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Rapid advancements in internet technology have made it possible to develop electronic commerce in general and internet shopping in particular. Easy access to a vast number of existing internet stores enables buyers to customize their shopping processes to minimize the total purchase cost. This paper aims to investigate a novel internet shopping problem, which consists of the diversification of a given list of products to buy among many stores and to use discounts offered by the stores.

The adequate discrete optimization problem referred to as internet shopping optimization problem with price sensitivity discounts (ISOPwD) is investigated, which turned out to be strongly nondeterministic polynomial (NS)-hard. Two heuristic solution algorithms have been derived using the tabu search (TS) and the simulated annealing (SA) metaheuristics for having a solution in a reasonable time. The algorithms have been assessed via computational experiments, and they have been compared with another algorithm known from the literature that has been elaborated for a simpler version of ISOPwD.

The conducted evaluation has shown the advantage of both heuristic algorithms on the algorithm known from the literature. Moreover, the TS-based algorithm outperformed the other one in terms of the total cost incurred by customers and the computational time.

The special primary piecewise linear discounting function is only taken into account. Other possible discounts connected, for example, with bundles of products and (or) coupons are not considered.

The elaborated algorithms can be recommended for internet shopping providers who want to introduce the ability to search a cost-optimized set of products in their databases or for applications that combine offers from various online retailers, e.g. internet price comparison services and auction sites.

The novelty of considered ISOPwD, in comparison with similar problems discussed in the literature, deals with an arbitrary number of purchased products, the possibility to buy an identical product in different stores and the consideration of the weight, the amount and the availability of goods as parameters of ISOPwD.

The purpose of this paper is to present a study of the effect of different types of annealing schedules for a ribonucleic acid (RNA) secondary structure prediction algorithm based on simulated annealing (SA).

An RNA folding algorithm was implemented that assembles the final structure from potential substructures (helixes). Structures are encoded as a permutation of helixes. An SA searches this space of permutations. Parameters and annealing schedules were studied and fine-tuned to optimize algorithm performance.

In comparing with mfold, the SA algorithm shows comparable results (in terms of F-measure) even with a less sophisticated thermodynamic model. In terms of average specificity, the SA algorithm has provided surpassing results.

Most of the underlying thermodynamic models are too simplistic and incomplete to accurately model the free energy for larger structures. This is the largest limitation of free energy-based RNA folding algorithms in general.

The algorithm offers a different approach that can be used in practice to fold RNA sequences quickly.

The algorithm is one of only two SA-based RNA folding algorithms. The authors use a very different encoding, based on permutation of candidate helixes. The in depth study of annealing schedules and other parameters makes the algorithm a strong contender. Another benefit is that new thermodynamic models can be incorporated with relative ease (which is not the case for algorithms based on dynamic programming).

As far as the authors know, no research has already been carried out on the multi-floor dynamic facility layout problem (MF-DFLP) in the continuous form regarding the flexible bay structure, the number and the variable location of the elevator. Therefore, the present paper models the given problem and attempts to find a sub-optimal solution for it using a meta-heuristic simulated annealing (SA) algorithm.

The efficient use of resources has always been a prominent matter for decision-makers. Many reasons including land use, construction considerations and proximity of departments have led to the design of multi-floor facilities. On the other hand, their fast-evolving environment calls for dynamic planning. Therefore, in this paper, a model and the SA algorithm for MF-DFLP are presented.

After presenting a mathematical model, the problem was solved precisely in a small size using the GAMS software. Also, a near-optimal solution method using a SA meta-heuristic algorithm is suggested and the proposed algorithm was run in the MATLAB software. To evaluate the presented model and the proposed solution, some test cases were considered in two aspects. The first aspect was the test cases that are newly generated in small, medium and large sizes to compare the exact optimal solution with the results of the meta-heuristic algorithm. Eight test cases with small sizes were solved using the GAMS software, the optimum solutions were obtained in a reasonable time, and the cost of their solutions was equal to that of the SA algorithm. Eight test cases with medium sizes were run in the GAMS software with the time limit of 80,000 s, and the SA algorithm had performed better for these test cases. Two test cases were also considered in large size that GAMS could not solve them, whereas the SA algorithm successfully found a proper solution for each. The second aspect included the test cases from the literature. The result showed that suggested algorithm is more capable of finding best solutions than compared algorithms.

In this paper, an unequal area MF-DFLP was studied in a continuous layout form in which the location and number of the elevators were considered to be variable, and the layouts were considered with flexible bay structure. These conditions were investigated for the first time.

The purpose of this paper is to provide an effective solution method for the truck and trailer routing problem (TTRP) which is one of the important NP-hard combinatorial optimization problems owing to its multiple real-world applications. It is a generalization of the famous vehicle routing problem (VRP), involving a group of geographically scattered customers served by the vehicle fleet including trucks and trailers.

The meta-heuristic solution approach based on bat algorithm (BA) in which a local search procedure performed by five different neighborhood structures is developed. Moreover, a self-adaptive (SA) tuning strategy to preserve the swarm diversity is implemented. The effectiveness of the proposed SA-BA is investigated by an experiment conducted on 21 benchmark problems that are well known in the literature.

Computational results indicate that the proposed SA-BA algorithm is computationally efficient through comparison with other existing algorithms found from the literature according to solution quality. As for the actual computational time, the SA-BA algorithm outperforms others. However, the scaled computational time of the SA-BA algorithm underperforms the other algorithms.

In this work the authors show that the proposed SA-BA is effective as a method for the TTRP problem. To the authors’ knowledge, the BA has not been applied previously, as in this work, to solve the TTRP problem.

One of the most important problems concerning the toll roads is the setting of an appropriate cost for traveling through private arcs of a transportation network. The purpose of this paper is to consider this problem by stating it as a bilevel programming (BLP) model. At the upper level, one has a public regulator or a private company that manages the toll roads seeking to increase its profits. At the lower level, several companies-users try to satisfy the existing demand for transportation of goods and/or passengers, and simultaneously, to select the routes so as to minimize their travel costs. In other words, what is sought is kind of a balance of costs that bring the highest profit to the regulating company (the upper level) and are still attractive enough to the users (the lower level).

With the aim of providing a solution to the BLP problem in question, a direct algorithm based on sensitivity analysis (SA) is proposed. In order to make it easier to move (if necessary) from a local maximum of the upper level objective function to another, the well-known “filled function (FF)” method is used.

The paper proposes and tests two versions of the heuristic algorithm to solve the toll optimization problem (TOP) based upon SA for linear programming (LP) problems. The algorithm makes use of an SA procedure for the LP problem at the lower level, as well as of the “filled” function technicalities in order to reach the global optimum when “jammed” at some local optimum. Numerical experiments with a series of small and medium dimension test problems show the proposed algorithm’s robustness and decent convergence characteristics.

Numerical experiments with a series of small- and medium dimension test problems show the proposed algorithm’s robustness and reasonable convergence characteristics. In particular, while ceding in efficiency to other algorithms when solving small problems, the proposed method wins in the case of medium (higher dimensional) test models. Because of that, one can expect a serious real-life impact on the TOP when the proposed methods and/or their improved versions are developed further to be applicable in practice in the near future.

The proposed algorithms are original and perform well when solving small and medium test numerical problems. The proposed heuristics aim at filling in a gap in a series of numerical approaches to the solution of TOP problem listed in the Introduction. To the authors knowledge, no systematic attempts to apply the SA tools to the toll assigned problem have been recently made. Moreover, the combination of these powerful tools with the “FFs” techniques brings forward some new global optimization ideas. Exactly these features build up the knowledge this specific paper offers in relation to previous relevant works.

This paper aims to present a simulated annealing (SA) algorithm to search the optimal solution of reliability‐redundancy allocation problems (RRAP) with nonlinear resource constraints.

The developed SA algorithm is coded in C++ and is applied to reliability design problems which include the series system (P1(a) and P1(b)), the series‐parallel system (P2), and the complex (bridge) system (P3). The numerical experiments are executed on an IBM‐PC compatible with a Pentium IV 2.0 GHz. The results are compared with those of previous studies.

The SA algorithm can find better solutions comparable to the previous studies in all problems except the problem P1(b). The difference on the order of 10⁻⁴ between the best and worst for all problems indicates good solution convergence of the SA algorithm. Note that the CPU times for these problems are within a few seconds by Pentium IV 2.0 GHz (P1(a) =2.78 sec, P1(b) =3.37 sec, P2=1.38 sec, and P3=1.40 sec).

The application of the SA is expanded to the RRAP, which can help reliability engineers design the system reliability.

With the continuous upgrading of the production mode of the manufacturing system, the characteristics of multi-variety, small batch and mixed fluidization are presented, and the production environment becomes more and more complex. To improve the efficiency of solving multi-objective flexible job shop scheduling problem (FJSP), an improved hybrid particle swarm optimization algorithm (IH-PSO) is proposed.

After reviewing literatures on FJSP, an IH-PSO algorithm for solving FJSP is developed. First, IH-PSO algorithm draws on the crossover and mutation operations of genetic algorithm (GA) algorithm and proposes a new method for updating particles, which makes the offspring particles inherit the superior characteristics of the parent particles. Second, based on the improved simulated annealing (SA) algorithm, the method of updating the individual best particles expands the search scope of the domain and solves the problem of being easily trapped in local optimum. Finally, analytic hierarchy process (AHP) is used in this paper to solve the optimal solution satisfying multi-objective optimization.

Through the benchmark experiment and the production example experiment, it is verified that the proposed algorithm has the advantages of high quality of solution and fast speed of convergence.

This method does not consider the unforeseen events that occur during the process of scheduling and cause the disruption of normal production scheduling activities, such as machine breakdown.

IH-PSO algorithm combines PSO algorithm with GA and SA algorithms. This algorithm retains the advantage of fast convergence speed of traditional PSO algorithm and has the characteristic of inheriting excellent genes. In addition, the improved SA algorithm is used to solve the problem of falling into local optimum.

This research provides an efficient scheduling method for solving the FJSP problem.

This research proposes an IH-PSO algorithm to solve the FJSP more efficiently and meet the needs of multi-objective optimization.

The purpose of this paper is to compare the effectiveness of two meta‐heuristics in solving the problem of scheduling maintenance operations and jobs processing on a single machine.

The two meta‐heuristic algorithms, tabu search and simulated annealing are hybridized using the properties of an optimal schedule identified in the existing literature to the problem. A lower bound is also suggested utilizing these properties.

In a numerical experimentation with large size problems, the best‐known heuristic algorithm to the problem is compared with the tabu search and simulated annealing algorithms. The study shows that the meta‐heuristic algorithms outperform the heuristic algorithm. In addition, the developed meta‐heuristics tend to be more robust against the problem‐related parameters than the existing algorithm.

A future work may consider the possibility of machine failure along with the preventive maintenance. This relaxes the assumption that the machine cannot fail but it is rather maintained preventively. The multi‐criteria scheduling can also be considered as an avenue of future work. The problem can also be considered with stochastic parameters such that the processing times of the jobs and the maintenance related parameters are random and follow a known probability distribution function.

The usefulness of meta‐heuristic algorithms is demonstrated for solving a large scale NP‐hard combinatorial optimization problem. The paper also shows that the utilization of the directed search methods such as hybridization could substantially improve the performance of a meta‐heuristic.

This research highlights the impact of utilizing the directed search methods to cause hybridization in meta‐heuristic and the resulting improvement in their performance for large‐scale optimization.

Robots are used in assembly lines because of their higher flexibility and lower costs. The purpose of this paper is to develop mathematical models and simulated annealing algorithms to solve the robotic assembly line balancing (RALB-II) to minimize the cycle time.

Four mixed-integer linear programming models are developed and encoded in CPLEX solver to find optimal solutions for small-sized problem instances. Two simulated annealing algorithms, original simulated annealing algorithm and restarted simulated annealing (RSA) algorithm, are proposed to tackle large-sized problems. The restart mechanism in the RSA methodology replaces the incumbent temperature with a new temperature. In addition, the proposed methods use iterative mechanisms for updating cycle time and a new objective to select the solution with fewer critical workstations.

The comparative study among the tested algorithms and other methods adapted verifies the effectiveness of the proposed methods. The results obtained by these algorithms on the benchmark instances show that 23 new upper bounds out of 32 tested cases are achieved. The RSA algorithm ranks first among the algorithms in the number of updated upper bounds.

Four models are developed for RALBP-II and their performance is evaluated for the first time. An RSA algorithm is developed to solve RALBP-II, where the restart mechanism is developed to replace the incumbent temperature with a new temperature. The proposed methods also use iterative mechanisms and a new objective to select the solution with fewer critical workstations.

The purpose of this paper is twofold. First, to propose an operational model for aircraft maintenance routing problem (AMRP) rather than tactical models that are commonly used in the literature. Second, to develop a fast and responsive solution method in order to cope with the frequent changes experienced in the airline industry.

Two important operational considerations were considered, simultaneously. First one is the maximum flying hours, and second one is the man-power availability. On the other hand, ant colony optimization (ACO), simulated annealing (SA), and genetic algorithm (GA) approaches were proposed to solve the model, and the upper bound was calculated to be the criteria to assess the performance of each meta-heuristic. After attempting to solve the model by these meta-heuristics, the authors noticed further improvement chances in terms of solution quality and computational time. Therefore, a new solution algorithm was proposed, and its performance was validated based on 12 real data from the EgyptAir carrier. Also, the model and experiments were extended to test the effect of the operational considerations on the profit.

The computational results showed that the proposed solution algorithm outperforms other meta-heuristics in finding a better solution in much less time, whereas the operational considerations improve the profitability of the existing model.

The authors focused on some operational considerations rather than tactical considerations that are commonly used in the literature. One advantage of this is that it improves the profitability of the existing models. On the other hand, identifying future research opportunities should help academic researchers to develop new models and improve the performance of the existing models.

The experiment results showed that the proposed model and solution methods are scalable and can thus be adopted by the airline industry at large.

In the literature, AMRP models were cast with approximated assumption regarding the maintenance issue, while neglecting the man-power availability consideration. However, in this paper, the authors attempted to relax that maintenance assumption, and consider the man-power availability constraints. Since the result showed that these considerations improve the profitability by 5.63 percent in the largest case. The proposed operational considerations are hence significant. Also, the authors utilized ACO, SA, and GA to solve the model for the first time, and developed a new solution algorithm. The value and significance of the new algorithm appeared as follow. First, the solution quality was improved since the average improvement ratio over ACO, SA, and GA goes up to 8.30, 4.45, and 4.00 percent, respectively. Second, the computational time was significantly improved since it does not go beyond 3 seconds in all the 12 real cases, which is considered much lesser compared to ACO, SA, and GA.