Total Tardiness Minimization in a Single-Machine with Periodical Resource Constraints

In this paper we introduce a variant of the single machine considering resource restriction per period. The objective function to be minimized is the total tardiness.  We proposed an integer linear programming modeling based on a bin packing formulation. In view of the NP-hardness of the introduced variant, heuristic algorithms are required to find high-quality solutions within an admissible computation times. In this sense, we present a new hybrid matheuristic called Relax-and-Fix with Variable Fixing Search (RFVFS).  This innovative solution approach combines the relax-and-fix algorithm and a strategy for the fixation of decision variables based on the concept of the variable neighborhood search metaheuristic. As statistical indicators to evaluate the solution procedures under comparison, we employ the Average Relative Deviation Index (ARDI) and the Success Rate (SR). We performed extensive computational experimentation with a testbed composed by 450 proposed test problems. Considering the results for the number of jobs, the RFVFS returned ARDI and SR values of 35.6% and 41.3%, respectively. Our proposal outperformed the best solution approach available for a closely-related problem with statistical significance

Hybrid Genetic Bees Algorithm applied to Single Machine Scheduling with Earliness and Tardiness Penalties

This paper presents a hybrid Genetic-Bees Algorithm based optimised solution for the single machine scheduling problem. The enhancement of the Bees Algorithm (BA) is conducted using the Genetic Algorithm's (GA's) operators during the global search stage. The proposed enhancement aims to increase the global search capability of the BA gradually with new additions. Although the BA has very successful implementations on various type of optimisation problems, it has found that the algorithm suffers from weak global search ability which increases the computational complexities on NP-hard type optimisation problems e.g. combinatorial/permutational type optimisation problems. This weakness occurs due to using a simple global random search operation during the search process. To reinforce the global search process in the BA, the proposed enhancement is utilised to increase exploration capability by expanding the number of fittest solutions through the genetical variations of promising solutions. The hybridisation process is realised by including two strategies into the basic BA, named as â\u80\u9creinforced global searchâ\u80\u9d and â\u80\u9cjumping functionâ\u80\u9d strategies. The reinforced global search strategy is the first stage of the hybridisation process and contains the mutation operator of the GA. The second strategy, jumping function strategy, consists of four GA operators as single point crossover, multipoint crossover, mutation and randomisation. To demonstrate the strength of the proposed solution, several experiments were carried out on 280 well-known single machine benchmark instances, and the results are presented by comparing to other well-known heuristic algorithms. According to the experiments, the proposed enhancements provides better capability to basic BA to jump from local minima, and GBA performed better compared to BA in terms of convergence and the quality of results. The convergence time reduced about 60% with about 30% better results for highly constrained jobs

Exact and Heuristic Hybrid Approaches for Scheduling and Clustering Problems

This thesis deals with the design of exact and heuristic algorithms for scheduling and clustering combinatorial optimization problems. All the works are linked by the fact that all the presented methods arebasically hybrid algorithms, that mix techniques used in the world of combinatorial optimization. The algorithms are all efficient in practice, but the one presented in Chapter 4, that has mostly theoretical interest. Chapter 2 presents practical solution algorithms based on an ILP model for an energy scheduling combinatorial problem that arises in a smart building context. Chapter 3 presents a new cutting stock problem and introduce a mathematical formulation and a heuristic solution approach based on a heuristic column generation scheme. Chapter 4 provides an exact exponential algorithm, whose importance is only theoretical so far, for a classical scheduling problem: the Single Machine Total Tardiness Problem. The relevant aspect is that the designed algorithm has the best worst case complexity for the problem, that has been studied for several decades. Furthermore, such result is based on a new technique, called Branch and Merge, that avoids the solution of several equivalent sub-problems in a branching algorithm that requires polynomial space. As a consequence, such technique embeds in a branching algorithm ideas coming from other traditional computer science techniques such as dynamic programming and memorization, but keeping the space requirement polynomial. Chapter 5 provides an exact approach based on semidefinite programming and a matheuristic approach based on a quadratic solver for a fractional clustering combinatorial optimization problem, called Max-Mean Dispersion Problem. The matheuristic approach has the peculiarity of using a non-linear MIP solver. The proposed exact approach uses a general semidefinite programming relaxation and it is likely to be extended to other combinatorial problems with a fractional formulation. Chapter 6 proposes practical solution methods for a real world clustering problem arising in a smart city context. The solution algorithm is based on the solution of a Set Cover model via a commercial ILP solver. As a conclusion, the main contribution of this thesis is given by several approaches of practical or theoretical interest, for two classes of important combinatorial problems: clustering and scheduling. All the practical methods presented in the thesis are validated by extensive computational experiments, that compare the proposed methods with the ones available in the state of the art

A hybrid heuristic approach for single machine scheduling with release times

International audienceIn this work we consider the well-known one-machine total completion time sequencing problem subject to release times. We present a very large scale neighborhood search heuristic based on mathematical programming. This heuristic makes use of the positional completion time formulation of the problem in which valid inequalities are added. The proposed procedure compares favorably with the state of the art heuristic