IMO B is best because:

Industrialisation and modern methods of insect control have improved the standard of living around the globe while at the same time they have introduced some 100,000 dangerous chemical pollutants, having gone virtually unregulated since they were developed more than 50 years ago.

(A) while at the same time they have introduced some 100,000 dangerous chemical pollutants, having
We do not need Having...having is past perfect participle...it tells that the unregulation happened before they were introduced. We need to have "have" to tell the action that started sometime back and continues in the present.

(B) while at the same time introducing some 100,000 dangerous chemical pollutants that have
Corrrect.

(C) while they have introduced some 100,000 dangerous chemical pollutants at the same time, which have
Which modifies time...which should modify pollutants.

(D) but introducing some 100,000 dangerous chemical pollutants at the same time that have
that incorrectly modifies time....

(E) but at the same time introducing some 100,000 dangerous chemical pollutants, having
Same reasoning as "A".

One can look at the problem this way

There are two ideas 1.0 the main one and 2.0 a secondary one , which must be connected to the MC using a subordinating conjunctions ect..

MC : I and M .........................around the globe

Sub : While .................................

Here while is used to show contrast

At the same time should be placed close to while or else the meaning changes ( Ex: C. D )

Can not use but ....( D. E out )

Left with A and B , in A having is ambiguous

Hence answer is B