We consider heuristic algorithms for the resource-constrained project scheduling problem. Starting with a literature survey, we summarize the basic components of heuristic approaches. We briefly describe so-called X -pass methods which are based on priority rules as well as metaheuristic algorithms. Subsequently, we present the results of our in-depth computational study. Here, we evaluate the performance of several state-of-the-art heuristics from the literature on the basis of a standard set of test instances and point out to the most promising procedures. Moreover, we analyze the behavior of the heuristics with respect to their components such as priority rules and metaheuristic strategy. Finally, we examine the impact of problem characteristics such as project size and resource scarceness on the performance.

Experimental evaluation of state-of-the-art heuristics for the resource-constrained project scheduling problem

The application of multiobjective evolutionary algorithms to many-objective optimization problems often faces challenges in terms of diversity and convergence. On the one hand, with a limited population size, it is difficult for an algorithm to cover different parts of the whole Pareto front (PF) in a large objective space. The algorithm tends to concentrate only on limited areas. On the other hand, as the number of objectives increases, solutions easily have poor values on some objectives, which can be regarded as poor bottleneck objectives that restrict solutions’ convergence to the PF. Thus, we propose a coevolutionary particle swarm optimization with a bottleneck objective learning (BOL) strategy for many-objective optimization. In the proposed algorithm, multiple swarms coevolve in distributed fashion to maintain diversity for approximating different parts of the whole PF, and a novel BOL strategy is developed to improve convergence on all objectives. In addition, we develop a solution reproduction procedure with both an elitist learning strategy (ELS) and a juncture learning strategy (JLS) to improve the quality of archived solutions. The ELS helps the algorithm to jump out of local PFs, and the JLS helps to reach out to the missing areas of the PF that are easily missed by the swarms. The performance of the proposed algorithm is evaluated using two widely used test suites with different numbers of objectives. Experimental results show that the proposed algorithm compares favorably with six other state-of-the-art algorithms on many-objective optimization.

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Coevolutionary Particle Swarm Optimization With Bottleneck Objective Learning Strategy for Many-Objective Optimization

An improved NSGA-III algorithm with adaptive mutation operator for Big Data optimization problems

Behavior of crossover operators in NSGA-III for large-scale optimization problems

With the increasing attention paid to many-objective optimization in the evolutionary multi-objective optimization community, various approaches have been proposed to solve many-objective problems. However, existing experimental comparative studies are usually restricted to a few methods. Few studies have encompassed most of the recently proposed state-of-the-art approaches and made an experimental comparison. To this end, this paper offers a systematic comparison of 13 algorithms covering various categories to solve many-objective problems. The experimental comparison is conducted on three groups of test functions by using two performance metrics and a visual observation in the decision space. The experimental results demonstrate that different approaches have different search abilities. None of the test approaches outperform the others on all types of problems. However, some of the approaches are competitive on a large number of test problems. Moreover, inconsistent results from the hypervolume and the inverted generational distance metrics are revealed in this paper. Based on these comparative results, researchers can obtain useful suggestions for choosing appropriate algorithms for different problems.

Evolutionary Many-Objective Optimization: A Comparative Study of the State-of-the-Art

Decomposition via scalarization is a basic concept for multiobjective optimization. The weighted sum (WS) method, a frequently used scalarizing method in decomposition-based evolutionary multiobjective (EMO) algorithms, has good features such as computationally easy and high search efficiency, compared to other scalarizing methods. However, it is often criticized by the loss of effect on nonconvex problems. This paper seeks to utilize advantages of the WS method, without suffering from its disadvantage, to solve many-objective problems. A novel decomposition-based EMO algorithm called multiobjective evolutionary algorithm based on decomposition LWS (MOEA/D-LWS) is proposed in which the WS method is applied in a local manner. That is, for each search direction, the optimal solution is selected only amongst its neighboring solutions. The neighborhood is defined using a hypercone. The apex angle of a hypervcone is determined automatically in a priori . The effectiveness of MOEA/D-LWS is demonstrated by comparing it against three variants of MOEA/D, i.e., MOEA/D using Chebyshev method, MOEA/D with an adaptive use of WS and Chebyshev method, MOEA/D with a simultaneous use of WS and Chebyshev method, and four state-of-the-art many-objective EMO algorithms, i.e., preference-inspired co-evolutionary algorithm, hypervolume-based evolutionary, $\boldsymbol {\theta }$ -dominance-based algorithm, and SPEA2+SDE for the WFG benchmark problems with up to seven conflicting objectives. Experimental results show that MOEA/D-LWS outperforms the comparison algorithms for most of test problems, and is a competitive algorithm for many-objective optimization.

Localized Weighted Sum Method for Many-Objective Optimization

This paper addresses weapon selection and planning problems (WSPPs), which can be considered as an amalgamation of project portfolio and project scheduling problems. A multi-objective optimization model is proposed for WSPPs. The objectives include net present value (NPV) and effectiveness. To obtain the Pareto optimal set, a multi-objective evolutionary algorithm is presented for the problem. The basic procedure of NSGA-Ⅱ is employed. The problem-specific chromosome representation and decoding procedure, as well as genetic operators are redesigned for WSPPs. The dynamic nature of the planning environment is taken into account. Dynamic changes are modeled as the occurrences of countermeasures of specific weapon types. An adaptation process is proposed to tackle dynamic changes. Furthermore, we propose a flexibility measure to indicate a solution's ability to adapt in the presence of changes. The experimental results and analysis of a hypothetical case study are presented in this research.

https://www.aimsciences.org/article/exportPdf?id=8722a5bb-7d8b-4355-a898-3b5859e5688f

A multi-objective approach for weapon selection and planning problems in dynamic environments

In the real world, project construction usually suffers various uncertain factors. Traditionally, uncertainty is modelled as either random variables or dynamic events. This paper addresses the case that the information about uncertainty is partially known when developing project schedules. The concept of resilience is introduced into project scheduling problems with resource constraint to measure a schedule's ability to absorb possible perturbation. The definition of resilience is given based on project equilibriums. Since the calculation of resilience is time intensive, a new surrogate measure is proposed to indicate schedule resilience. Correlation analysis between resilience and proposed surrogate measure is carried out. The experimental results suggest that the proposed surrogate measure is more appropriate to indicate resilience than makespan or total free slack.

https://www.aimsciences.org/article/exportPdf?id=294c7ddc-6fdf-4133-88f2-0db2f216f9c7

Resilience analysis for project scheduling with renewable resource constraint and uncertain activity durations

In terms of generating offspring solutions, simulated binary crossover (SBX) and differential evolution (DE) are two of the most representative reproduction operators in evolutionary multi-objective algorithms (EMOAs). However, they are found as less effective on multi-objective problems (MOPs) with complicated Pareto optimal set (PS). Under mild conditions, the PS of an MOP is an ( m − 1 ) -dimensional piecewise continuous manifolds where m is the number of objectives. Inspired from this regularity property, this study proposes a simple yet effective reproduction operator, namely, PCA-assisted reproduction (PCA-ar). Specifically, the PCA-ar first applies principal component analysis (PCA) method to construct a new decision space with reduced number of dimensions based on the information extracted from several well converged solutions. The PS is then estimated by a hyperplane in the new decision space. To this end, new offspring are sampled from the estimated PS, and then re-converted to the original decision space for fitness calculation. In order to systematically examine the effectiveness of the PCA-ar operator, we integrate it into NSGA-II and MOEA/D, and compare the derived algorithms, nNSGA-II and nMOEA/D, with their original versions (NSGA-II with SBX operator and MOEA/D with DE operator) as well as the regularity model based multi-objective estimated distribution algorithm (RM-MEDA) on the modified DTLZ benchmarks with up to 8 objectives. Experimental results show that nNSGA-II and nMOEA/D outperform the competitor EMOAs for most of problems, which indicate that the PCA-ar is effective. Lastly, the PCA-ar is also demonstrated to have good scalability to the number of decision variables.

Zhongbao Zhou

Papers

Localized Weighted Sum Method for Many-Objective Optimization

A multi-objective approach for weapon selection and planning problems in dynamic environments

Resilience analysis for project scheduling with renewable resource constraint and uncertain activity durations

PCA-assisted reproduction for continuous multi-objective optimization with complicated Pareto optimal set