Randomised Algorithms and Constraint Logic

We propose a declarative-based implementation of randomised algorithms, which exploits the Constraint Logic Programming (CLP) paradigm. For the high-level formalisation of probabilistic programs expressing such algorithms we actually refer to a generalisation of CLP, namely the Probabilistic Concurrent Constraint Programming (PCCP) language, previously introduced in DW97]. This language provides a construct for probabilistic choice which allows us to express randomness in a program. PCCP also includes synchro-nisation and concurrency aspects. However, for the purpose of this work, the (probabilistic) CLP fragment of PCCP is suucient. We present a meta-interpreter for this language. This is just a standard prolog meta-interpreter, suitably extended so as to deal with probabilistic choice. For the constraint solving, the meta-interpreter exploits existing constraint handling facilities (and in more concrete terms to the SICStus 3.#6 system). This is possible because the design of PCCP does not require any additional structure on the underlying constraint system (e.g. fuzzy or belief systems). We demonstrate the use of this system for implementing randomised algorithms. In particular, we give an extensive treatment of two popular (generic) randomised algorithms, namely Simulated Annealing and Randomised Rounding, and we discuss some instantia-tions of these algorithms for solving two well-known optimisation problems, namely the travelling salesman (TSP) and the maximum satisfaction (MAX SAT) problem.