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Abstract This paper proposes a novel decomposition method based on user-preference and developed a variation of the decomposition based multi-objective optimization algorithm (MOEA/D) targeting only solutions in a small region of the Pareto-front defined by the preference information supplied by the decision maker (DM). This is particularly advantageous for solving multi-objective optimization problems (MOPs) with more than 3 objectives, i.e., many-objective optimization problems (MaOPs). As the number of objectives increases, the ability of an EMO algorithm to approximate the entire Pareto front (PF) is rapidly diminishing. In this paper, we first propose a novel scalarizing function making use of a series of new reference points derived from a reference point specified by the DM in the preference model. Based on this scalarizing function, we then develop a user-preference-based EMO algorithm, namely R-MOEA/D. One key merit of R-MOEA/D is that it does not rely on an estimation of the ideal point, which may impact significantly the performances of state-of-the-art decomposition based EMO algorithms. Our experimental results on multi-objective and many-objective benchmark problems have shown that R-MOEA/D provides a more direct and efficient search towards the preferred PF region, resulting in competitive performances. In an interactive setting when the DM changes the reference point during optimization, R-MOEA/D has a faster response speed and performance than the compared algorithms, showing its robustness and adaptability to changes of the preference model. Furthermore, the effectiveness of R-MOEA/D is verified on a real-world problem of reservoir flood control operations. [ABSTRACT FROM AUTHOR]

Abstract Grey Wolf Optimizer (GWO) algorithm is a relatively new algorithm in the field of swarm intelligence for solving continuous optimization problems as well as real world optimization problems. The Grey Wolf Optimizer is the only algorithm in the category of swam intelligence which is based on leadership hierarchy. This paper has three important aspects- Firstly, for improving the search ability by grey wolf a modified algorithm RW-GWO based on random walk has been proposed. Secondly, its performance is exhibited in comparison with GWO and state of art algorithms GSA, CS, BBO and SOS on IEEE CEC 2014 benchmark problems. A non-parametric test Wilcoxon and Performance Index Analysis has been performed to observe the impact of improving the leaders in the proposed algorithm. The results presented in this paper demonstrate that the proposed algorithm provide a better leadership to search a prey by grey wolves. The third aspect of the paper is to use the proposed algorithm and GWO on real life application problems. It is concluded from this article that RW-GWO algorithm is an efficient and reliable algorithm for solving not only continuous optimization problems but also for real life optimization problems. [ABSTRACT FROM AUTHOR]

Abstract A new model and solution for the multi-objective heterogeneous vehicle routing and scheduling problem, with energy minimizing, is presented in this paper. The concept of heterogeneities is concerned with the ownership of fleets. Ownership heterogeneities occur when the private fleet is not sufficient and the company has to rent some vehicles from external carriers to complete the shipments. A new mathematical formulation for vehicle routing problem with time windows (VRPTW) is also presented using the proposed concept of heterogeneities. Moreover, unlike prior attempts to minimize cost by minimizing overall traveling distance, the model also incorporates energy minimizing which meets the latest requirements of green logistics. This paper considers the customers' priority for servicing as well. The proposed model is interpreted as multi-objective optimization and used in two scenarios where, in the first scenario (I), the energy consumed and the total number of vehicles are minimized and the total satisfaction rate of customers is maximized. In the second scenario (II) the distance traveled by the vehicles, the total number of rental vehicles and the fuel consumed by the private vehicles are minimized and the total satisfaction is maximized. A new solution based on an evolutionary algorithm is proposed and its performance on several completely random instances is compared to the non-dominated sorting genetic algorithm II (NSGA II) and CPLEX Solver. The efficiency and effectiveness of the proposed approach is further demonstrated through several computational experiments. Highlights • Considering the ownership of vehicles and the available fleet as heterogeneous VRPTW (HVRPTW). • Considering a reduction in fuel consumption in modeling of the proposed HVRPTW. • Considering the customers' priority which are highly relevant to the customers' satisfaction level. • Using a direct interpretation of the proposed model as a multi-objective problem. • The computational experiments on data sets illustrate the efficiency and effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

Abstract This paper summarizes the two testbeds, datasets, and results of the IEEE PES Working Group on Modern Heuristic Optimization (WGMHO) 2017 Competition on Smart Grid Operation Problems. The competition is organized with the aim of closing the gap between theory and real-world applications of evolutionary computation. Testbed 1 considers stochastic OPF (Optimal Power Flow) based Active-Reactive Power Dispatch (ARPD) under uncertainty and Testbed 2 large-scale optimal scheduling of distributed energy resources. Classical optimization methods are not able to deal with the proposed optimization problems within a reasonable time, often requiring more than one day to provide the optimal solution and a significant amount of memory to perform the computation. The proposed problems can be addressed using modern heuristic optimization approaches, enabling the achievement of good solutions in much lower execution times, adequate for the envisaged decision-making processes. Results from the competition show that metaheuristics can be successfully applied in search of efficient near-optimal solutions for the Stochastic Optimal Power Flow and large-scale energy resource management problems. [ABSTRACT FROM AUTHOR]

Abstract Home health care structures provide cares for the elderly, people with disabilities or patients with chronic conditions. Since the increase in demand, organizations providing home health care are eager to optimize their activities. The planning of caregivers' activities must optimize several objectives, often conflicting, that requires an extensive time to obtain a fair and valid schedule. In this paper, we address the multi-objective home health care problem with the aim of ensuring the applicability of the planning. To that end, the objectives considered in the proposed model are the minimization of the total working time of the caregivers, while maximizing the quality of service and minimizing the maximal working time difference among nurses and auxiliary nurses. A memetic algorithm for multi-objective optimization is proposed to solve the problem. Computational results on benchmark instances from the literature highlight the efficiency of the proposed algorithm in comparison with other existing metaheuristics thanks to four comparison metrics. As well, an analysis of the results exposes the trade-off between the three objectives. As a result, requiring a minimum caregivers' travel time solution leads to scarcity of the available solutions and so, cannot be demanding on the quality of the other objectives. [ABSTRACT FROM AUTHOR]

Abstract This paper proposes a push and pull search (PPS) framework for solving constrained multi-objective optimization problems (CMOPs). To be more specific, the proposed PPS divides the search process into two different stages: push and pull search stages. In the push stage, a multi-objective evolutionary algorithm (MOEA) is used to explore the search space without considering any constraints, which can help to get across infeasible regions very quickly and to approach the unconstrained Pareto front. Furthermore, the landscape of CMOPs with constraints can be probed and estimated in the push stage, which can be utilized to conduct the parameter setting for the constraint-handling approaches to be applied in the pull stage. Then, a modified form of a constrained multi-objective evolutionary algorithm (CMOEA), with improved epsilon constraint-handling, is applied to pull the infeasible individuals achieved in the push stage to the feasible and non-dominated regions. To evaluate the performance regarding convergence and diversity, a set of benchmark CMOPs and a real-world optimization problem are used to test the proposed PPS (PPS-MOEA/D) and state-of-the-art CMOEAs, including MOEA/D-IEpsilon, MOEA/D-Epsilon, MOEA/D-CDP, MOEA/D-SR, C-MOEA/D and NSGA-II-CDP. The comprehensive experimental results show that the proposed PPS-MOEA/D achieves significantly better performance than the other six CMOEAs on most of the tested problems, which indicates the superiority of the proposed PPS method for solving CMOPs. [ABSTRACT FROM AUTHOR]

Abstract A recent discovery has attracted the attention of many researchers in the field of genetic programming: given individuals with particular characteristics of alignment in the error space, called optimally aligned, it is possible to reconstruct a globally optimal solution. Furthermore, recent preliminary experiments have shown that an indirect search consisting of looking for optimally aligned individuals can have benefits in terms of generalization ability compared to a direct search for optimal solutions. For this reason, defining genetic programming systems that look for optimally aligned individuals is becoming an ambitious and important objective. Nevertheless, the systems that have been introduced so far present important limitations that make them unusable in practice, particularly for complex real-life applications. In this paper, we overcome those limitations, and we present the first usable alignment-based genetic programming system, called nested alignment genetic programming (NAGP). The presented experimental results show that NAGP is able to outperform two of the most recognized state-of-the-art genetic programming systems on four complex real-life applications. The predictive models generated by NAGP are not only more effective than the ones produced by the other studied methods but also significantly smaller and thus more manageable and interpretable. [ABSTRACT FROM AUTHOR]

Abstract The Artificial Bee Colony (ABC) algorithm is a swarm intelligence approach which has initially been proposed to solve optimisation of mathematical test functions with a unique neighbourhood search mechanism. This neighbourhood search mechanism could not be directly applied to combinatorial discrete optimisation problems. In order to tackle combinatorial discrete optimisation problems, the employed and onlooker bees need to be equipped with problem-specific perturbative heuristics. However, a large variety of problem-specific heuristics are available, and it is not an easy task to select an appropriate heuristic for a specific problem. In this paper, a hyper-heuristic method, namely a Modified Choice Function (MCF), is applied such that it can regulate the selection of the neighbourhood search heuristics adopted by the employed and onlooker bees automatically. The Lin-Kernighan (LK) local search strategy is integrated to improve the performance of the proposed model. To demonstrate the effectiveness of the proposed model, 64 Traveling Salesman Problem (TSP) instances available in TSPLIB are evaluated. On average, the proposed model solves the 64 instances to 0.055% from the known optimum within approximately 2.7 min. A performance comparison with other state-of-the-art algorithms further indicates the effectiveness of the proposed model. [ABSTRACT FROM AUTHOR]

Abstract Distributed assembly permutation flowshop scheduling problem (DAPFSP) has important applications in modern assembly systems. In this paper, we present three variants of the discrete invasive weed optimization (DIWO) for the DAPFSP with total flowtime criterion. For solving such a problem, we present a two-level representation that consists of a product permutation and a number of job sequences. We introduce neighbourhood operators for both the product permutation and job sequences. We design effective local search procedures respectively for product-permutation-based neighbourhood and job-sequence-based neighbourhood. By combining the problem-specific knowledge and the idea of invasive weed optimization, we present three DIWO-based algorithms: a two-level discrete invasive weed optimization (TDIWO), a discrete invasive weed optimization with hybrid search operators (HDIWO), and a HDIWO with selection probability. The algorithms explore the two neighbourhoods in quite a different way. We calibrate the presented DIWO algorithms by means of the design of experimental method, and carry out a comprehensive computational campaign based on the 810 benchmark instances in the literature. The numerical experiments show that the presented DIWO algorithms perform significantly better than the other competing algorithms in the literature. Among the proposed algorithms, HDIWO is the best one. [ABSTRACT FROM AUTHOR]

Abstract In this paper, we propose an adaptive multi-objective evolutionary algorithm for multi-objective optimization problems (MOPs). In the algorithm, a clustering approach is employed to learn the Pareto optimal set's manifold structure adaptively, in accordance with the regularity property of MOPs, along the evolution. An advanced sampling strategy is developed for the generation of promising offspring from the learned structure. To generate trial solution, each non-dominated solution at present generation is Gaussian-perturbed using the variance-covariance matrix within its cluster. The other new features include 1) an adaptive hybridization of the developed sampling strategy with a differential evolution (DE) operator which aims to combine local and global information; 2) a reusing scheme which is to reduce the computational cost on modeling (clustering); and 3) an adaptive strength Pareto based approach which is to adaptively determine the contribution of the developed sampling strategy and the DE operator for balancing exploration and exploitation. The developed algorithm was empirically compared with four well-known MOEAs on a number of test instances with complex Pareto optimal set structure and complicated Pareto fronts. Experimental results suggest that it outperforms the compared algorithms on these test instances in terms of two commonly-used measure metrics. The effectiveness of the developed sampling strategy, the reusing scheme, the hybrid strategy, and the adaptive strategy was also empirically validated. [ABSTRACT FROM AUTHOR]

Abstract This paper presents a novel framework for improving the performance of multi-population algorithms in solving dynamic optimization problems (DOPs). The fundamental idea of the proposed framework is to incorporate the concept of scheduling into multi-population methods with the aim to allocate more function evaluations to the best performing sub-populations. Two methods are developed based on the proposed framework, each of which uses a different approach for scheduling the sub-populations. The first method combines the quality of sub-populations and the degree of diversity among them into a single feedback parameter for detecting the best performing sub-population. The second method uses the learning automata as the central unit for performing the scheduling operation. In order to validate the applicability of the proposed methods, they are incorporated into three well-known algorithms for DOPs. The experimental results show the efficiency of the scheduling approach for improving the multi-population methods on the moving peaks benchmark (MPB) and generalized dynamic benchmark generator. [ABSTRACT FROM AUTHOR]

Multi-objective optimization under uncertainty has gained considerable attention in recent years due to its practical applications in real-life. Many studies have been conducted on this topic, but almost all of them transformed the problem into a mono-objective one or just neglected the effects of uncertainty on the outcomes. This paper addresses specific uncertain multi-objective problems in which uncertainty is expressed by means of triangular fuzzy numbers. To handle these problems, we introduced a new approach able to solve them without any transformation by considering fuzziness propagation to the objective functions. The proposed approach is composed of two main contributions: First, a fuzzy Pareto dominance is defined for ranking the generated fuzzy solutions. Second, a generic fuzzy extension of well-known evolutionary algorithms is suggested as resolution methods. An experimental study on multi-objective Vehicle Routing Problems (VRP) with uncertain demands is finally carried to evaluate our approach. [ABSTRACT FROM AUTHOR]

The Bees Algorithm has been successfully applied for over a decade to a large number of optimisation problems. However, a mathematical analysis of its search capabilities, the effects of different parameters used, and various design choices has not been carried out. As a consequence, optimisation of the Bees Algorithm has so far relied on trial-and-error experimentation. This paper formalises the Bees Algorithm in a rigorous mathematical description, beyond the qualitative biological metaphor. A review of the literature is presented, highlighting the main variants of the Bees Algorithm, and its analogies and differences compared with other optimisation methods. The local search procedure of the Bees Algorithm is analysed, and the results experimentally checked. The analysis shows that the progress of local search is mainly influenced by the size of the neighbourhood and the stagnation limit in the site abandonment procedure, rather than the number of recruited foragers. In particular, the analysis underlines the trade-off between the step size of local search (a large neighbourhood size favours quick progress) and the likelihood of stagnation (a small neighbourhood size prevents premature site abandonment). For the first time, the implications of the choice of neighbourhood shape on the character of the local search are clarified. The paper reveals that, particularly in high-dimensional spaces, hyperspherical neighbourhoods allow greater search intensification than hypercubic neighbourhoods. The theoretical results obtained in this paper are in good agreement with the findings of several experimental studies. It is hoped that the new mathematical formalism here introduced will foster further understanding and analysis of the Bees Algorithm, and that the theoretical results obtained will provide useful parameterisation guidelines for applied studies. [ABSTRACT FROM AUTHOR]