effort, but to exit if it determines that the timing constraints cannot be met.