Serialize / Deserialize a complex type for Json with object references and dictionaries that have a complex type as a key

I am trying to serialize / deserialize a complex type. I want to keep references to objects, which means that if an instance of an object is referenced several times in the object graph, during deserialization, I want the deserializer to only create this instance once and reference it several times (against creating an instance of the object several times )

The second thing I need a system in is a dictionary in which the key is a complex type.

I was able to achieve both with serialization of DataContractSerializer in XML. However, I cannot find a Json serializer that can do this. I tried Json.NET and ServiceStack but no luck.

See the sample code below:

using System;
using System.Collections.Generic;
using System.IO;
using System.Linq;
using System.Runtime.Serialization;
using System.Text;
using System.Xml;
using Newtonsoft.Json;

namespace Serialization
{
    class Program
    {

        static void Main(string[] args)
        {
            var transportModel = CreateSampleModel();


            //Serialize with DataContractSerializer
            var serializer = new DataContractSerializer(typeof(TransportModel), null, int.MaxValue, false, true, null, null);
            string serializedObjectXml;
            using (var sw = new StringWriter())
            {
                using (var writer = new XmlTextWriter(sw))
                {
                    serializer.WriteObject(writer, transportModel);
                    writer.Flush();
                    serializedObjectXml = sw.ToString();
                }
            }

            //Deserialize with DataContractSerializer
            byte[] byteArray = Encoding.ASCII.GetBytes(serializedObjectXml);
            var stream = new MemoryStream(byteArray);
            var deserializedObjectXml = serializer.ReadObject(stream);


            //Serialize with Json.NET
            var serializedObjectJson=JsonConvert.SerializeObject(transportModel);

            //Deserialize with Json.NET - this fails because of the key in the dictionary being a complex type
            var deserializedObjectJson = JsonConvert.DeserializeObject(serializedObjectJson);
        }


        static TransportModel CreateSampleModel()
        {
            var transportModel = new TransportModel();

            // dests
            var fra = new Destination
            {
                Id = 0,
                Name = "FRA",
                Demand = 900
            };
            var det = new Destination
            {
                Id = 1,
                Name = "DET",
                Demand = 1200
            };


            var dests = new List<Destination> { fra, det};

            //origs
            var gary = new Origin
            {
                Id = 0,
                Name = "GARY",
                Supply = 1400,
                Cost = new Dictionary<Destination, int>{
                    {fra, 39},
                    {det, 14}
                }
            };


            var origs = new List<Origin> { gary};

            transportModel.Destinations = dests;
            transportModel.Origins = origs;

            return transportModel;
        }
    }

    [DataContract]
    class Destination
    {
        [DataMember]
        public int Id { get; set; }
        [DataMember]
        public string Name { get; set; }
        [DataMember]
        public int Demand { get; set; }
    }

    [DataContract]
    class Origin
    {
        [DataMember]
        public int Id { get; set; }
        [DataMember]
        public string Name { get; set; }
        [DataMember]
        public int Supply { get; set; }
        [DataMember]
        public Dictionary<Destination, int> Cost { get; set; }
    }

    [DataContract]
    class TransportModel
    {
        [DataMember]
        public List<Origin> Origins;
        [DataMember]
        public List<Destination> Destinations;

        public TransportModel()
        {
            Origins = new List<Origin>();
            Destinations = new List<Destination>();
        }
    }
}