Improved Construction Heuristics and Iterated Local Search for the Routing and Wavelength Assignment Problem

Abstract

Abstract. This paper deals with the design of improved construction heuristics and iterated local search for the Routing and Wavelength Assignment problem (RWA). Given a physical network and a set of communication requests, the static RWA deals with the problem of assigning suitable paths and wavelengths to the requests. We introduce benchmark instances from the SND library to the RWA and argue that these instances are more challenging than previously used random instances. We analyze the properties of several instances in detail and propose an improved construction heuristic to handle 'problematic' instances. Our iterated local search finds the optimum for most instances.

A Distributed Memetic Algorithm for the Routing and Wavelength Assignment Problem

“…In [10], we presented a new set of benchmark instances, on which an iterated local search (ILS) algorithm was applied. The ILS consists of a local search (LS) and a mutation operator.…”

“…1) which is used to create a population-based memetic algorithm (MA) for the static RWA. Based on the ILS presented in [10], the MA adds the feature to handle populations of solutions and to recombine two solutions to one offspring solution.…”

“…pG,s(r) ← ΨG,s(r, λs) route request on the first possible wavelength 12: return s or a mutation step as introduced in [10] is performed. The mutation strength can be varied, the actually used strategy is 10%↓ 2 % (starting with mutation strength 10 % and decreasing in each iteration by 2 % until reaching the fixed minimum of 1 %) as in [11].…”

“…The mutation strength can be varied, the actually used strategy is 10%↓ 2 % (starting with mutation strength 10 % and decreasing in each iteration by 2 % until reaching the fixed minimum of 1 %) as in [11]. Once a provisional offspring has been created, this individual is improved by the LS used in [10]. For each individual of the next generation, offspring and parent are compared and the better one is kept.…”

“…2. W. l. o. g. parent solution a is better than b as defined by the length-lex ordering from [10]. The offspring solution s is initialized as a copy of a.…”