Conditional Markov Chain Search for the Simple Plant Location Problem Improves Upper Bounds on Twelve Körkel–Ghosh Instances

Abstract

We address a family of hard benchmark instances for the Simple Plant Location Problem (also known as the Uncapacitated Facility Location Problem). The recent attempt by Fischetti et al. [16] to tackle the Körkel-Ghosh instances resulted in seven new optimal solutions and 22 improved upper bounds. We use automated generation of heuristics to obtain a new algorithm for the Simple Plant Location Problem. In our experiments, our new algorithm matched all the previous best known and optimal solutions, and further improved 12 upper bounds, all within shorter time budgets compared to the previous efforts.Our algorithm design process is split into two phases: (i) development of algorithmic components such as local search procedures and mutation operators, and (ii) composition of a metaheuristic from the available components. Phase (i) requires human expertise and often can be completed by implementing several simple domain-specific routines known from the literature. Phase (ii) is entirely automated by employing the Conditional Markov Chain Search (CMCS) framework. In CMCS, a metaheuristic is flexibly defined by a set of parameters, called configuration. Then the process of composition of a metaheuristic from the algorithmic components is reduced to an optimisation problem seeking the best performing CMCS configuration.We discuss the problem of comparing configurations, and propose a new efficient technique to select the best performing configuration from a large set. To employ this method, we restrict the original CMCS to a simple deterministic case that leaves us with a finite and manageable number of meaningful configurations.

Algorithm Configuration: Learning Policies for the Quick Termination of Poor Performers

“…We used CMCS, a recent framework that defines the behaviour of a multicomponent optimisation algorithm with a set of numeric parameters [2,3]. We used three problem domains: the Simple Plant Location Problem (SPLP) [2], the Far From Most String Problem (FFMSP) (the details of our components, testbed, etc. are not yet published) and the Bipartite Boolean Quadratic Problem (BBQP) [3].…”

“…We generated all 'meaningful' 3-component configurations with deterministic control mechanism, thus ending up with a finite number of configurations. We do not include details of exactly what these mean (see [3,2]), as for the purposes of this paper, these can simply be regarded as a categorical set of potential options, and defining the "C-space". The goal of the work is to find configurations that are the best performers, with respect to the long-run L-space, but exploiting their properties with respect to the short-run S-space in order to reduce the overall time budget.…”

Conditional Markov Chain Search for the Generalised Travelling Salesman Problem for Warehouse Order Picking

“…Conditional Markov Chain Search (CMCS) is a modern framework designed for automated generation of optimisation heuristics [9]- [11]. It is a single-point metaheuristic based on multiple components treated as black boxes.…”

“…Testing all these configurations would be impractical. We follow the idea proposed in [11] and only consider 'meaningful' configurations. We further restrict ourselves to configurations that use exactly three components.…”