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what will happen when the maximum velocities are large, with vij (t) << Vmax,j for all time steps, t = 1, , nt This will limit the maximum range of velocities, and thus the chances of a position to change to bit 1 For example, if Vmax,j = 10, and vij (t) = 5, then the normalized velocity is vij (t) = 05, with only a 50% chance that xij (t + 1) = 1 This normalization approach may therefore cause premature convergence to bad solutions due to limited exploration abilities A more natural normalization of velocities is obtained by using the sigmoid function That is, 1 vij (t) = sig(vij (t)) = (1689) 1 + e vij (t) Using equation (1689), the position update changes to xij (t + 1) = 1 if r3j (t) < sig(vij (t + 1)) 0 otherwise (1690)

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with r3j (t) U (0, 1) The velocity, vij (t), is now a probability for xij (t) to be 0 or 1 For example, if vij (t) = 0, then prob(xij (t + 1) = 1) = 05 (or 50%) If vij (t) < 0, then prob(xij (t + 1) = 1) < 05, and if vij (t) > 0, then prob(xij (t + 1) = 1) > 05 Also note that prob(xij (t) = 0) = 1 prob(xij (t) = 1) Note that xij can change even if the value of vij does not change, due to the random number r3j in the equation above It is only the calculation of position vectors that changes from the real-valued PSO The velocity vectors are still real-valued, with the same velocity calculation as given in equation (162), but including the inertia weight That is, xi , yi , y Bnx while vi Rnx The binary PSO is summarized in Algorithm 1613 Algorithm 1613 binary PSO Create and initialize an nx -dimensional swarm; repeat for each particle i = 1, , ns do if f (xi ) < f (yi ) then yi = xi ; end y if f (yi ) < f ( ) then y = yi ; end end for each particle i = 1, , ns do update the velocity using equation (162); update the position using equation (1690); end until stopping condition is true;

12 ENTERPRISE PERFORMANCE VERSUS ENTERPRISE INTEGRATION CEOs and department secretaries talk about enterprise performance When speaking with IT professionals, they talk enterprise integration What s the difference Answering this question takes considerable explanation, although in so doing, we can introduce some perspectives that will ultimately permit our readers to appreciate the focus on smart data to which we are headed Enterprise Integration There are two principal de nitions on the Web, for instance One says that enterprise integration (EI) is the alignment of strategies, business processes, and information systems, technologies, and data across organizational boundaries We discussed this with electronic magazine publisher guru Bob Thomas, who had a magazine called Business Integration Journal He changed the name to Align Journal, emphasizing that alignment of IT strategy and enterprise strategy is essential to optimizing performance We subscribe to this idea Another de nition of enterprise integration refers to internal coordination processes among different core activities The rst de nition expresses a more external and global view, while the second de nition is more inwardly focused The trouble with inwardly focused enterprise integration is that the result is often stovepiping What is wrong with stovepiping It adds extra costs and often results in islands of automation that require extra effort, ranging from manual intervention to extra programming and maintenance to share and process data A popular notion the past few years is transformation Applied to the enterprise, it means qualitative change This was the primary topic in the 2008 political campaign and is a central theme of the new presidency According to some, transformation applied to defense is the term used for new methods in warfare integrating communication and technology We think that it is much more and note the absence of the key term, data, from this de nition We advised the DoD Business Transformation Of ce that transformation requires an enterprise view With that we developed what we called the service-oriented enterprise (SOE) management paradigm We draw from this experience to explain our views about enterprise integration SOE is a management paradigm and strategy directed at improving performance from enterprise integration and from engineering information for interoperability The Electronic Logistics Information Trading Exchange (ELITE) was a speci c program managed by the Of ce of Secretary of Defense, Unique Identi er (UID) Program and in concert with the Logistics Enterprise Service Program Of ce at the Defense Logistics Agency (DLA).

This section describes a few PSO variations for solving constrained problems, multiobjective optimization problems, problems with dynamically changing objective functions and to locate multiple solutions

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