SAT-decoding in evolutionary algorithms for discrete constrained optimization problems

Abstract

Abstract-For complex optimization problems, several population-based heuristics like Multi-Objective Evolutionary Algorithms have been developed. These algorithms are aiming to deliver sufficiently good solutions in an acceptable time. However, for discrete problems that are restricted by several constraints it is mostly a hard problem to even find a single feasible solution. In these cases, the optimization heuristics typically perform poorly as they mainly focus on searching feasible solutions rather than optimizing the objectives.In this paper, we propose a novel methodology to obtain feasible solutions from constrained discrete problems in populationbased optimization heuristics. At this juncture, the constraints have to be converted into the Propositional Satisfiability Problem (SAT). Obtaining a feasible solution is done by the DPLL algorithm which is the core of most modern SAT solvers. It is shown in detail how this methodology is implemented in Multiobjective Evolutionary Algorithms. The SAT solver is used to obtain feasible solutions from the genetic encoded information on arbitrarily hard solvable problems where common methods like penalty functions or repair strategies are failing. Handmade test cases are used to compare various configurations of the SAT solver. On an industrial example, the proposed methodology is compared to common strategies which are used to obtain feasible solutions.

Combined system synthesis and communication architecture exploration for MPSoCs

“…With the binary encoding and linear constraint from the previous section, the design space exploration problem as stated in Def. 1 can be carried out efficiently by using the heuristic SAT decoding optimization approach [9]. This hybrid optimization approach based on an Evolutionary Algorithm and a PB (pseudo boolean) solver allows the optimization of multiple conflicting and non-linear objectives under linear constraints in a binary search space.…”

“…Former approaches rely on straightforward heuristic optimization algorithms, i.e., Evolutionary Algorithms and Simulated Annealing, and do in general not perform well for such hard constrained problems. In order to solve this problem appropriately, the design space is encoded symbolically by linear constraints with binary variables, and a state-of-the-art hybrid optimization approach [9,10] is used to enable an adequate optimization of complex systems. The remainder of the paper is organized as follows: Section 2 introduces the graph-based exploration model and its symbolic encoding.…”

A Feasibility-Preserving Crossover and Mutation Operator for Constrained Combinatorial Problems

“…In case of p(x) = 0, the greedy algorithm stops since x is a feasible solution. The SAT decoding approach [2] is in the following denoted as satdec. The feasibility-preserving approach proposed in this work is denoted as satop.…”

“…Constraints that are not linearizable have to be handled by common methods like penalty functions. However, many problems have linear constraints only [1] or are dominated by the number of linear constraints [2]. In the following, this paper assumes that all constraints are linear.…”

“…In [2], a decoding strategy [6] known as SAT decoding is presented that overcomes these drawbacks. By using a Pseudo-Boolean (PB) solver [7] as a decoder, this method always obtains feasible solutions by mapping from a bounded search space to feasible solutions.…”