Integrated Local Search Technique With Reptile Search Algorithm for Solving Large‐Scale Bound Constrained Global Optimization Problems

Local search is an emerging paradigm for combinatorial search which has recently been shown to be very effective for a large number of combinatorial problems. It is based on the idea of navigating the search space by iteratively stepping from one solution to one of its neighbors, which are obtained by applying a simple local change to it. In this paper we present LOCAL++, an object-oriented framework to be used as a general tool for the development and implementation of local search algorithms in C++. The framework comprises a hierarchy of abstract template classes, one for each local search technique taken into account (i.e. hill-climbing, simulated annealing and tabu search). Each class specifies and implements the invariant part of the algorithm built according to the technique, and is supposed to be specialized by a concrete class once a given search problem is considered, so as to implement the problem-dependent part of the algorithm. LOCAL++ comprises also a set of abstract classes for creating new techniques by combining different search techniques and different neighborhood relations. The architecture of LOCAL++ provides a principled modularization for the solution of combinatorial search problems, and helps the designer deriving a neat conceptual scheme of the application, thus facilitating the development and debugging phases. LOCAL++ proved to be flexible enough for the implementation of the algorithms solving various scheduling problems. Copyright © 2000 John Wiley & Sons, Ltd.

Constraint Programming typically uses the technique of depth-first branch and bound as the method of solving optimization problems. Although this method can give the optimal solution, for large problems, the time needed to find the optimal can be prohibitive. This paper introduces a method for using local search techniques within a Constraint Programming framework, and applies this technique to vehicle routing problems. We introduce a Constraint Programming model for vehicle routing, and a system for integrating Constraint Programming and local search techniques. We then describe how the method can be accelerated by handling core constraints using fast local checks, while other more complex constraints are left to the constraint propagation system. We have coupled our local search method with a meta-heuristic to avoid the search being trapped in local minima. Several meta-heuristics are investigated ranging from a simple Tabu Search method to Guided Local Search. An empirical study over benchmark problems shows the relative merits of these techniques. Investigations indicate that the specific long-term memory technique used by Guided Local Search can be used as a diversification method for Tabu Search, resulting in significant benefit. Several new best solutions on the Solomon problems are found in relatively few iterations of our algorithm.

Genetic algorithms (GAs) have such potentials for realizing emergent searches that local search techniques, such as simulated annealings, and parallel local search techniques, like other evolutionary computation such as evolution strategies and evolutionary programmings, do not have. Crossover operators bring these potentials because they can emerge their neighborhood structures as populations evolve. The paper presents a realization of emergent searches by GAs. First, we show difficulties for local search techniques to solve double circle TSPs, and discuss how emergent searches can overcome such difficulties. Second, we propose guidelines to achieve emergent searches by GAs; the characteristics preserving encodings/crossovers design and the diversity maintaining generation alternation models design. According to these guidelines, we actually realize GAs to solve double circle TSPs.

In this paper, a convex filled function method for solving constrained global optimization problems is proposed. A convex filled function is proposed by combining the idea of filled function in unconstrained global optimization and the idea of penalty function in constrained optimization. Then a convex filled function method for obtaining a global minimizer or an approximate global minimizer of the constrained global optimization problem is presented. Some numerical results demonstrate the efficiency of this global optimization method for solving constrained global optimization problems.

Employee timetabling is the operation of assigning employees to tasks in a set of shifts during a fixed period of time, typically a week. We present a general definition of employee timetabling problems (ETPs) that captures many real world problem formulations and includes complex constraints. We investigate the use of several local search techniques for solving ETPs. In particular, we propose a generalization of local search that makes use of a novel search space that includes also partial assignments. We describe the distinguishing features of this generalized local search that allows it to navigate the search space effectively.We show that, on large and difficult instances of real world ETPs, where systematic search fails, local search methods perform well and solve the hardest instances. According to our experimental results on various local search techniques, generalized local search is the best method for solving large ETP instances.KeywordsCost FunctionSearch SpaceLocal SearchTabu SearchSoft ConstraintThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

This paper describes a multi‐start with clustering strategy for use on constrained optimization problems. It is based on the characteristics of non‐linear constrained global optimization problems and extends a strategy previously tested on unconstrained problems. Earlier studies of multi‐start with clustering found in the literature have focused on unconstrained problems with little attention to non‐linear constrained problems. In this study, variations of multi‐start with clustering are considered including a simulated annealing or random search procedure for sampling the design domain and a quadratic programming (QP) sub‐problem used in cluster formation. The strategies are evaluated by solving 18 non‐linear mathematical problems and six engineering design problems. Numerical results show that the solution of a one‐step QP sub‐problem helps predict possible regions of attraction of local minima and can enhance robustness and effectiveness in identifying local minima without sacrificing efficiency. In comparison to other multi‐start techniques found in the literature, the strategies of this study can be attractive in terms of the number of local searches performed, the number of minima found, whether the global minimum is located, and the number of the function evaluations required. Copyright © 2002 John Wiley & Sons, Ltd.

Local search techniques have been applied in variant global optimization methods. The effect of local search to the function landscape can make multimodal problems easier to solve. For evolutionary algorithms, the usage of the step size control concept normally will result in failure by the individual to escape from the local optima during the final stage. We propose an algorithm combining landscape approximation and local search (LALS) which is designed to tackle those difficult multimodal problems. We demonstrate that LALS can solve problems with very rough landscapes and also that LALS has very good global reliability.

With the increasing amount of distributed generation (DG) integrated into electrical distribution networks, various operational problems, such as excessive power losses, over-voltage and thermal overloading issues become gradually remarkable. Innovative approaches for power flow and voltage controls are required to ensure the power quality, as well as to accommodate large DG penetrations. Using power electronic devices is one of the approaches. In this paper, a multi-objective optimization framework was proposed to improve the operation of a distribution network with distributed generation and a soft open point (SOP). An SOP is a distribution-level power electronic device with the capability of real-time and accurate active and reactive power flow control. A novel optimization method that integrates a Multi-Objective Particle Swarm Optimization (MOPSO) algorithm and a local search technique – the Taxi-cab method, was proposed to determine the optimal set-points of the SOP, where power loss reduction, feeder load balancing and voltage profile improvement were taken as objectives. The local search technique is integrated to fine tune the non-dominated solutions obtained by the global search technique, overcoming the drawback of MOPSO in local optima trapping. Therefore, the search capability of the integrated method is enhanced compared to the conventional MOPSO algorithm. The proposed methodology was applied to a 69-bus distribution network. Results demonstrated that the integrated method effectively solves the multi-objective optimization problem, and obtains better and more diverse solutions than the conventional MOPSO method. With the DG penetration increasing from 0 to 200%, on average, an SOP reduces power losses by 58.4%, reduces the load balance index by 68.3% and reduces the voltage profile index by 62.1%, all compared to the case without an SOP. Comparisons between SOP and network reconfiguration showed the outperformance of SOP in operation optimization.

In this paper a hybrid adaptive genetic algorithm is proposed for solving constrained optimization problems. Genetic algorithm proposed here combines adaptive penalty method and smoothing technique in order to make the algorithm not needing parameters tuning and easily escaping from the local optimal solutions. Meanwhile, local line search technique is introduced and a new crossover operator is designed for getting much faster algorithm convergence. If there is no feasible solutions in the current population, finding feasible solutions is prior to finding optimal solution, otherwise the exploitation for global optimal solution based on a certain smoothing function at the best feasible solution in the current population and the exploration for whole search space are processing at the same time. The performance of the algorithm is tested on thirteen benchmark functions in the literature and the results indicate that the algorithm proposed here is robust and effective.

A hybrid adaptive genetic algorithm is proposed for solving constrained optimization problems. The algorithm combines adaptive penalty method and smoothing technique in order to get no parameter tuning and easily escaping from the local optimal solutions. Meanwhile, local line search technique is introduced and a new crossover operator is designed for getting much faster convergence. The performance of the algorithm is tested on thirteen benchmark functions and the results indicate that the proposed algorithm is robust and effective.

We consider the problem of selecting a portfolio of assets that provides the investor a suitable balance of expected return and risk. With respect to the seminal mean-variance model of Markowitz, we consider additional constraints on the cardinality of the portfolio and on the quantity of individual shares. Such constraints better capture the real-world trading system, but make the problem more difficult to be solved with exact methods. We explore the use of local search techniques, mainly tabu search, for the portfolio selection problem. We compare the combine previous work on portfolio selection that makes use of the local search approach and we propose new algorithms that combine different neighborhood relations. In addition, we show how the use of randomization and of a simple form of adaptiveness simplifies the setting of a large number of critical parameters. Finally, we show how our techniques perform on public benchmarks.

The optimal power flow (OPF) problem is a well-known non-convex optimization problem that aims to minimize the cost of electric power generation subject to consumer demand, the physics of power flow, and technological constraints. To find an optimal solution to this problem, local search techniques such as interior point methods are typically used. However, due to the non-convex nature of the problem, these methods are likely to result in a sub-optimal solution. The goal of this paper is to characterize the worst-case performance of local search on the OPF problem. To accomplish this, we formulate the OPF problem as a canonical quadratically-constrained quadratic program (QCQP). Then, we study the problem of finding the worst-case local minimum of this QCQP, which is non-convex and hard to solve in general. We find a relaxation of this problem into a semidefinite program (SDP) and show that it is exact for certain cases. Using some test cases which are known to have multiple local minima, we demonstrate the effectiveness of the proposed relaxation to bound the worst-case local minimum. We compare the obtained upper bound on local minima to the lower bound provided by the standard SDP relaxation of the OPF problem to understand how much SDP outperforms local search for a given problem.

Several contemporary multi-objective surrogate-based algorithms use some kind of local search operator. The search technique used in this operator can largely affect the performance of the multi-objective optimizer as a whole, however, little attention is often paid to the selection of this technique. In this paper, we compare three different local search techniques and evaluate their effect on the performance of two different surrogate based multi-objective optimizers. The algorithms are evaluated using the well known ZDT and WFG benchmark suites and recommendations are made based on the results.

Optimization of distribution piping network in district cooling system using genetic algorithm with local search

Different approaches in the hybridization of constraint programming and local search techniques have been recently proposed in the literature. In this paper we investigate two of them, namely the employment of local search to improve a solution found by constraint programming and the exploitation of a constraint model to perform the exploration of the local neighborhood. We apply the two approaches to a real-world personnel rostering problem arising at the department of neurology of the Udine University hospital and we report on computational studies on both real-world and randomly generated structured instances. The results highlight the benefits of the hybridization approach w.r.t. their component algorithms.