解决方法如下：

1. 首先，我们需要安装并引用AutoMapper和JsonApiSerializer.JsonApi.Relationship库。您可以使用NuGet包管理器来安装它们。

Install-Package AutoMapper
Install-Package JsonApiSerializer.JsonApi.Relationship

2. 创建一个映射配置类，用于配置AutoMapper的映射规则。

using AutoMapper;

public class MappingProfile : Profile
{
    public MappingProfile()
    {
        CreateMap()
            .ForMember(dest => dest.Relationships, opt => opt.MapFrom(src => src.Relationships));
    }
}

3. 在您的代码中，使用AutoMapper进行映射。

var config = new MapperConfiguration(cfg => {
    cfg.AddProfile();
});
var mapper = config.CreateMapper();

var source = new SourceClass
{
    Relationships = new List
    {
        new Relationship { Id = 1, Name = "Relationship 1" },
        new Relationship { Id = 2, Name = "Relationship 2" }
    }
};

var destination = mapper.Map(source);

4. 通过JsonApiSerializer.JsonApi.Relationship库，您可以将映射后的对象转换为JSON格式。

using JsonApiSerializer.JsonApi;
using JsonApiSerializer.JsonApi.WellKnown;

var jsonApiDocument = new Document
{
    Data = new Resource
    {
        Type = "destination",
        Id = "1",
        Attributes = new Dictionary
        {
            { "name", destination.Name }
        },
        Relationships = new Dictionary
        {
            { "relationships", new RelationshipObject { Data = new List() } }
        }
    }
};

foreach (var relationship in destination.Relationships)
{
    jsonApiDocument.Data.Relationships["relationships"].Data.Add(new ResourceIdentifierObject
    {
        Type = "relationship",
        Id = relationship.Id.ToString()
    });
}

var json = JsonApiSerializer.JsonApi.JsonApiSerializer.Serialize(jsonApiDocument);

这样，您就可以通过AutoMapper和JsonApiSerializer.JsonApi.Relationship库来实现对象之间的映射和生成JSON格式的输出。请根据您的需求调整映射规则和JSON输出格式。