added text on optima and on bounds of the objective function

bibliography/bibliography.bib

@@ -18,20 +18,24 @@ @string { winter
 
 %%authors
 @string { a_aaronson_scott = "Scott Aaronson" }
+@string { a_aarts_emile_h_l = "Emile H.\ L.\ Aarts" }
 @string { a_adams_joseph = "Joseph Adams" }
 @string { a_applegate_david_lee = "David Lee Applegate" }
 @string { a_arantes_leonardo = "Leonardo Arantes" }
 @string { a_bachem_achim = "Achim Bachem" }
 @string { a_bachmann_paul_gustav_heinrich = "Paul Gustav Heinrich Bachmann" }
+@string { a_bai_ruibin = "Ruibin Bai" }
 @string { a_balas_egon = "Egon Balas" }
-@string { a_brabazon_anthony = "Anthony Brabazon" }
 @string { a_banerji_ranan_b = "Ranan B.\ Banerji" }
 @string { a_beasley_john_edward = "John Edward Beasley" }
 @string { a_beckmann_martin = "Martin Beckmann" }
 @string { a_bernaden_john = "John Bernaden" }
 @string { a_bixby_robert_e = "Robert E.\ Bixby" }
 @string { a_blazewicz_jacek = "Jacek B{\l}a{\.z}ewicz" }
 @string { a_bohlinger_jean_d = "Jean D.\ Bohlinger" }
+@string { a_brabazon_anthony = "Anthony Brabazon" }
+@string { a_bronstein_alexander_m = "Alexander M.\ Bronstein" }
+@string { a_bronstein_michael_m = "Michael M.\ Bronstein" }
 @string { a_bui_tung_x = "Tung X.\ Bui" }
 @string { a_burkard_rainer_e = "Rainer E.\ Burkard" }
 @string { a_cagnoni_stefano = "Stefano Cagnoni" }
@@ -44,6 +48,7 @@ @string { a_coffman_edward_g
 @string { a_cook_stephen_arthur = "Stephen Arthur Cook" }
 @string { a_cook_william_john = "William John Cook" }
 @string { a_davis_jim = "Jim Davis" }
+@string { a_de_causmaecker_patrick = "Patrick {De Causmaecker}" }
 @string { a_delorme_maxence = "Maxence Delorme" }
 @string { a_demirkol_ebru = "Ebru Demirkol" }
 @string { a_dhakal_sandeep = "Sandeep Dhakal" }
@@ -63,12 +68,14 @@ @string { a_fogel_david_b
 @string { a_friedrich_tobias = "Tobias Friedrich" }
 @string { a_garey_michael_r = "Michael R.\ Garey" }
 @string { a_geihs_kurt = "Kurt Geihs" }
+@string { a_gharbi_anis = "Anis Gharbi" }
 @string { a_giacobini_mario = "Mario Giacobini" }
 @string { a_gonzalez_arce_teofilo_francisco = "Teofilo Francisco {Gonzalez Arce}" }
 @string { a_gorldt_christian = "Christian Gorldt" }
 @string { a_goycoolea_marcos = "Marcos Goycoolea" }
 @string { a_graham_ronald_lewis = "Ronald Lewis Graham" }
 @string { a_graves_stephen_c = "Stephen C.\ Graves" }
+@string { a_grendrau_michel = "Michel Gendreau" }
 @string { a_groetschel_martin = "Martin Gr{\"o}tschel" }
 @string { a_gutin_gregory_z = "Gregory Z.\ Gutin" }
 @string { a_hammer_peter_l = "Peter L.\ Hammer" }
@@ -78,31 +85,39 @@ @string { a_henning_andre
 @string { a_hermann_mario = "Mario Hermann" }
 @string { a_iori_manuel = "Manuel Iori" }
 @string { a_jain_anant_singh = "Anant Singh Jain" }
+@string { a_john_robert_i = "Robert I.\ John" }
 @string { a_johnson_david_stiffler = "David Stifler Johnson" }
 @string { a_johnson_e_l = "E.\ L.\ Johnson" }
 @string { a_johnson_selmer_martin = "Selmer Martin Johnson" }
 @string { a_juenger_michael = "Michael J{\"u}nger" }
 @string { a_karp_richard_m = "Richard M.\ Karp" }
+@string { a_kendall_graham = "Graham Kendall" }
 @string { a_klein_robert = "Robert Klein" }
+@string { a_kimmel_ron = "Ron Kimmel" }
 @string { a_kobayashi_shigenobu = "Shigenobu Kobayashi" }
 @string { a_koopmans_tjalling_charles = "Tjalling Charles Koopmans" }
 @string { a_korte_bernhard_h = "Bernhard H.\ Korte" }
+@string { a_labidi_mohamed = "Mohamed Labidi" }
+@string { a_laborie_philippe = "Philippe Laborie" }
 @string { a_landau_edmund = "Edmund Landau" }
 @string { a_lawler_eugene_leighhton = "Eugene Leighton Lawler" }
 @string { a_lawrence_stephen_r = "Stephen R.\ Lawrence" }
 @string { a_lenstra_jan_karel = "Jan Karel Lenstra" }
+@string { a_li_jiawei = "Jiawei Li" }
 @string { a_liu_weichen = "Weichen Liu" }
 @string { a_liu_zhen = "Zhen Liu" }
 @string { a_lodi_anrea = "Andrea Lodi" }
 @string { a_machado_penousal = "Penousal Machado" }
 @string { a_manderick_bernard = "Bernard Manderick" }
 @string { a_manner_reinhard = "Reinhard M{\"a}nner" }
 @string { a_martello_silvano = "Silvano Martello" }
+@string { a_mccollum_barry = "Barry {McCollum}" }
 @string { a_mccormack_jon = "Jon {McCormack}" }
 @string { a_meeran_sheik = "Sheik Meeran" }
 @string { a_mehta_sanjay_v = "Sanjay V.\ Mehta" }
 @string { a_michalewicz_matthew = "Matthew Michalewicz" }
 @string { a_michalewicz_zbigniew = "Zbigniew Michalewicz" }
+@string { a_michel_laurent = "Laurent Michel" }
 @string { a_miller_raymond_e = "Raymond E.\ Miller" }
 @string { a_monaci_michele = "Michele Monaci" }
 @string { a_muth_john_f = "John F.\ Muth" }
@@ -122,13 +137,16 @@ @string { a_porter_james
 @string { a_potts_chris_n = "Chris N.\ Potts" }
 @string { a_preuss_mike = "Mike Preu{\ss}" }
 @string { a_punnen_abraham_p = "Abraham P.\ Punnen" }
+@string { a_qu_rong = "Rong Qu" }
 @string { a_reinelt_gerhard = "Gerhard Reinelt" }
 @string { a_reinhard_kai = "Kai Reinhard" }
 @string { a_rinnooy_kan_a_h_k = "Alexander Hendrik George {Rinnooy Kan}" }
 @string { a_rothlauf_franz = "Franz Rothlauf" }
+@string { a_sabar_nasser = "Nasser Sabar" }
 @string { a_sahni_sartaj = "Sartaj Sahni" }
 @string { a_sarli_michael = "Michael Sarli" }
 @string { a_scheithauer_guntram = "Guntram Scheithauer" }
+@string { a_shaw_paul = "Paul Shaw" }
 @string { a_shmoys_david_b = "David B.\ Shmoys" }
 @string { a_shylo_oleg_v = "Oleg V.\ Shylo" }
 @string { a_sprague_jr_ralph_h = "Ralph H.\ {Sprague Jr.}" }
@@ -143,7 +161,10 @@ @string { a_toth_paolo
 @string { a_ullman_jeffrey_d = "Jeffrey D.\ Ullman" }
 @string { a_uzsoy_reha = "Reha Uzsoy" }
 @string { a_vaccari_renzo = "Renzo Vaccari" }
+@string { a_vaessens_rob_j_m = "Rob J.\ M.\ Vaessens" }
 @string { a_van_hoorn_jelke_jeron = "Jelke Jeroen {van Hoorn}" }
+@string { a_vanden_berghe_greet = "Greet {Vanden Berghe}" }
+@string { a_vilim_petr = "Petr Vil{\'i}m" }
 @string { a_weise_thomas = "Thomas Weise" }
 @string { a_whitley_l_darrell = "L.\ Darrell Whitley" }
 @string { a_wilson_james_m = "James M.\ Wilson" }
@@ -152,6 +173,7 @@ @string { a_wu_david_s
 @string { a_wu_yuezhong = "Yuezhong Wu" }
 @string { a_yamada_takeshi = "Takeshi Yamada" }
 @string { a_yang_shengxiang = "Shengxiang Yang" }
+@string { a_yee_angelina = "Angelina Yee" }
 @string { a_zawack_daniel = "Daniel Zawack" }
 @string { a_zipkin_paul_h = "Paul H.\ Zipkin" }
 
@@ -180,8 +202,10 @@ @string { p_springer_nature_america
 @string { p_springer_nature_switzerland = "{Springer Nature America {AG}}" }
 @string { p_springer_new_york = "{Springer}" }
 @string { p_springer_science_business_media = "{Springer Science+Business Media, {LLC}}" }
+@string { p_springer_switzerland = "{Springer}" }
 @string { p_springer_verlag_gmbh = "{Springer-Verlag {GmbH}}" }
 @string { p_taylor_and_francis = "{Taylor and Francis Ltd.}" }
+@string { p_technion_cs = "{Technion {--} Israel Institute of Technology}, {Computer Science Department}" }
 @string { p_teubner_b_g = "{B.\ G.\ Teubner}" }
 @string { p_university_of_applied_sciences_western_switzerland = "{University of Applied Sciences of Western Switzerland}" }
 @string { p_university_of_waterloo_dco = "{University of Waterloo, Department of Combinatorics and Optimization}" } 
@@ -200,7 +224,9 @@ @string { l_germany_heidelberg
 @string { l_germany_jena = "{{Jena}, {Th{\"u}ringen}, {Germany}}" }
 @string { l_germany_leipzig = "{{Leipzig}, {Sachsen}, {Germany}}" }
 @string { l_germany_tubingen = "{{T{\"u}bingen}, {Baden-W{\"u}rttemberg}, {Germany}}" }
+@string { l_israel_haifa = "{Israel}, {Haifa}" }
 @string { l_netherlands_amsterdam = "{{Amsterdam}, {The Netherlands}}" }
+@string { l_spain_barcelona = "{{Barcelona}, {Spain}}" }
 @string { l_switzerland_cham = "{{Cham}, {Switzerland}}" }
 @string { l_switzerland_yverdon = "{{Yverdon}, {Switzerland}}" }
 @string { l_usa_atlanta = "{{Atlanta}, {GA}, {USA}}" }
@@ -246,8 +272,10 @@ @string { pa_springer_nature_america
 @string { pa_springer_nature_switzerland = l_switzerland_cham }
 @string { pa_springer_new_york = l_usa_new_york }
 @string { pa_springer_science_business_media = l_switzerland_cham }
+@string { pa_springer_switzerland = l_switzerland_cham }
 @string { pa_springer_verlag_gmbh = "{{Berlin/Heidelberg}, {Germany}}" }
 @string { pa_taylor_and_francis = l_uk_london }
+@string { pa_technion_cs = l_israel_haifa }
 @string { pa_teubner_b_g = l_germany_leipzig }
 @string { pa_university_of_applied_sciences_western_switzerland = l_switzerland_yverdon }
 @string { pa_university_of_waterloo_dco = l_canada_waterloo }
@@ -280,6 +308,13 @@ @xdata{j_ejor
  address = pa_elsevier
 }
 
+@xdata{j_enidm,
+ journal = {Electronic Notes in Discrete Mathematics},
+ issn = {1571-0653},
+ publisher = p_elsevier,
+ address = pa_elsevier
+}
+
 @xdata{j_ijoc,
  journal = {{{INFORMS} Journal on Computing}},
  issn = {1091-9856},
@@ -413,6 +448,21 @@ @xdata{ser_lncs
  issn = {0302-9743},
 }
 
+@xdata{ser_lntcs,
+ series = {Theoretical Computer Science and General Issues ({LNTCS}), sub-series of Lecture Notes in Computer Science ({LNCS})},
+ xdata = {ser_lncs},
+ issn = {2512-2010},
+ publisher = p_springer_switzerland,
+ address = pa_springer_switzerland
+}
+
+@xdata{ser_mics,
+ series = {Monographs in Computer Science},
+ publisher = p_springer_new_york,
+ address = pa_springer_new_york,
+ issn = {0172-603X}
+}
+
 @xdata{ser_orcsis,
  series = {Operations Research/Computer Science Interfaces Series},
  publisher = p_springer_new_york,
@@ -519,6 +569,27 @@ @article{B1990OLDTPBEM
  doi = {10.1057/jors.1990.166}
 }
 
+@incollection{BB2009NO,
+ author = a_bronstein_alexander_m # { and } # a_bronstein_michael_m,
+ title = {Numerical Optimization},
+ booktitle = {Project {TOSCA} {--} Tools for Non-Rigid Shape Comparison and Analysis},
+ publisher = p_technion_cs,
+ address = pa_technion_cs,
+ date = {2009-01-25},
+ url = {https://tosca.cs.technion.ac.il/book/slides/Stanford09_optimization.ppt},
+ urldate = {2023-12-16},
+ addendum = {Slides related to the book \citetitle{BBK2008NGONRS}~\cite{BBK2008NGONRS}}
+}
+
+@book{BBK2008NGONRS,
+ author = a_bronstein_alexander_m # { and } # a_bronstein_michael_m # { and } # a_kimmel_ron,
+ title = {Numerical Geometry of Non-Rigid Shapes},
+ xdata = {ser_mics},
+ date = {2008-09},
+ doi = {10.1007/978-0-387-73301-2},
+ isbn = {978-0-387-73300-5}
+}
+
 @incollection{BCPP1998TQAP,
  author = a_burkard_rainer_e # { and } # a_cela_eranda # { and } # a_pardalos_panos_m # { and } # a_pitsoulis_leonidas_s,
  title = {The Quadratic Assignment Problem},
@@ -691,6 +762,16 @@ @article{GJR1991OCOPADMACS
  doi = {10.1007/BF01415960},
 }
 
+@article{GL2010ETSMBRSFTJSSP,
+ author = a_gharbi_anis # { and } # a_labidi_mohamed,
+ title = {Extending the Single Machine-Based Relaxation Scheme for the Job Shop Scheduling Problem},
+ xdata = {j_enidm},
+ volume = {36},
+ pages = {1057--1064},
+ date = {2010-08},
+ doi = {10.1016/j.endm.2010.05.134}
+}
+
 @incollection{GLLRK1979OAAIDSASAS,
  author = a_graham_ronald_lewis # { and } # a_lawler_eugene_leighhton # { and } # a_lenstra_jan_karel # { and } # a_rinnooy_kan_a_h_k,
  title = {Optimization and Approximation in Deterministic Sequencing and Scheduling: {A} Survey},
@@ -796,11 +877,24 @@ @book{K2000SORCP
  title = {Scheduling of Resource-Constrained Projects},
  xdata = {ser_orcsis},
  number = {10},
- year = {2000},
+ date = {2000},
  doi = {10.1007/978-1-4615-4629-0},
  isbn = {978-0-7923-8637-7}
 }
 
+@article{KBBDCGJLMPQSVBY2016GLPFOR,
+ author = a_kendall_graham # { and } # a_bai_ruibin # { and } # a_blazewicz_jacek # { and } # a_de_causmaecker_patrick # { and } # a_grendrau_michel # { and } # a_john_robert_i # { and } #  a_li_jiawei # { and } # a_mccollum_barry # { and } # a_pesch_erwin # { and } # a_qu_rong # { and } # a_sabar_nasser # { and } # a_vanden_berghe_greet # { and } # a_yee_angelina,
+ title = {Good Laboratory Practice for Optimization Research},
+ xdata = {j_jors},
+ date = {2016},
+ volume = {67},
+ number = {4},
+ pages = {676--689},
+ doi = {10.1057/jors.2015.77},
+ url = {http://www.graham-kendall.com/papers/ketal2016.pdf},
+ urldate = {2023-12-16}
+}
+
 @book{L1909HDLVDVDP,
  author = a_landau_edmund,
  title = {{Handbuch der Lehre von der Verteilung der Primzahlen}},
@@ -965,6 +1059,16 @@ @proceedings{PROC2009EVOWORKSHOPS
  doi = {10.1007/978-3-642-01129-0}
 }
 
+@proceedings{PROC2015CPAIOR,
+ booktitle = {Proceedings of 12th International Conference on {AI} and {OR} Techniques in Constriant Programming for Combinatorial Optimization Problems {(CPAIOR'2015)}, } # may # {~18-22, 2015, } # l_spain_barcelona,
+ xdata = {ser_lntcs},
+ number = {9075},
+ date = {2015},
+ editor = a_michel_laurent,
+ doi = {10.1007/978-3-319-18008-3},
+ isbn = {978-3-319-18007-6}
+}
+
 @proceedings{PROC2016GECCOCompanion,
  editor = a_friedrich_tobias # { and } # a_neumann_frank # { and } # a_sutton_andrew_m,
  title = {Companion Material Proceedings of the Genetic and Evolutionary Computation Conference {(GECCO'16)}, } # jul # {~20-24, 2016, } # l_usa_denver,
@@ -1075,6 +1179,17 @@ @book{T1993SI
  date = {1993}
 }
 
+@article{VAL1996JSSBLS,
+ author = a_vaessens_rob_j_m # { and }  # a_aarts_emile_h_l # { and } # a_lenstra_jan_karel,
+ title = {Job Shop Scheduling by Local Search},
+ xdata = {j_ijoc},
+ volume = {8},
+ number = {3},
+ pages = {302--317},
+ date = {1996-22},
+ doi = {10.1287/ijoc.8.3.302}
+}
+
 @online{vH2015JSIAS,
  author = a_van_hoorn_jelke_jeron,
  title = {Job Shop Instances and Solutions},
@@ -1106,6 +1221,16 @@ @article{vH2018TCSOBOBIOTJSSP
  doi = {10.1007/s10951-017-0547-8}
 }
 
+@inproceedings{VLS2015FDSFCBS,
+ author = a_vilim_petr # { and } # a_laborie_philippe # { and } # a_shaw_paul,
+ title = {Failure-Directed Search for Constraint-Based Scheduling},
+ crossref = {PROC2015CPAIOR},
+ pages = {437--453},
+ doi = {10.1007/978-3-319-18008-3_30},
+ url = {https://www.researchgate.net/publication/280223626},
+ urldate = {2023-12-17}
+}
+
 @article{W2003GCACA,
  author = a_wilson_james_m,
  title = {Gantt Charts: {A} Centenary Appreciation},

book.tex

@@ -5,6 +5,7 @@
 % prepare and set the book margins
 \setlrmarginsandblock{3cm}{3cm}{*}%
 \setulmarginsandblock{2.5cm}{2.5cm}{*}%
+\setlength{\parskip}{3pt}%
 \checkandfixthelayout%
 %
 \usepackage{styles/styles}%  import our own basic styles

notation/math.sty

@@ -14,18 +14,20 @@
 \mbox{If $f(x)={\mathcal{O}}(g(x))$,} then there exist positive numbers~$x_0\in\realNumbersP$ and~$c\in\realNumbersP$ such that~\mbox{$f(x)\leq c*g(x)\forall x\geq x_0$}~\cite{B1894DAZDVPB,L1909HDLVDVDP}. %
 In other words, ${\mathcal{O}}(g(x))$~describes an upper bound for function growth.}%
 %
-\protected\gdef\Pprefix{\ensuremath{\mathcal{P}}}%
-\protected\gdef\NPprefix{\ensuremath{\mathcal{NP}}}%
-\protected\gdef\NPhard{\NPprefix-hard}%
+\protected\gdef\@Pprefix{\ensuremath{\mathcal{P}}}%
+\protected\gdef\@NPprefix{\ensuremath{\mathcal{NP}}}%
+\newSymbol{NPhard}{\mbox{\@NPprefix\textnormal{-hard}}}{NP-hard}{Algorithms that guarantee to find the optimal solutions of \@NPprefix\nobreakdash-hard problems need a runtime that is exponential in the problem scale in the worst case.}%
 %
 \protected\gdef\elementOf#1#2{\ensuremath{#1.#2}}%
 \protected\gdef\arrayIndex#1#2{\ensuremath{#1_{#2}}}%
 \protected\gdef\subArray#1#2#3{\ensuremath{#1[\intRange{#2}{#3}]}}%
 \protected\gdef\arrayIndexx#1#2#3{\ensuremath{#1_{#2,#3}}}%
 \protected\gdef\arrayItemElement#1#2#3{\ensuremath{\elementOf{\arrayIndex{#1}{#2}}{#3}}}%
 %
-\newSymbol{lowerBound}{\ensuremath{\mathrm{lb}}}{lb}{the lower bound of a function, i.e., \ensuremath{\lowerBound(f)\leq f(x)\forall x}}%
-\newSymbol{upperBound}{\ensuremath{\mathrm{ub}}}{ub}{the upper bound of a function, i.e., \ensuremath{\upperBound(f)\geq f(x)\forall x}}%
+\DeclareMathOperator{\@lowerBound}{lb}%
+\newFunc{lowerBound}{\ensuremath{\@lowerBound}}{lb(f(x))}{f(x)}{the lower bound of a function~$f$, i.e., \ensuremath{\@lowerBound(f)\leq f(x)\forall x}, see \autoref{def:lowerBound}}%
+\DeclareMathOperator{\@upperBound}{ub}%
+\newFunc{upperBound}{\ensuremath{\@upperBound}}{ub(f(x))}{f(x)}{the upper bound of a function, i.e., \ensuremath{\@upperBound(f)\geq f(x)\forall x}}%
 \newSymbol{random}{\ensuremath{\mathfrak{R}}}{R}{a random number}%
 %
 \protected\gdef\probability{\ensuremath{P}}%

notation/optimization.sty

@@ -26,14 +26,14 @@ A search operator $\@searchOp:\searchSpace^n\mapsto\searchSpace$ with $n\in\natu
 \newSymbol{obspel}{\ensuremath{z}}{z}{%
 an objective value returned by the objective function~\objf, see \autoref{def:objectiveValue}}%
 %
-\newSymbol{nFeasible}{\ensuremath{\#\mathrm{feasible}}}{feasible}{%
+\newSymbol{nFeasible}{\ensuremath{\#\mathrm{feasible}}}{\#feasible}{%
 the number of feasible solutions in the solution space~\solutionSpace, see \autoref{def:feasibility}}%
 %
 \protected\gdef\fitness{\ensuremath{v}}%
 %
-\protected\gdef\localOptimum#1{\ensuremath{#1^{\times}}}%
-\protected\gdef\globalOptimum#1{\ensuremath{#1^{\star}}}%
-\protected\gdef\bestSoFar#1{\ensuremath{#1_{b}}}%
+\newSuperscript{localOptimum}{\ensuremath{\times}}{.*}{the superscript $\times$~symbol denotes that $\circ$ is a local optimum}%
+\newSuperscript{globalOptimum}{\ensuremath{\star}}{.*}{the superscript $\star$~symbol denotes that $\circ$ is a global optimum}%
+\newSubscript{bestSoFar}{\ensuremath{b}}{.b}{the subscript~$b$ denotes that $\circ$ is the best-so-far element of an optimization process}%
 %
 \protected\gdef\iteration{\ensuremath{\tau}}%
 %

scripts/pdflatex.sh

@@ -90,6 +90,7 @@ rm "$documentName.snm" || true
 rm "$documentName.spl" || true
 rm "$documentName.synctex" || true
 rm "$documentName.synctex.gz" || true
+rm "$documentName.thm" || true
 rm "$documentName.toc" || true
 rm "$documentName.upa" || true
 rm "$documentName.upb" || true
@@ -304,6 +305,7 @@ rm "$documentName.snm" || true
 rm "$documentName.spl" || true
 rm "$documentName.synctex" || true
 rm "$documentName.synctex.gz" || true
+rm "$documentName.thm" || true
 rm "$documentName.toc" || true
 rm "$documentName.upa" || true
 rm "$documentName.upb" || true