[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-82634-en":3,"doc-seo-82634-105":29,"detail-sidebar-cat-0-en-105":91},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":20,"is_deleted":4,"is_public":20,"is_downloadable":20,"audit_status":20,"page_count":21,"language":22,"language_code":23,"site_id":24,"html_lang":23,"table_of_contents":25,"faqs":26,"seo_title":13,"seo_description":14,"update_tm":27,"read_time":28},82634,16904993612988,"Olivia Brown","https://ap-avatar.wpscdn.com/davatar_a8503ba1806abce46bf441b54a3ca4cd",8,"Research & Report","When Algebraic Symmetry Breaking Meets Solvers An Experimental Study","An experimental evaluation compares automatically generated polynomial symmetry-breaking constraints for integer linear programs across multiple solver execution modes. Building on an algebraic method introduced at ISSAC 2026, the study contrasts native quadratic handling, solver-internal reformulation, and explicit linearization on near half-capacity bin-packing benchmarks. Results from mathematical programming and SMT engines show solver-dependent effectiveness: compact quadratic breaker families can improve performance, while linearization, large breaker sets, or reformulations can negate gains by increasing model size or degrading search behavior.","arXiv :2607 .0 1726v 1 [ cs . SC] 2 Jul 2026  \nWhen Algebraic Symmetry Breaking Meets Solvers: An Experimental Study  \nM˘ad˘alina Era¸scu 1 and Johannes Middeke2  \n1 Faculty of Informatics, West University of Timis, oara, Timis, oara, Romania  \n[madalina.erascu@e-uvt.ro](madalina.erascu@e-uvt.ro)  \n2 Temple University, Japan Campus, Tokyo, Japan  \n[johannes.middeke@tuj.temple.edu](johannes.middeke@tuj.temple.edu)  \nAbstract  \nWe present an experimental evaluation of automatically generated polynomial symmetry breaking constraints for integer linear programs. Starting from the method that we introduced at the International Symposium on Symbolic and Algebraic Computation (ISSAC) 2026, we compare solver native quadratic handling, solver-internal reformulation, and explicit linearization on near half-capacity bin-packing benchmarks.  \nExperiments with several mathematical programming solvers and satisfiability modulo theory solvers show that the effectiveness of polynomial symmetry breaking is strongly solver-dependent. Compact quadratic breaker families can improve performance, whereas linearization, large breaker sets, or solver reformulations may offset these gains through increased model size or less favorable search behavior. These results suggest that automatically generated symmetry breakers should be evaluated in a solver-aware manner rather than treated as solver-independent additions to a model.  \n1 Introduction  \nOptimization and automated reasoning, including constraint programming [9, 19], mixedinteger programming [15, 13 , 18], satisfiability [1, 4], and satisfiability modulo theory [6], typically treat symmetries as redundant branches of the search tree to be pruned. A common way to address this redundancy is to add constraints which eliminate as many symmetric solutions as possible. These are the so-called symmetry breaking constraints which can be exploited, for example, in a static manner [17, 6], i.e., adding constraints a priori to restrict feasibility to orbit representatives.  \nIn [7], we introduced an algebraic method for automatically generating symmetry-breaking constraints. Given the symmetry group of an integer linear program and a polynomial template h, the method constructs breaker families of the form h (Px) − h(x) ≤ 0. Unlike existing constructions, our method naturally yields both linear and nonlinear breakers and can be implemented with standard computer algebra tools. Experiments on bin-packing instances showed that quadratic breakers can outperform both linear variants and Gurobi’s [10] built-in symmetry handling.  \nThese results raise a natural question: do the observed gains come from the breakers themselves, or from how a specific solver processes them? This is particularly important for quadratic breakers, since some solvers handle quadratic constraints natively, some reformulate them internally, and others require linear constraints, hence explicit linearization must be applied.  \nThe goal of this paper is to study this solver dependence experimentally with different types of solvers: mathematical programming solvers such as Gurobi [10], CPLEX [14], and SCIP [12], the nonlinear and combinatorial optimization solver Hexaly [11], and the SMT solver Z3 [5] .  \nWe make three contributions: (1) an experimental comparison of native quadratic, solverreformulated, and explicitly linearized polynomial symmetry breakers; (2) evidence that compact quadratic breakers can help, but their effect is solver- and size-dependent; (3) a reproducible benchmark suite and artifact [8] for evaluating solver-aware symmetry breaking.  \nOur experiments show that polynomial symmetry breaking is highly solver-sensitive. Compact quadratic breaker families (few variables, few permutations) often remain beneficial when handled natively, whereas reformulation or linearization may introduce variables and constraints that reduce or eliminate this advantage. Moreover, the same breaker family may improve performance for one so","cbCaiiAdScWOsyvK","https://ap.wps.com/l/cbCaiiAdScWOsyvK","pdf",443841,1,13,"English","en",105,"# Introduction\n## Background: Polynomial Symmetry Breaking","[{\"question\":\"What symmetry-breaking approach is evaluated in the study?\",\"answer\":\"The paper evaluates automatically generated polynomial symmetry-breaking constraints for integer linear programs, constructed using an algebraic method based on a polynomial template and the ILP symmetry group.\"},{\"question\":\"How do the experiments compare different solver treatments of symmetry breakers?\",\"answer\":\"They compare native quadratic handling, solver-internal reformulation, and explicit linearization of the polynomial symmetry breakers across several mathematical programming solvers and SMT solvers.\"},{\"question\":\"Why might solver-aware evaluation matter for polynomial symmetry breakers?\",\"answer\":\"Because effectiveness depends on how a solver preprocesses and searches, the same breaker family can help one solver while slowing another, especially when linearization or reformulation increases model size or changes search behavior.\"}]",1784181941,33,{"code":4,"msg":30,"data":31},"ok",{"site_id":24,"language":23,"slug":32,"title":13,"keywords":33,"description":14,"schema_data":34,"social_meta":86,"head_meta":88,"extra_data":90,"updated_unix":27},"when-algebraic-symmetry-breaking-meets-solvers-an-experimental-study","",{"@graph":35,"@context":85},[36,53,68],{"@type":37,"itemListElement":38},"BreadcrumbList",[39,43,47,50],{"item":40,"name":41,"@type":42,"position":20},"https://docshare.wps.com","Home","ListItem",{"item":44,"name":45,"@type":42,"position":46},"https://docshare.wps.com/document/","Document",2,{"item":48,"name":12,"@type":42,"position":49},"https://docshare.wps.com/document/research-report/",3,{"item":51,"name":13,"@type":42,"position":52},"https://docshare.wps.com/document/when-algebraic-symmetry-breaking-meets-solvers-an-experimental-study/82634/",4,{"url":51,"name":13,"@type":54,"author":55,"headline":13,"publisher":57,"fileFormat":60,"inLanguage":23,"description":14,"dateModified":61,"datePublished":62,"encodingFormat":60,"isAccessibleForFree":63,"interactionStatistic":64},"DigitalDocument",{"name":9,"@type":56},"Person",{"url":40,"name":58,"@type":59},"DocShare","Organization","application/pdf","2026-07-17","2026-07-16",true,{"@type":65,"interactionType":66,"userInteractionCount":20},"InteractionCounter",{"@type":67},"ViewAction",{"@type":69,"mainEntity":70},"FAQPage",[71,77,81],{"name":72,"@type":73,"acceptedAnswer":74},"What symmetry-breaking approach is evaluated in the study?","Question",{"text":75,"@type":76},"The paper evaluates automatically generated polynomial symmetry-breaking constraints for integer linear programs, constructed using an algebraic method based on a polynomial template and the ILP symmetry group.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"How do the experiments compare different solver treatments of symmetry breakers?",{"text":80,"@type":76},"They compare native quadratic handling, solver-internal reformulation, and explicit linearization of the polynomial symmetry breakers across several mathematical programming solvers and SMT solvers.",{"name":82,"@type":73,"acceptedAnswer":83},"Why might solver-aware evaluation matter for polynomial symmetry breakers?",{"text":84,"@type":76},"Because effectiveness depends on how a solver preprocesses and searches, the same breaker family can help one solver while slowing another, especially when linearization or reformulation 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