Save images with phimagemanager to custom album?

Answer in Objective-C and cleaned up a bit.

__block PHFetchResult *photosAsset;
__block PHAssetCollection *collection;
__block PHObjectPlaceholder *placeholder;

// Find the album
PHFetchOptions *fetchOptions = [[PHFetchOptions alloc] init];
fetchOptions.predicate = [NSPredicate predicateWithFormat:@"title = %@", @"YOUR_ALBUM_TITLE"];
collection = [PHAssetCollection fetchAssetCollectionsWithType:PHAssetCollectionTypeAlbum
                                                      subtype:PHAssetCollectionSubtypeAny
                                                      options:fetchOptions].firstObject;
// Create the album
if (!collection)
{
    [[PHPhotoLibrary sharedPhotoLibrary] performChanges:^{
        PHAssetCollectionChangeRequest *createAlbum = [PHAssetCollectionChangeRequest creationRequestForAssetCollectionWithTitle:@"YOUR_ALBUM_TITLE"];
        placeholder = [createAlbum placeholderForCreatedAssetCollection];
    } completionHandler:^(BOOL success, NSError *error) {
        if (success)
        {
            PHFetchResult *collectionFetchResult = [PHAssetCollection fetchAssetCollectionsWithLocalIdentifiers:@[placeholder.localIdentifier]
                                                                                                            options:nil];
            collection = collectionFetchResult.firstObject;
        }
    }];
}

// Save to the album
[[PHPhotoLibrary sharedPhotoLibrary] performChanges:^{
    PHAssetChangeRequest *assetRequest = [PHAssetChangeRequest creationRequestForAssetFromImage:[UIImage imageWithData:imageData]];
    placeholder = [assetRequest placeholderForCreatedAsset];
    photosAsset = [PHAsset fetchAssetsInAssetCollection:collection options:nil];
    PHAssetCollectionChangeRequest *albumChangeRequest = [PHAssetCollectionChangeRequest changeRequestForAssetCollection:collection
                                                                                                                  assets:photosAsset];
    [albumChangeRequest addAssets:@[placeholder]];
} completionHandler:^(BOOL success, NSError *error) {
    if (success)
    {
        NSString *UUID = [placeholder.localIdentifier substringToIndex:36];
        self.photo.assetURL = [NSString stringWithFormat:@"assets-library://asset/asset.PNG?id=%@&ext=JPG", UUID];
        [self savePhoto];
    }
    else
    {
        NSLog(@"%@", error);
    }
}];

The bit at the end with the UUID was something I found on another StackOverflow thread for creating a replacement for AssetURL property from an ALAsset.

Note: See chris' comment below for more complete answer.

This is how I do:

At the top:

import Photos

var image: UIImage!
var assetCollection: PHAssetCollection!
var albumFound : Bool = false
var photosAsset: PHFetchResult!
var assetThumbnailSize:CGSize!
var collection: PHAssetCollection!
var assetCollectionPlaceholder: PHObjectPlaceholder!

Creating the album:

func createAlbum() {
    //Get PHFetch Options
    let fetchOptions = PHFetchOptions()
    fetchOptions.predicate = NSPredicate(format: "title = %@", "camcam")
    let collection : PHFetchResult = PHAssetCollection.fetchAssetCollectionsWithType(.Album, subtype: .Any, options: fetchOptions)
    //Check return value - If found, then get the first album out
    if let _: AnyObject = collection.firstObject {
        self.albumFound = true
        assetCollection = collection.firstObject as! PHAssetCollection
    } else {
        //If not found - Then create a new album
        PHPhotoLibrary.sharedPhotoLibrary().performChanges({
            let createAlbumRequest : PHAssetCollectionChangeRequest = PHAssetCollectionChangeRequest.creationRequestForAssetCollectionWithTitle("camcam")
            self.assetCollectionPlaceholder = createAlbumRequest.placeholderForCreatedAssetCollection
            }, completionHandler: { success, error in
                self.albumFound = success

                if (success) {
                    let collectionFetchResult = PHAssetCollection.fetchAssetCollectionsWithLocalIdentifiers([self.assetCollectionPlaceholder.localIdentifier], options: nil)
                    print(collectionFetchResult)
                    self.assetCollection = collectionFetchResult.firstObject as! PHAssetCollection
                }
        })
    }
}

When saving the photo:

func saveImage(){
        PHPhotoLibrary.sharedPhotoLibrary().performChanges({
            let assetRequest = PHAssetChangeRequest.creationRequestForAssetFromImage(self.image)
            let assetPlaceholder = assetRequest.placeholderForCreatedAsset
            let albumChangeRequest = PHAssetCollectionChangeRequest(forAssetCollection: self.assetCollection, assets: self.photosAsset)
            albumChangeRequest!.addAssets([assetPlaceholder!])
            }, completionHandler: { success, error in
                print("added image to album")
                print(error)

                self.showImages()
        })
    }

Showing the images from that album:

func showImages() {
        //This will fetch all the assets in the collection

        let assets : PHFetchResult = PHAsset.fetchAssetsInAssetCollection(assetCollection, options: nil)
        print(assets)

        let imageManager = PHCachingImageManager()
        //Enumerating objects to get a chached image - This is to save loading time
        assets.enumerateObjectsUsingBlock{(object: AnyObject!,
            count: Int,
            stop: UnsafeMutablePointer<ObjCBool>) in

            if object is PHAsset {
                let asset = object as! PHAsset
                print(asset)

                let imageSize = CGSize(width: asset.pixelWidth, height: asset.pixelHeight)

                let options = PHImageRequestOptions()
                options.deliveryMode = .FastFormat

                imageManager.requestImageForAsset(asset, targetSize: imageSize, contentMode: .AspectFill, options: options, resultHandler: {(image: UIImage?,
                    info: [NSObject : AnyObject]?) in
                    print(info)
                    print(image)
                })
            }
        }