Automated semantic web service composition is one of the critical research challenges of service-oriented computing, since it allows users to create an application simply by specifying the inputs that the application requires, the outputs it should produce, and any constraints it should respect. The composition problem has been handled using a variety of techniques, from Artificial Intelligence (AI) planning to optimization algorithms. However no approach so far has focused on handling three composition dimensions simultaneously , producing solutions that are: (1) fully functional (i.e. fully executable) by using a mechanism of semantic matching between the services involved in the solutions, (2) are optimised according to non-functional Quality of Service (QoS) measurements , and (3) respect global QoS constraints. This paper presents a novel approach based on a Harmony Search (HS) algorithm that addresses these three dimensions simultaneously through a fitness function, to select the optimal or near optimal solution in semantic web service composition. In our approach, the search space is modeled as a Planning Graph structure which encodes all the possible composition solutions for a given user request. To improve the selection process we have compared the original Harmony Search algorithm with its recently developed variants Improved Harmony Search (IHS) algorithm and Global Best Harmony Search (GHS) algorithm. An experimentation of the approach conducted with an extended version of the Web Service Challenge 2009 dataset showed that: 1) our approach is efficient and effective to extract the optimal or near optimal composition in diverse scenarios; and 2) both variants IHS and GHS algorithms have brought improvements in terms of fitness and execution time.