It is often the case that suppressing the intercept leads to regression coefficients that don't make sense. In my experience, there are rarely cases where suppressing the intercept makes sense, even if the scientific plausibility suggests that it might be justifiable (such as stopping distance versus cruising speed or creatinine clearance versus kidney mass in grams). This is a problem of extrapolation.

Just eyeballing these data, I imagine that the estimated intercept would be a largely non-zero value. Since these data appear to come from some sort of computing time, comparing flops versus elapsed time, etc. the non-zero intercept could have a host of interpretations such as a boot time for running a process, a system lag as memory is allocated for an operation, or any other non-neglible system processes that aren't measured as part of an experimental run. Furthermore, and more subtle, there may be non-linear effects which are influencing your results.

My first recommendation is to look at the output from running pairs(fit). And just look at the trend.

Nonetheless, if your goal is to simply find optimal positive coefficients in the model, you can do so with using by-hand optimization, either ML or Gibb's sampling, though don't be surprised if those results make no sense. Example of by-hand optimization:

X <- model.matrix(~ tinst+tmem+tcom-1, data=fit)
y <- fit$tcyc
negLogLik <- function(b) {
  b <- exp(b)     ## restrict to positive only values
  yhat <- b %*% X ## calculate fitted
  var(y-yhat)     ## 
}

nlm(negLogLik, c(1,1,1))

It is often the case that suppressing the intercept leads to regression coefficients that don't make sense. In my experience, there are rarely cases where suppressing the intercept makes sense, even if the scientific plausibility suggests that it might be justifiable (such as stopping distance versus cruising speed or creatinine clearance versus kidney mass in grams: you LEAVE the intercept IN with such analyses!). This is a problem of extrapolation.

Just eyeballing these data, I imagine that the estimated intercept would be a largely non-zero value. Since these data appear to come from some sort of computing time, comparing flops versus elapsed time, etc. the non-zero intercept could have a host of interpretations such as a boot time for running a process, a system lag as memory is allocated for an operation, or any other non-neglible system processes that aren't measured as part of an experimental run. Furthermore, and more subtle, there may be non-linear effects which are influencing your results. The regression coefficient from intercept-in OLS still provides a great way of estimating the first order linear trend through those data, even if the trend is curvilinear... only when you leave the intercept IN.

My first recommendation is to look at the output from running pairs(fit). And just look at the trend.

Nonetheless, if your goal is to simply find optimal positive coefficients in the model, you can do so with using by-hand optimization, either ML or Gibb's sampling, though don't be surprised if those results make no sense. Example of by-hand optimization:

X <- model.matrix(~ tinst+tmem+tcom-1, data=fit)
y <- fit$tcyc
negLogLik <- function(b) {
  b <- exp(b)     ## restrict to positive only values
  yhat <- b %*% X ## calculate fitted
  -var(y-yhat)    ## objective foo
}

nlm(negLogLik, c(1,1,1)) ## minimize objective foo