Objective as a Feature for Robust Search Strategies

Abstract

In constraint programming the search strategy entirely guides the solving process, and drastically affects the running time for solving particular problem instances. Many features have been defined so far for the design of efficient and robust search strategies, such as variables' domains, constraint graph, or even the constraints triggering fails. In this paper, we propose to use the objective functions of constraint optimization problems as a feature to guide search strategies. We define an objective-based function, to monitor the objective bounds modifications and to extract information. This function is the main feature to design a new variable selection heuristic, whose results validate human intuitions about the objective modifications. Finally, we introduce a simple but efficient combination of features, to incorporate the objective in the state-of-the-art search strategies. We illustrate this new method by testing it on several classic optimization problems, showing that the new feature often yields to a better running time and finds better solutions in the given time.

Automatic Streamlining for Constrained Optimisation

“…Furthermore, there are several methods for devising good search strategies for constrained optimisation problems. Recent research suggest using machine learning to design a promising search ordering [8], using solution density as a heuristic indicator [31] and a number of value ordering heuristics to find good solutions early [30,11]. Streamlining constraints can potentially be used in combination with the existing methods for devising good variable and value selection heuristics to achieve even better results.…”

Finding Good Subtrees for Constraint Optimization Problems Using Frequent Pattern Mining

“…Secondly, to examine the efficiency of FPMS, the following variable heuristics are considered: the classic dom/wdeg (DW) (Boussemart et al 2004) and ABSO, which is the combination of OBS (Palmieri and Perez 2018) and activitybased search (Michel and Van Hentenryck 2012). The following value heuristics are considered: BIVS (Fages and Prud'Homme 2017), the classic minimum value of domain (MinVS) and the OBS value selector (OBSVS) (Palmieri and Perez 2018). We have plugged FPMS into four search strategies including DW+BIVS, ABSO+BIVS, ABSO+MinVS and ABSO+OBSVS, which are recommended in (Fages and Prud'Homme 2017;Palmieri and Perez 2018).…”

“…The following value heuristics are considered: BIVS (Fages and Prud'Homme 2017), the classic minimum value of domain (MinVS) and the OBS value selector (OBSVS) (Palmieri and Perez 2018). We have plugged FPMS into four search strategies including DW+BIVS, ABSO+BIVS, ABSO+MinVS and ABSO+OBSVS, which are recommended in (Fages and Prud'Homme 2017;Palmieri and Perez 2018). All search strategies without FPMS are collectively coined as naive search.…”

“…Counting-Based Search (Pesant 2016) uses cost-based solution density to guide search. Objective-Based Selector (OBS) (Palmieri and Perez 2018) uses objective variables as a feature for decisions within search strategies. To find good solutions early, the Bound-Impact Value Selector (BIVS) (Fages and Prud'Homme 2017) chooses the value of a variable that would lead to the best objective bound after a propagation.…”

Learning Objective Boundaries for Constraint Optimization Problems

“…Others rely on branching heuristics and constraint propagation to find close bounds early [33]. Recent works have also considered including the objective variable as part of the search and branch heuristic [16,31]. By exploiting a trained ML model, our approach Bion adds an additional bounding step before the solver execution but it does not replace the solvers' bounding mechanisms.…”