Abstract. In this paper, we extend the Support Based Distributed Optimization (SBDO) algorithm to support problems which do not have a total pre-order over the set of solutions. This is the case in common real life problems that have multiple objective functions. In particular, decision support problems. These disparate objectives are not well supported by existing Distributed Constraint Optimization Problem (DCOP) techniques, which assume a single cost or utility function. As a result, existing Distributed COP techniques (with some recent exceptions) require that all agents subscribe to a common objective function and are therefore unsuitable for settings where agents have distinct, competing objectives. This makes existing constraint optimization technologies unsuitable for many decision support roles, where the decision maker wishes to observe the different trade-offs before making a decision.Key words: Multi-objective Optimisation, Constraints, Semi-Rings.AMS subject classifications. 65K10, 97H401. Introduction. The simple approach of modelling DCOPs, where the cost/utility of a solution is measured as a single real number, is quite restrictive. This approach can only represent problems where there is a total pre-order over the solutions. Many real world problems only have a partial order over the solutions. Examples of these problems include problems with multiple objectives and problems with qualitative valuations. To further complicate things, a problem may include a mix of qualitative and quantitive valuations.Bistarelli's c-semiring framework [3] is very successful for modelling problems in the Constraint Optimisation Problem (COP) domain. The Distributed Constraint Optimisation Problem (DCOP) domain introduces several new modelling challenges over centralised problems. These challenges include agent responsibility, privacy, cooperating/competing agents and no global objective. Further, these challenges lead to classes of DCOP problems which have not been addressed in the literature so far. The existing modelling frameworks do not support these new classes of problems, so we are proposing a new modelling framework inspired by c-semirings.We have identified three classes of problems within the DCOP domain which can not be adequately described using c-semirings; equitable problems, maximisation problems and 'committee' problems. For equitable problems, we specifically refer to problems with an objective of the form 'minimise the maximum difference between the best and worst criteria'. Examples of these problems include distributing rewards to a team, assigning jobs to workers and minimise the impact of flood mitigation. Some examples of maximisation problems include maximise profit within a supply chain, maximise the value of targets tracked in a sensor network and maximise the area a team of drones can search. Committee problems are when a group of agents must agree on one (or more) shared decisions. This includes problems such as deciding on a requirements specification or a CEO's bonus package.Equitabl...