zbMATH — the first resource for mathematics

Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
A memetic algorithm for minimizing the total weighted completion time on a single machine under step-deterioration. (English) Zbl 1177.90169
Summary: We consider minimizing total weighted completion time criteria on a single machine. Jobs processing times are step function of its starting time and all jobs have a common due date. First, we present some new lemmas and dominance properties for this NP-hard problem, and then a memetic algorithm using these properties is developed. We compare the solutions of the memetic algorithm with optimal solutions obtained from complete enumeration. The results show that the average percentage error of the proposed algorithm from optimal solutions is about 2% and as the variance of processing time increase, the percentage errors decrease.
90B35Scheduling theory, deterministic
[1]Mosheiov, G.: Scheduling jobs with step-deterioration; minimizing makespan on a single and multi-machine, Comput ind eng 28, 869-879 (1995)
[2]Sundararaghavan, P. S.; Kunnathur, A. S.: Single machine scheduling with start time dependent processing times: some solvable cases, Eur J oper res 79, 394-403 (1994) · Zbl 0816.90088 · doi:10.1016/0377-2217(94)90048-5
[3]Gupta, S. K.; Kunnathur, A. S.; Dandapai, K.: Optimal repayment policies for multiple loans, Omega 15, 323-330 (1987)
[4]Tanaev, V. S.; Gordon, V. S.; Shafransky, Y. M.: Schedule theory, single-stage systems, (1994)
[5]Gupta, J. N. D.; Gupta, S. K.: Single facility scheduling with nonlinear processing time, Comput ind eng 14, 387-393 (1988)
[6]Chen, Z. L.: A note on single-processor scheduling with time-dependent execution times, Oper res lett 17, 127-129 (1995) · Zbl 0841.90072 · doi:10.1016/0167-6377(94)00058-E
[7]Cheng, T. C. E.; Ding, Q.: Single machine scheduling with deadlines and increasing rate of processing times, Acta inform 36, 673-692 (2000) · Zbl 0958.68018 · doi:10.1007/s002360050170
[8]Mosheiov, G.: Scheduling jobs under simple linear deterioration, Comput oper res 21, 653-659 (1994) · Zbl 0810.90074 · doi:10.1016/0305-0548(94)90080-9
[9]Kunnathur, A. S.; Gupta, S. K.: Minimizing the makespan with late start penalties added to processing times in a single facility scheduling problem, Eur J oper res 47, 56-64 (1990) · Zbl 0717.90034 · doi:10.1016/0377-2217(90)90089-T
[10]Kubiak, W.; Van De Velde, S. L.: Scheduling deteriorating jobs to minimize makespan, Nav res log 45, 511-523 (1998) · Zbl 0936.90026 · doi:10.1002/(SICI)1520-6750(199808)45:5<511::AID-NAV5>3.0.CO;2-6
[11]Cheng, T. C. E.; Ding, Q.: Single machine scheduling with step-deteriorating processing times, Eur J oper res 134, 623-630 (2001) · Zbl 0984.90014 · doi:10.1016/S0377-2217(00)00284-8
[12]Jeng, A. A. K.; Lin, B. M. T.: Makespan minimization in single-machine scheduling with step-deterioration of processing times, J oper res soc 55, 247-256 (2004) · Zbl 1095.90038 · doi:10.1057/palgrave.jors.2601693
[13]Jeng, A. A. K.; Lin, B. M. T.: Minimizing the total completion time in single-machine scheduling with step-deteriorating jobs, Comput oper res 32, 521-536 (2005) · Zbl 1077.90025 · doi:10.1016/j.cor.2003.08.001
[14]Alidaee, B.; Womer, N. K.: Scheduling with time dependent processing times: review and extensions, J oper res soc 50, 711-720 (1999) · Zbl 1054.90542
[15]Cheng, T. C. E.; Ding, Q.; Lin, B. M. T.: A concise survey of scheduling with time-dependent processing times, Eur J oper res 152, 1-13 (2003) · Zbl 1030.90023 · doi:10.1016/S0377-2217(02)00909-8
[16]Hart, W. E.; Krasnogor, N.; Smith, J. E.: Recent advances in memetic algorithms, (2004)
[17]Merz P. Memetic algorithms for combinatorial optimization problems: fitness landscapes and effective search strategies. PhD dissertation, University of Siegen, Germany; 2000.
[18]Merz, P.; Freisleben, B.: Fitness landscapes, memetic algorithms and greedy operators for graph bi-partitioning, Evol comput 8, 61-91 (1999)
[19]Burke, E. K.; Smith, A. J.: Hybrid evolutionary techniques for the maintenance scheduling problem, IEEE trans power syst 15, 122-128 (2000)
[20]Cheng, R. W.; Gen, M.: Parallel machine scheduling problems using memetic algorithms, Comput ind eng 33, 761-764 (1997)
[21]Ong, Y. S.; Keane, A. J.: Meta-lamarckian learning in memetic algorithms, IEEE trans evol comput 8, 99-110 (2004)
[22]Ishibuchi, H.; Yoshida, T.; Murata, T.: Balance between genetic search and local search in memetic algorithms for multi objective permutation flowshop scheduling, IEEE trans evol comput 7, 204-223 (2003)
[23]Qian, B.; Wang, L.; Huang, D. -X.; Wang, X.: Scheduling multi-objective job shops using a memetic algorithm based on differential evolution, Int J adv manuf technol 35, 1014-1027 (2008)
[24]Franca, P. M.; Mendes, A.; Moscato, P.: A memetic algorithm for a total tardiness single machine scheduling problem, Eur J oper res 132, 224-242 (2001) · Zbl 0996.90042 · doi:10.1016/S0377-2217(00)00140-5
[25]Davis L. Applying adaptive algorithm to epistemic domain. In: Proceeding of the international joint conference on artificial intelligence. Los Altos, CA: Morgan Kaufmann Publishers; 1985. p. 162 – 4.
[26]Oliver I, Smith D, Holland J. A study of permutation crossover operation on the traveling salesman problem. In: Proceedings of the 2nd international conference on genetic algorithm and their application, Cambridge, MA, USA.
[27]Rabbani, M.; Layegh, J.; Ebrahim, R. Mohammad: Determination of number of kanbans in a supply chain system via memetic algorithm, Adv eng softw 40, No. 6, 431-437 (2009) · Zbl 1157.90540 · doi:10.1016/j.advengsoft.2008.07.001