The series of MaxSAT Evaluations, organized yearly since 2006, has been the main forum for evaluating the state of the art in solvers for the Boolean optimization paradigm of maximum satisfiability (MaxSAT). This article provides an overview of the 2018 MaxSAT Evaluation, including a description of the main changes made in 2017 under a new organizing team, an overview of the solvers and benchmarks submitted in 2018, and detailed results of the 2018 evaluation.

MaxSAT Evaluation 2018: New Developments and Detailed Results

This paper introduces a new anytime algorithm for Weighted MaxSAT consisting of two main algorithmic components. First, we propose a new efficient polarity selection heuristic and an enhancement to the variable decision heuristic for SAT-based anytime Weighted MaxSAT solving (and, more generally, for solving any optimization problem with a SAT-based anytime algorithm). Second, we enhance an existing Bit-vector Optimization-based algorithm for solving Unweighted MaxSAT and generalize it to Weighted MaxSAT. Our resulting Weighted MaxSAT solver outscores the state-of-the-art solvers in the settings of both the 60-second and 300-second weighted incomplete tracks of MaxSAT Evaluation 2018. In addition, we describe a new application of incremental anytime Weighted MaxSAT solving: placement at the physical design stage of Computer-aided Design (CAD).

Anytime Weighted MaxSAT with Improved Polarity Selection and Bit-Vector Optimization

We present a MaxSAT algorithm designed to find high-quality solutions when faced with a tight time budget, e.g. five minutes. The motivation stems from the fact that, for many practical applications, time resources are limited and thus a ‘good solution’ suffices. We identify three weaknesses of the linear MaxSAT algorithm that prevent it from effectively computing low-violation solutions early in the search and develop a novel approach inspired by local search to address these issues. Our varying resolution method initially considers a rough view of the soft clauses (low resolution) and with time refines and adds the remaining constraints until the original problem is solved (high resolution). In addition, we combine the technique with solution-guided search. We experimentally evaluate our approach on test bed benchmarks from the MaxSAT Evaluation 2018 and show that improvements can be achieved over the baseline linear MaxSAT algorithm.

Techniques Inspired by Local Search for Incomplete MaxSAT and the Linear Algorithm: Varying Resolution and Solution-Guided Search

The optimization space of a compiler is the set of every possible sequence of optimizations that said compiler can use. The exploration of the optimization space of any mainstream compiler has been, for decades, hampered by the lack of benchmarks. However, recent efforts from different research groups have made available a large quantity of compilable code that can be, today, used to overcome this problem. In this paper, we use 15,000 programs from a public collection to explore the optimization space of LLVM, focusing on code-size reduction. This exploration reveals that the probability of beating the default optimization levels of LLVM with random sequences ranges from 10% (considering opt -Oz) to 19% (considering clang -Os). Yet, the distribution of probabilities is uneven across programs: the default levels work well for most programs, and poorly for a few. Based on these observations, we introduce the notion of an Optimization Cache, a table of programs to optimization sequences that can be used to support predictive compilation. We then use an optimization cache to build what we call a Default Covering Set: a small ensemble of optimization sequences that, once combined, tend to be good for any program. Optimization caches and default covering sets are used independently. The former, when applied onto MiBench, yield programs that are 11.9% smaller than programs produced by opt -Os, on average. The latter produce programs 12.5% smaller.

Exploring the space of optimization sequences for code-size reduction: insights and tools

Quantum computing (QC) is anticipated to provide a speedup over classical approaches for specific problems in optimization, simulation, and machine learning. With the advances in quantum computing toward practical applications, the need to analyze and compare different quantum solutions is increasing. While different low-level benchmarks exist, they often do not provide sufficient insights into real-world application-level performance. We propose an application-centric benchmark method and the QUantum computing Application benchmaRK (QUARK) framework to foster the investigation and creation of application benchmarks for QC. This paper establishes three significant contributions: (1) it makes a case for application-level benchmarks and provides an in-depth "pen and paper" benchmark formulation of two reference problems: robot path and vehicle option optimization from the industrial domain; (2) it proposes the open-source QUARK framework for designing, implementing, executing, and analyzing benchmarks; (3) it provides multiple reference implementations for these two reference problems based on different known, and where needed, extended, classical and quantum algorithmic approaches and analyzes their performance on different types of infrastructures.

QUARK: A Framework for Quantum Computing Application Benchmarking

Incomplete MaxSAT solving aims to quickly find a solution that attempts to minimize the sum of the weights of the unsatisfied soft clauses without providing any optimality guarantees. In this paper, we propose two approximation strategies for improving incomplete MaxSAT solving. In one of the strategies, we cluster the weights and approximate them with a representative weight. In another strategy, we break up the problem of minimizing the sum of weights of unsatisfiable clauses into multiple minimization subproblems. Experimental results show that approximation strategies can be used to find better solutions than the best incomplete solvers in the MaxSAT Evaluation 2017.

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Approximation Strategies for Incomplete MaxSAT

The formidable increase in the number of smaller and smarter embedded devices has compelled programmers to develop more and more specialized application programs for these systems. These resource intensive programs that have to be executed on limited memory systems make a strong case for compiler optimizations that reduce the executable size of programs. Standard compilers (like LLVM) offer an out-of-the-box -Oz optimization option—just a series of compiler optimization passes—that is specifically targeted for the reduction of the generated executable size. In this paper, we aim to analyze the effects of optimizations of LLVM compiler on the reduction of executable size. Specifically, we take the size of the executable as a metric and attempt to divide the -Oz series into logical groups and study their individual effects; while also study the effect of their combinations. Our preliminary study over SPEC CPU 2017 benchmarks gives us an insight into the comparative effect of the groups of passes on the executable size. Our work has potential to enable the user to tailor a custom series of passes so as to obtain the desired executable size.

An analysis of executable size reduction by LLVM passes

Incomplete MaxSAT solving aims to quickly find a solution that attempts to minimize the sum of the weights of unsatisfied soft clauses without providing any optimality guarantees. In this paper, we propose two approximation strategies for improving incomplete weighted MaxSAT solving. In one of the strategies, we cluster the weights and approximate them with a representative weight. In another strategy, we break up the problem of minimizing the sum of weights of unsatisfiable clauses into multiple minimization subproblems. We have implemented these strategies in a tool Open-WBO-Inc. Using the subproblem minimization strategy, Open-WBO-Inc placed first and second in the weighted incomplete tracks in the MaxSAT Evaluation 2018 whereas the strategy based on weight approximation was placed fourth. We compare these strategies with the best incomplete MaxSAT solvers on benchmarks taken from MaxSAT Evaluation 2017 and MaxSAT Evaluation 2018 and show that the strategies proposed are competitive with the best of the solvers.

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Open-WBO-Inc: Approximation Strategies for Incomplete Weighted MaxSAT

Incomplete MaxSAT solving aims to quickly find a solution that attempts to minimize the sum of the weights of the unsatisfied soft clauses without providing any optimality guarantees. 
In this paper, we propose two approximation strategies for improving incomplete MaxSAT solving. In one of the strategies, we cluster the weights and approximate them with a representative weight. In another strategy, we break up the problem of minimizing the sum of weights of unsatisfiable clauses into multiple minimization subproblems. Experimental results show that approximation strategies can be used to find better solutions than the best incomplete solvers in the MaxSAT Evaluation 2017.

Prateek Kumar

Papers

Approximation Strategies for Incomplete MaxSAT

An analysis of executable size reduction by LLVM passes

Open-WBO-Inc: Approximation Strategies for Incomplete Weighted MaxSAT

Approximation Strategies for Incomplete MaxSAT