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248 Massimiliano Vasilemultiagent exploration. The proposed approach is here tested at first on a well known suiteof multiobjective optimisation problems and compared to known algorithms and then on onestandard mission analysis problems and compared to some state of the art global optimisationtools either based on deterministic or stochastic methods2. Problem FormulationIn many practical cases both single and multiobjective problems require the identification ofmultiple optimal solutions and therefore to reconstruct a set of values and not just a singleone. Therefore the general problem, no matter if single or multiple objective, could be to finda set X of feasible solutions x such that a property P (x) is true for all x ∈ X ⊆ D:X = {x ∈ D | P (x)} (1)where the domain D is a hyperectangle defined by the upper and lower bounds on the componentsof the vector x:D = {x i | x i ∈ [b l i, b u i ] ⊆ R, i = 1, . . . , n} (2)All the solutions satisfying property P are here defined to be optimal with respect to P or P-optimal and X can be said to be a P-optimal set. Now property P might not identify a uniqueset therefore a global optimal set X o can be defined such that all the elements of X o dominatethe elements of any other X:X o = {x ∗ ∈ D | P (x ∗ ) ∧ ∀x ∈ X ⇒ x ∗ ≺ x} (3)where ≺ represents the dominance of the x ∗ solution over the x solution. In the case of singleobjective function, the set X may contain all solutions that are local minimisers or are belowa given value. In this case if more than one solution exists within the required domain D theinterest could be more to find a number of solutions forming the set X, rather than finding theglobal optimum with a high level of accuracy. In the case of multiobjective optimization, if Pis a dominance condition or Pareto optimality condition for the solution x then the solution isPareto-optimal if P (x) is true.3. Multiagent Collaborative SearchThe proposed multiagent collaborative search is based on the following principle: each oneof a set of agents explores locally the solution space within a hypercube (local environmentperception), at the end of each exploration session agents showing improvements communicate(collaborate) with the others, their findings. A pool of embryonic agents is maintainedin order to randomly generate new agents. A filter is used to select exploring and embryonicagents: if an agent falls out of the filter, is inserted in the pool.Each solution x is associated to an agent j and is represented by a string, of length n, containingin the first m components integer values and in the remaining n − m componentsreal values. This particular encoding allows the treatment of problems with a mixed integerrealdata structure. A hypercube S is associated to each agent x j , the hypercube, enclosinga region of the solution space surrounding the individual, is defined by a set of intervalsS = S 1 xS 2 xS n ⊆ D l , where x i ∈ S i . The solution space is then explored locally by acquiringinformation about the landscape within each region S and globally using a population ofagents. A sequence of actions is then performed by each agent x j according to a behaviouralscheme β j , in order to acquire a minimum set of samples sufficient to decide in which directionto take the next move. For an agent x j , a behavioural scheme is a collection of displacement