Local Search Based on a Local Utopia Point for the Multiobjective Travelling Salesman Problem

MEMPSODE: A global optimization software based on hybridization of population-based algorithms and local searches

In this paper, a greedy heuristic and two local search algorithms, 1-opt local search and k-opt local search, are proposed for the unconstrained binary quadratic programming problem (BQP). These heuristics are well suited for the incorporation into meta-heuristics such as evolutionary algorithms. Their performance is compared for 115 problem instances. All methods are capable of producing high quality solutions in short time. In particular, the greedy heuristic is able to find near optimum solutions a few percent below the best-known solutions, and the local search procedures are sufficient to find the best-known solutions of all problem instances with n ≤ 100. The k-opt local searches even find the best-known solutions for all problems of size n ≤ 250 and for 11 out of 15 instances of size n e 500 in all runs. For larger problems (n e 500, 1000, 2500), the heuristics appear to be capable of finding near optimum solutions quickly. Therefore, the proposed heuristics—especially the k-opt local search—offer a great potential for the incorporation in more sophisticated meta-heuristics.

Hybrid algorithms for the twin–screw extrusion configuration problem

Perturbed Decomposition Algorithm applied to the multi-objective Traveling Salesman Problem

The goal of this research is to analyze how individual learning interacts with an evolutionary algorithm in its search for best candidates for the Busy Beaver problem. To study this interaction, two learning models, implemented as local search procedures, are proposed. Experimental results show that, in highly irregular search spaces that are prone to premature convergence, local search methods are not an effective help to evolution. In addition, one interesting effect related to learning is reported: when the mutation rate is too high, learning acts as a repair, reintroducing some useful information that was lost.

Genetic local search for multi-objective combinatorial optimization

A modified quasisecant method for global optimization

Landing aircraft safely is an important operation that air traffic controllers have to deal with on a daily basis. For each arriving aircraft a runway and a landing time must be allocated. If these allocations can be done in an efficient way, it could give the airport a competitive advantage. The Aircraft Landing Problem (ALP) aims to minimize the deviation from a preferred target time of each aircraft. It is an NP-hard problem, meaning that we may have to resort to heuristic methods as exact methods may not be suitable, especially as the problem size increases. This paper proposes an iterated local search (ILS) algorithm for the ALP. ILS is a single solution based search methodology that successively invokes a local search procedure to find a local optimum solution. A perturbation operator is used to modify the current solution in order to escape from the local optimum and to provide a new solution for the local search procedure. As different problems and/or instances have different characteristics, the success of the ILS is highly dependent on the local search, the perturbation operator(s) and the perturbation strength. To address these issues, we utilize four perturbation operators and a time varying perturbation strength which changes as the algorithm progresses. A variable neighborhood descent algorithm is used as our local search. The proposed ILS generates high quality solutions for the ALP benchmark instances taken from the scientific literature, demonstrating its efficiency in terms of both solution quality and computational time. Moreover, the proposed ILS produces new best results for some instances.

An Enhanced multi-objective evolutionary optimization algorithm based on decomposition (E-MOEA-D) proposed for optimal placement of Distributed Generation (DG) and Electric Vehicle (EV) Fast Charging Station (FCS) in distribution system. The diversity of the evolutionary algorithm improves the convergence and diverse solution in the process of evolutionary optimization. The proposed algorithm is improved using enhanced diversity algorithm, which yield diverse candidate solutions in population. The optimal placement of DGs and FCS are formulated using three objective functions as i) Active power loss ii) Voltage deviation iii) DG cost. The proposed algorithm is simulated on IEEE-33 bus distribution system. The proposed algorithm is compared with other competitive multi-objective evolutionary algorithms such as decomposition based multi-objective evolutionary algorithm (MOEA-D) and Non-dominated sorting multi-objective evolutionary algorithm (NSGA-II).

An innovative method for the automatic design of optical systems is presented and verified. The proposed method is based on a multi-objective evolutionary memetic optimization algorithm. The multi-objective approach simultaneously, but separately, addresses the image quality, tolerance, and complexity of the system. The memetic technique breaks down the search for optical designs in to three different parts or phases: optical glass selection, exploration, and exploitation. The optical glass selection phase defines the most appropriate set of glasses for the system under design. The glass selection phase limits the available glasses from hundreds to just a few, drastically reducing the design space and significantly increasing the efficiency of the automatic design method. The exploration phase is based on an evolutionary algorithm (EA), more specifically, on a problem-tailored generalized extremal optimization (GEO) algorithm, named Optical GEO (O-GEO). The new EA incorporates many features customized for lens design, such as optical system codification and diversity operators. The trade-off systems found in the exploration phase are refined by a local search, based on the damped least square method in the exploitation phase. As a result, the method returns a set of trade-off solutions, generating a Pareto front. Our method delivers alternative and useful insights for the compromise solutions in a lens design problem. The efficiency of the proposed method is verified through real-world examples, showing excellent results for the tested problems.

In this study, an ABC-Local Search (ABC-Ls) method was proposed by including a new local search procedure into the standard artificial bee colony (ABC) algorithm to perform the parameter estimation of photovoltaic systems (PV). The aim of the proposed ABC-Ls method was to improve the exploration capability of the standard ABC with a new local search procedure in addition to the exploitation and exploration balance of the standard ABC algorithm. The proposed ABC-Ls method was first tested on 15 well-known benchmark functions in the literature. In the results of the Friedman Mean Rank test used for statistical analysis, ABC-Ls method successfully ranked first with a value of 1.300 in benchmark functions. After obtaining successful results on the benchmark tests, the proposed ABC-Ls method was applied to the single diode, double diode and Photowatt-PWP-201 PV modules of PV systems for parameter estimations. In addition, the proposed ABC-Ls method has been applied to the KC200GT PV module for parameter estimation under different temperature and irradiance conditions of the PV modules. The success of ABC-Ls method was compared with genetic algorithm (GA), particle swarm optimization (PSO) algorithm, ABC algorithm, tree seed algorithm (TSA), Jaya, Atom search optimization (ASO). The comparison results were presented in tables and graphics in detail. The RMSE values for the parameter estimation of single diode, double diode and Photowatt-PWP-201 PV module of the proposed ABC-LS method were found as 9.8602E−04, 9.8257E−04 and 2.4251E−03, respectively. In this context, the proposed ABC-LS method has been compared with the literature for parameter estimation of single diode, double diode and Photowatt-PWP-201 PV module and it has been found that it provides a parameter estimation similar or better than other studies. The proposed ABC-Ls method for parameter estimation of the KC200GT PV module under different conditions is shown in convergence graphs and box plots, where it achieves more successful, effective and stable results than GA, PSO, ABC, TSA, Jaya and ASO algorithms.

An important implementation issue in the design of hybrid evolutionary multiobjective optimization algorithms with local search (i.e., multiobjective memetic algorithms) is how to strike a balance between local search and global search. If local search is applied to all individuals at every generation, almost all computation time is spent by local search. As a result, global search ability of memetic algorithms is not well utilized. We can use three ideas for decreasing the computation load of local search. One idea is to apply local search to only a small number of individuals. This idea can be implemented by introducing a local search probability, which is used to choose only a small number of initial solutions for local search from the current population. Another idea is a periodical (i.e., intermittent) use of local search. This idea can be implemented by introducing a local search interval (e.g., every 10 generations), which is used to specify when local search is applied. The other idea is an early termination of local search. Local search for each initial solution is terminated after a small number of neighbors are examined. This idea can be implemented by introducing a local search length, which is the number of examined neighbors in a series of iterated local search from a single initial solution. In this paper, we discuss the use of these three ideas to strike a local-global search balance. Through computational experiments on a two-objective 500-item knapsack problem, we compare various settings of local search such as short local search from all individuals at every generation, long local search from only a few individuals at every generation, and periodical long local search from all individuals. Global search in this paper means genetic search by crossover and mutation in multiobjective memetic algorithms.

This chapter presents an evolutionary approach for solving the traveling salesman problem (TSP) and the TSP with backhauls (TSPB). We propose two evolutionary algorithms for solving the difficult TSPs. Our focus is on developing evolutionary operators based on conventional heuristics. We rely on a set of detailed computational experiments and statistical tests for developing an effective algorithm.The chapter starts with a careful survey of the algorithms for the TSP and the TSPB, with a special emphasis on crossover and mutation operators and applications on benchmark test instances. The second part addresses our first evolutionary algorithm. We explore the use of two tour construction heuristics, nearest neighbor and greedy, in developing new crossover operators.We focus on preserving the edges in the union graph constructed by edges of the parent tours.We let the heuristics exploit the building blocks found in this graph. This way, new solutions can inherit good blocks from both parents. We also combine the two crossover operators together in generating offspring to explore the potential gain due to synergy. In addition, we make use of 2-edge exchange moves as the mutation operator to incorporate more problem specific information in the evolution process. Our reproduction strategy is based on the generational approach. Experimental results indicate that our operators are promising in terms of both solution quality and computation time.In the third part of the chapter, we present the second evolutionary algorithm developed. This part can be thought of as an enhancement of the first algorithm. A common practice with such algorithms is to generate one child or two children from two parents. In the second implementation, we investigate the preservation of good edges available in more than two parents and generate multiple children.We use the steady-state evolution as a reproduction strategy this time and test the replacement of the worst parent or the worst population member to find the better replacement strategy. Our two mutation operators try to eliminate the longest and randomly selected edges and a third operator makes use of the cheapest insertion heuristic. The algorithm is finalized after conducting a set of experiments for best parameter settings and testing on larger TSPLIB instances. The second evolutionary algorithm is also implemented for solving randomly generated instances of the TSPB. Our experiments reveal that the algorithm is significantly better than the competitors in the literature. The last part concludes the chapter.KeywordsNetworks-GraphsTraveling Salesman ProblemsEvolutionary AlgorithmsCrossover OperatorMutation OperatorHeuristics

Office Space Allocation (OSA) is the task of correctly allocating the spatial resources of an institution to a set of entities by minimising the wastage of space and the violation of additional constraints. In this paper, an evolutionary local search algorithm is presented to tackle this problem. The evolutionary components of the algorithm include standard crossover and mutation operators and a relatively small population of individuals. The offspring produced by the evolutionary operators are subjected to a short but intense local search process. A very fast cost calculation method tailored for searching a large section of the search space is implemented. Extensive experimentation is carried out related to several parameters of the algorithm: the mutation rate, the population size, the length of the local search procedure after each mutation, hence the balance between the evolutionary and the local search stages, and the level of greediness of the local search process. The final results on 72 different data instances show that this hybrid evolutionary algorithm is very competitive with an integer programming model.

This study compared the performances of three state-of-theart evolutionary multi-objective optimization algorithms: the Non-Dominated Sorted Genetic Algorithm II (NSGA-II), the Epsilon-Dominance Non-Dominated Sorted Genetic Algorithm II (e -NSGA-II) and the Epsilon-Dominance Multi-Objective Evolutionary Algorithm ( e MOEA), on a constrained biobjective crop-mix planning problem (BCP). The BCP test case objectives were to: (i) maximize crop production and (ii) minimize planting area. The BCP problem was enumerated to provide the true Pareto-optimal solution set to facilitate rigorous testing of the evolutionary multi-objective optimization algorithms. The performances of the three algorithms were assessed and compared using three performance metrics (additive epsilon indicator, inverted generational distance and spacing). For the comparative study, a graphical comparison with respect to true Pareto front of optimal crop planning problem was provided. Results of the analyses indicated that the e MOEA greatly outperforms the NSGAII and the e -NSGA-II.