On the use of biased-randomized algorithms for solving non-smooth optimization problems

Soft constraints are quite common in real-life applications. For example, in freight transportation, the fleet size can be enlarged by outsourcing part of the distribution service and some deliveries to customers can be postponed as well; in inventory management, it is possible to consider stock-outs generated by unexpected demands; and in manufacturing processes and project management, it is frequent that some deadlines cannot be met due to delays in critical steps of the supply chain. However, capacity-, size-, and time-related limitations are included in many optimization problems as hard constraints, while it would be usually more realistic to consider them as soft ones, i.e., they can be violated to some extent by incurring a penalty cost. Most of the times, this penalty cost will be nonlinear and even noncontinuous, which might transform the objective function into a non-smooth one. Despite its many practical applications, non-smooth optimization problems are quite challenging, especially when the underlying optimization problem is NP-hard in nature. In this paper, we propose the use of biased-randomized algorithms as an effective methodology to cope with NP-hard and non-smooth optimization problems in many practical applications. Biased-randomized algorithms extend constructive heuristics by introducing a nonuniform randomization pattern into them. Hence, they can be used to explore promising areas of the solution space without the limitations of gradient-based approaches, which assume the existence of smooth objective functions. Moreover, biased-randomized algorithms can be easily parallelized, thus employing short computing times while exploring a large number of promising regions. This paper discusses these concepts in detail, reviews existing work in different application areas, and highlights current trends and open research lines

The AddACO: A bio-inspired modified version of the ant colony optimization algorithm to solve travel salesman problems

The Travel Salesman Problem (TSP) consists in finding the minimal-length closed tour that connects the entire group of nodes of a given graph. We propose to solve such a combinatorial optimization problem with the AddACO algorithm: it is a version of the Ant Colony Optimization method that is characterized by a modified probabilistic law at the basis of the exploratory movement of the artificial insects. In particular, the ant decisional rule is here set to amount in a linear convex combination of competing behavioral stimuli and has therefore an additive form (hence the name of our algorithm), rather than the canonical multiplicative one. The AddACO intends to address two conceptual shortcomings that characterize classical ACO methods: (i) the population of artificial insects is in principle allowed to simultaneously minimize/maximize all migratory guidance cues (which is in implausible from a biological/ecological point of view) and (ii) a given edge of the graph has a null probability to be explored if at least one of the movement trait is therein equal to zero, i.e., regardless the intensity of the others (this in principle reduces the exploratory potential of the ant colony). Three possible variants of our method are then specified: the AddACO-V1, which includes pheromone trail and visibility as insect decisional variables, and the AddACO-V2 and the AddACO-V3, which in turn add random effects and inertia, respectively, to the two classical migratory stimuli. The three versions of our algorithm are tested on benchmark middle-scale TPS instances, in order to assess their performance and to find their optimal parameter setting. The best performing variant is finally applied to large-scale TSPs, compared to the naive Ant-Cycle Ant System, proposed by Dorigo and colleagues, and evaluated in terms of quality of the solutions, computational time, and convergence speed. The aim is in fact to show that the proposed transition probability, as long as its conceptual advantages, is competitive from a performance perspective, i.e., if it does not reduce the exploratory capacity of the ant population w.r.t. the canonical one (at least in the case of selected TSPs). A theoretical study of the asymptotic behavior of the AddACO is given in the appendix of the work, whose conclusive section contains some hints for further improvements of our algorithm, also in the perspective of its application to other optimization problems

Reactive approach for automating exploration and exploitation in ant colony optimization

Ant colony optimization (ACO) algorithms can be used to solve nondeterministic polynomial hard problems. Exploration and exploitation are the main mechanisms in controlling search within the ACO. Reactive search is an alternative technique to maintain the dynamism of the mechanics. However, ACO-based reactive search technique has three (3) problems. First, the memory model to record previous search regions did not completely transfer the neighborhood structures to the next iteration which leads to arbitrary restart and premature local search. Secondly, the exploration indicator is not robust due to the difference of magnitudes in distance matrices for the current population. Thirdly, the parameter control techniques that utilize exploration indicators in their feedback process do not consider the problem of indicator robustness. A reactive ant colony optimization (RACO) algorithm has been proposed to overcome the limitations of the reactive search. RACO consists of three main components. The first component is a reactive max-min ant system algorithm for recording the neighborhood structures. The second component is a statistical machine learning mechanism named ACOustic to produce a robust exploration indicator. The third component is the ACO-based adaptive parameter selection algorithm to solve the parameterization problem which relies on quality, exploration and unified criteria in assigning rewards to promising parameters. The performance of RACO is evaluated on traveling salesman and quadratic assignment problems and compared with eight metaheuristics techniques in terms of success rate, Wilcoxon signed-rank, Chi-square and relative percentage deviation. Experimental results showed that the performance of RACO is superior than the eight (8) metaheuristics techniques which confirmed that RACO can be used as a new direction for solving optimization problems. RACO can be used in providing a dynamic exploration and exploitation mechanism, setting a parameter value which allows an efficient search, describing the amount of exploration an ACO algorithm performs and detecting stagnation situations

A study on the heterogeneous fleet of alternative fuel vehicles: Reducing CO2 emissions by means of biodiesel fuel

In the context of home healthcare services, patients may need to be visited multiple times by different healthcare specialists who may use a fleet of heterogeneous vehicles. In addition, some of these visits may need to be synchronized with each other for performing a treatment at the same time. We call this problem the Heterogeneous Fleet Vehicle Routing Problem with Synchronized visits (HF-VRPS). It consists of planning a set of routes for a set of light duty vehicles running on alternative fuels. We propose three population-based hybrid Artificial Bee Colony metaheuristic algorithms for the HF-VRPS. These algorithms are tested on newly generated instances and on a set of homogeneous VRPS instances from the literature. Besides producing quality solutions, our experimental results illustrate the trade-offs between important factors, such as CO2 emissions and driver wage. The computational results also demonstrate the advantages of adopting a heterogeneous fleet rather than a homogeneous one for the use in home healthcare services

the Bees Algorithm: a novel optimisation tool

This work introduces the Bees Algorithm, a new optimisation algorithm inspired by the foraging behaviour of honey-bees. In its basic version, the Bees Algorithm performs a kind of neighbourhood search combined with global random search and can be used for both continuous and discrete optimisation problems. An improved version of the Bees Algorithm including replacing global random search with interpolation and extrapolation, shrinking neighbourhood size, and abandoning sites with no new information was developed. The improved version could solve benchmark function optimisation problems with less sampling of the search space. The Bees Algorithm has been applied to mechanical design optimisation. Two standard mechanical design problems, the design of a welded beam structure and the design of coil springs, were used to benchmark the Bees Algorithm against other optimisation techniques. Computer-aided preliminary design can be regarded as a special case of optimisation, where the goal is to generate as many solutions as possible above a predefined performance threshold. The higher the number of solutions satisfying the preliminary selection criteria, the greater is the chance to produce a good final solution. An adapted version of the Bees Algorithm for discrete function optimisation was developed and tested on a simple machine design task, preliminary gearbox design. The test consists of finding alternative gearbox configurations that approximately produce the required output speeds using one of the available input speeds. Experimental results show that the Bees Algorithm outperforms random search and a genetic optimisation algorithm. A modified version of the Bees Algorithm was used to search for multiple Pareto optimal solutions in a multi-objective optimisation design problem. Compared to two non-dominated genetic algorithms, the Bees Algorithm was able to find more trade-off solutions. Finally, the Bees Algorithm was employed to train Radial Basis Function (RBF) neural networks for two different problems. Despite the high dimensionality of the problems - each bee represented 2345 parameters in the control chart pattern recognition case and 1581 parameters in the wood defect classification case - the algorithm successfully trained very accurate classifiers. Although the accuracies achieved were marginally lower than those obtained with conventional RBF training methods, the total output errors were less than those for conventionally RBF-trained networks with same number of hidden neurons

Comprehensive Taxonomies of Nature- and Bio-inspired Optimization: Inspiration Versus Algorithmic Behavior, Critical Analysis Recommendations

In recent algorithmic family simulates different biological processes observed in Nature in order to efficiently address complex optimization problems. In the last years the number of bio-inspired optimization approaches in literature has grown considerably, reaching unprecedented levels that dark the future prospects of this field of research. This paper addresses this problem by proposing two comprehensive, principle-based taxonomies that allow researchers to organize existing and future algorithmic developments into well-defined categories, considering two different criteria: the source of inspiration and the behavior of each algorithm. Using these taxonomies we review more than three hundred publications dealing with nature- inspired and bio-inspired algorithms, and proposals falling within each of these categories are examined, leading to a critical summary of design trends and similarities between them, and the identification of the most similar classical algorithm for each reviewed paper. From our analysis we conclude that a poor relationship is often found between the natural inspiration of an algorithm and its behavior. Furthermore, similarities in terms of behavior between different algorithms are greater than what is claimed in their public disclosure: specifically, we show that more than one-third of the reviewed bio-inspired solvers are versions of classical algorithms. Grounded on the conclusions of our critical analysis, we give several recommendations and points of improvement for better methodological practices in this active and growing research field

Machine scheduling using the Bees algorithm

Single-machine scheduling is the process of assigning a group of jobs to a machine. The jobs are arranged so that a performance measure, such as the total processing time or the due date, may be optimised. Various swarm intelligence techniques as well as other heuristic approaches have been developed for machine scheduling. Previously, the Bees Algorithm, a heuristic optimisation procedure that mimics honeybee foraging, was successfully employed to solve many problems in continuous domains. In this thesis, the Bees Algorithm is presented to solve various single-machine scheduling benchmarks, all of which, chosen to test the performance of the algorithm, are NP-hard and cannot be solved to optimality within polynomially-bounded time. To apply the Bees Algorithm for machine scheduling, a new neighbourhood structure is defined. Several local search algorithms are combined with the Bees Algorithm. This work also introduces an enhanced Bees Algorithm. Several additional features are considered to improve the efficiency of the algorithm such as negative selection, chemotaxis, elimination and dispersal which is similar to the ‘site abandonment’ strategy used in the original algorithm, and neighbourhood change. A different way to deploy neighbourhood procedures is also presented. ii Three categories of machine scheduling problems, namely, single machine with a common due date, total weighted tardiness, and total weighted tardiness with sequence-dependent setup are used to test the enhanced Bees Algorithm’s performance. The results obtained compare well with those produced by the basic version of the algorithm and by other well-known techniques

Evolutionary Computation 2020

Intelligent optimization is based on the mechanism of computational intelligence to refine a suitable feature model, design an effective optimization algorithm, and then to obtain an optimal or satisfactory solution to a complex problem. Intelligent algorithms are key tools to ensure global optimization quality, fast optimization efficiency and robust optimization performance. Intelligent optimization algorithms have been studied by many researchers, leading to improvements in the performance of algorithms such as the evolutionary algorithm, whale optimization algorithm, differential evolution algorithm, and particle swarm optimization. Studies in this arena have also resulted in breakthroughs in solving complex problems including the green shop scheduling problem, the severe nonlinear problem in one-dimensional geodesic electromagnetic inversion, error and bug finding problem in software, the 0-1 backpack problem, traveler problem, and logistics distribution center siting problem. The editors are confident that this book can open a new avenue for further improvement and discoveries in the area of intelligent algorithms. The book is a valuable resource for researchers interested in understanding the principles and design of intelligent algorithms