1. hoped to do indicates that its action or state occurs or exists after the action or state expressed by the predicate verb and has the potential to be realized.
They still hoped to find their missing son.
They still hope to find their lost son.
He hoped to settle in this country.
He hopes to settle down in the country.
He hoped to strengthen the position of the sciences in the leading universities.
He wanted to strengthen the position of the natural sciences among the leading universities.
He hoped to get a new truck and go back on the road.
He hopes to have a new truck and get back on the road.
He hoped to get rid of the pain in what was left of his knee.
He wanted to get rid of the pain in his knee.
They still hoped to salvage something from the wreck of their marriage.
They still hope to redeem something from their broken marriage.
MPs hoped to reverse Britain's opt-out from the treaty.
MPs want to overturn Britain's decision to withdraw from the treaty.
The divers hoped to unlock some of the secrets of the seabed.
Divers hope to uncover some of the secrets of the seabed.
The professor hoped to break the students of the habit of looking for easy answers.
The professor wants to break the habit of students trying to find answers without using their brains.
Perot hoped to run another series of campaign infomercials.
Perot is looking forward to a new round of campaign propaganda programs.
In this way, he hoped to put pressure on the British and thus to wring concessions from them.
In this way he hoped to put pressure on the British and thus force them to make concessions.
2. hoped to have done means that the action has not been realized, which has a counterfactual meaning. i.e. "would have hoped":
原希望……； 本来希望（指望）…… ，曾打算（企图），实际上没有希望成，即希望，企图，指望等落空了。 hoped to have done sth=had hoped to do sth
I hoped to have seen you yesterday, but I didn't have time.
Yesterday I would have liked to see you, but I wasn't available.
I hoped to have finished by 12.
I would have liked to have done it by 12 o'clock.
I hoped to have seen you before now.
I would have liked to see you before that.
I hoped to have found her .
I would have liked to have found her.
In World War Ⅱ，Japan hoped to have extended its power to the whole Asia，and it did not succeed.
In World War II, Japan originally hoped to expand its power throughout Asia, but was unsuccessful.
3.had hoped to do ԭ ......; Originally, ...... hope (hope) had been intended (attempted), but in fact there was no hope to come true, that is, hope, attempt, hope, etc. were in vain.
had hoped to do sth或者hoped to have done sth来表示过去未曾实现的希望。
I had hoped to meet Mr Thompson this morning , but I found nobody left in the room when I came in.
I had hoped to see Mr. Thompson this morning, but when I came in there was no one in the room.
I had hoped to brush up my Spanish
I had planned to brush up on my Spanish.
He had hoped to continue as a full-time career officer
He had hoped to continue working as a full-time professional clerk.
I had hoped to pass examination.
I had hoped to pass the exam.
The Europeans had hoped to win, and, indeed, had looked like winning
The Europeans have wanted to win for a long time, and they do look like they are going to win.
We had hoped to fill the back page with extra news; we're not quite there yet
We would have liked to have added some news to fill the last edition, but we are still far from it.
A hard-core group of right-wing senators had hoped to sway their colleagues.
A group of key right-wing senators have tried to sway their colleagues.
I had hoped to save some more money to buy a new car.
I would have liked to save up a little more to buy a new car.
I had hoped to see the film but couldn't get a ticket.
I was expecting to see that movie, but I didn't get a ticket.
He had hoped to sell more papers tonight to make more money to buy a cake for his mother and some seeds for his bird.
He had hoped to sell more newspapers tonight, earn more money to buy a cake for his mother, and some food for his birds.
College Entrance Examination Past Papers - 2015 Hubei
She had hoped to be a dancer. ＝She hoped to have been a dancer.
She used to wish she was a dancer.
had hoped that 和 had hoped to do或hoped to have done 都可以表示"本来希望做某事，但是后来实际上没有做成“的意思。 例如：
I had hoped that Jennifer would study medicine, but she didn't want to .
I had hoped that Jennifer would study medicine, but she didn't want to. (Oxford Guide to the Use of English, 4th Edition, 490.3)
We had hoped that you would be able to visit us .
We would have expected you to come and see us. (Didn't actually come) (Thin Ice English Idiomatic Dictionary, p.390)
They had hoped to see the film but couldn't get the tickets.
They had hoped to see the movie, but they couldn't get tickets.
They hoped to have seen the film but couldn't get the tickets. )（《薄冰英语惯用法词典》p.390）
4. When verbs like hope, expect, mean, intend, plan, suppose, think, want, etc., are used in the past tense or past perfect tense, the perfect form of the infinitive after it indicates the action that has not been fulfilled. And the perfect form of the infinitive of the verb in the general present tense of these verbs does not indicate the action that is not realized, but indicates the completion of the action,
I hope to have finished by now.
I hope it's done now.