Kuo-Ching Ying

• National Taipei University of Technology

The role of setup times in production planning and control was recognised in the late 1960s. Since then, a growing number of scheduling problems have accounted for sequence-dependent setup time variables. This study aims to provide a systematic review of setup times in the short-term production planning literature, using an objective, algorithm-bas...

The production of metal products is one of the main areas where supply chains benefit from adopting additive manufacturing (AM). Optimizing the production process facilitates the widespread adoption of AM by improving know-how and reducing costs. This study offers a twofold contribution to facilitate the implementation of Additive Manufacturing Sch...

Engineering, procurement, and construction projects are time-intensive and subject to resource constraints. Modern project planning software requires optimization algorithms to schedule tasks while considering resource availability. A comprehensive review of the optimization algorithms used in project planning has not yet been conducted. This study...

The Single-Machine Scheduling Problem (SMSP) serves as the cornerstone of scheduling theory. Almost all developments in production planning and control were initially introduced and tested within single-machine production settings. Exploring the literature on SMSPs illuminates the entire development trajectory of scheduling theory. This study emplo...

Metaheuristics can benefit from analyzing patterns and regularities in data to perform more effective searches in the solution space. In line with the emerging trend in the optimization literature, this study introduces the Reinforcement-learning-based Alpha-List Iterated Greedy (RAIG) algorithm to contribute to the advances in machine learning-bas...

Volatility in the supply chain of critical products, notably the vaccine shortage during the pandemic, influences livelihoods and may lead to significant delays and long waiting times. Considering the capital- and time-intensive nature of capacity expansion plans, strategic operational production decisions are required best to address the supply-de...

The research on the Parallel Machine Scheduling Problem (PMSP) has undergone significant development. The most recent comprehensive review of published studies dates back to early 2001. This article presents an algorithmic review of PMSPs, using Main Path Analysis (MPA) to identify seminal knowledge diffusion and development trajectories. This rese...

This article contributes to the additive manufacturing-based production planning literature by developing a Mixed-Integer Linear Programming (MILP) formulation for the Identical Parallel 3D-Printing Machines Scheduling Problem considering batching, multiple build platforms of restricted sizes, and sequence-independent setup times. Besides, a custom...

System-wide optimization of distributed manufacturing operations enables process improvement beyond the standalone and individual optimality norms. This study addresses the production planning of a distributed manufacturing system consisting of three stages: production of parts (subcomponents), assembly of components in Original Equipment Manufactu...

Integrating component and final assembly production plans is critical to optimizing the global supply chain production system. This research extends the distributed assembly permutation flowshop scheduling problem to consider unrelated assembly machines and sequence-dependent setup times. A mixed-integer linear programming (MILP) model and a novel...

Sequence-dependent setup times and precedence delays occur frequently in various production environments. This study investigates the single machine scheduling problem with setup times and precedence delays that occur in an amplifier assembly company. This study proposes a novel mixed-integer linear programming model and a lean iterated greedy algo...

Recent developments in artificial intelligence (AI) have greatly influenced progress in various industries. While the complexity of the construction industry makes it an essential and potential area for AI applications, there has been no analysis conducted on the main development paths for the applications of AI technologies in the construction ind...

This study focused on the no-wait jobshop scheduling problem (NWJSP), which is NP-hard in the strong sense. A new benchmarking algorithm, named backtracking multi-start simulated annealing (BMSA), is presented in this study for minimizing the total completion time in NWJSPs. To effectively and efficiently find (near-) optimal schedules, the simulat...

As a disruptive technology, additive manufacturing (AM) is revolutionizing manufacturing supply chains. AM consists of producing 3-dimensional objects through layer-by-layer addition of compound material based on digital models. The scheduling of AM operations differs from traditional (i.e., subtractive and injection molding) manufacturing with a s...

Integrated scheduling of distributed manufacturing operations has implications for supply chain optimization and requires further investigations to facilitate its application area for various industry settings. This study extends the limited literature of the distributed two-stage production-assembly scheduling problems offering a twofold contribut...

Sequence-dependent setup times (SDSTs) and delayed precedence (DP) occur commonly in various manufacturing settings. This study investigated the single machine scheduling problem with SDSTs and DP constraints arising in an amplifier assembly company. A mixed-integer linear programming model and a lean iterated greedy (LIG) algorithm is proposed to...

With many industrial applications in the production sector, the hybrid flowshop scheduling problem (HFSP) has received wide recognition in the scheduling literature. Given the NP-hard nature of the HFSP, which is characterized by highly intractable solution spaces, effective solution approaches are of particular interest to facilitate the real-worl...

Supply chain-oriented scheduling problems have received recent recognition among production research scholars due to their ability in integrating production planning and control across manufacturing systems. This study contributes to the literature of the distributed scheduling problems developing an original Mixed-Integer Linear Programming (MILP)...

In the field of operations research, the vehicle routing problem with time windows (VRPTW) has been widely studied because it is extensively used in practical applications. Real-life situations discussed in the relevant research include time windows and vehicle capabilities. Among the constraints in a VRPTW, the practical consideration of the fairn...

With the rapid technological and economic development, a growing number of companies are employing robots for their production and service operations. Motion planning is a fundamental topic in robotics that has received wide attention due to its importance in the development of industry 4.0 and intelligent manufacturing systems. This study sought t...

Setup operations and waiting time between production procedures are prime examples of non-value-adding activities that can be alleviated through well-informed production decisions. Application of the No-wait Flowshop Group Scheduling Problems with Sequence-Dependent Setup Times (NWFGSP_SDST) as an optimization tool helps maintain the setup and wait...

Production environment in modern industries, like integrated circuits manufacturing, fiberglass processing, steelmaking, and ceramic frit, is characterized by zero idle-time between inbound and outbound jobs on every machine; this technical requirement improves energy efficiency, hence, has implications for cleaner production in other production si...

Advanced analytics benefits lean manufacturing by upgrading the scheduling problems into operational strategic tools that help minimize non-value-adding activities. Considering production environments with prevalent setup operations, this study develops an Unsupervised Learning-based Artificial Bee Colony (ULABC) algorithm to improve the effectiven...

Just-in-time production in large enterprises along with the factory’s limited space highlights the need for scheduling tools that consider blocking conditions. This study contributes to the scheduling literature by developing an effective metaheuristic to address the Blocking Flowshop Scheduling Problems with Sequence-Dependent Setup-Times (BFSP wi...

Robotic assembly plays a principal role in intelligent manufacturing and Industry 4.0. Well-informed coordination between the robotic arms and the control modules is of paramount importance in the design and planning of automated systems. Given the time-extensive nature of assembly sequence planning and the need for labor-intensive coding and coord...

Given the significant proportion of the outsourced parts, components, and the complex assembly structure of the automobiles, agriculture machinery and heavy industry equipment, distributed production and flexible assembly are much-needed production scheduling settings to optimise their global supply chains. This research extends the distributed ass...

Protein Function Module (PFM) identification in Protein-Protein Interaction Networks (PPINs) is one of the most important and challenging tasks in computational biology. The quick and accurate detection of PFMs in PPINs can contribute greatly to the understanding of the functions, properties, and biological mechanisms in research on various disease...

Production management of perishable goods is highly complex and requires well-informed decisions in corresponding stages. In such production environments, scheduling problems with time constraints are of high relevance to ensure the timely flow of the work-in-process material and goods. This study introduces the no-wait flowshop scheduling problem...

Scheduling problems play an increasingly significant role in the design and optimization of highly computerized and automated production systems. Given the importance of just-in-time production in advanced manufacturing, scheduling methods should enable the users to consider various blocking situations in a zero work-in-process scheme. In this situ...

Scheduling decisions are of certain cachet in production and operations management. Many extensions are developed to help address different scheduling industrial situations, one of which, the Mixed-Blocking Permutation Flowshop Scheduling Problem (MBPFSP), has gained recent recognition due to its wide industrial applications both in manufacturing a...

Given the importance of production planning and control in the design of flexible services and manufacturing systems, scheduling problems with interfering jobs are much-needed optimization tools to respond to heterogeneous and fluctuating market demands in a timely fashion. This study contributes to the scheduling literature by developing an effect...

This paper presents a multi-start simulated annealing with bi-directional shift timetabling (MSA-BST) algorithm for solving the no-wait jobshop scheduling problem (NWJSP). To enhance the quality of the solution, a bi-directional shift timetabling procedure that allows delay timetabling and consequently enlarges the search space is embedded into the...

This paper proposes an effective and efficient multi-temperature simulated annealing (MTSA) algorithm to minimise the makespan of a job-shop under the constraint that machines are not continuously available for processing during the whole scheduling horizon. The proposed MTSA algorithm uses an embedded multi-temperature mechanism to vary the therma...

Setup time consists of all the activities that need to be completed before the production process takes place. The extant scheduling predominantly relies on simplistic methods, like the average value obtained from historical data, to estimate setup times. Such methods are incapable of representing the real industry situation, especially when the se...

This study evaluates various Mixed Integer Programming (MIP) formulations for solving single-machine and parallel-machine scheduling problems, with the objective of minimizing the total completion time and the makespan of jobs. Through extensive numerical study, the MIP formulation, which is suitable for dealing with each specific single-machine or...

This article deals with the problem of sequencing N jobs on a single machine with a restrictive common due window. The objective is to minimize the total weighted earliness-tardiness penalties, which conform to just-in-time (JIT) manufacturing. A novel backtracking simulated annealing (BSA) algorithm with a backtracking mechanism and an effective c...

This paper studies a single-machine scheduling problem with two competing agents in which the performance criteria of the first and second agents are to minimize the mean lateness and number of tardy jobs, respectively. Due to the non-deterministic polynomial-time hardness of this problem, we propose an effective and efficient algorithm, denominate...

For double-sided circuit boards, a wave soldering carrier is generally used to shield the devices mounted on the surface of the first side of the printed circuit board (PCB), so that the solder joints are not melted again through exposure to tin wave, causing the devices to deviate or fall as a result of flushing. However, carrier adoption increase...

Mask data preparation (MDP) is a part of the mask data process for fabricating semiconductors, and its importance has commonly been neglected. This work proposes an integer linear programming (ILP) model and two meta-heuristics, a genetic algorithm (GA) and a simulated annealing (SA), for solving the mask data preparation scheduling problem (MDPSP)...

This paper proposes an extension of the mixed no-wait flowshop scheduling problem (MNFSP) which considers sequence-dependent setup times (SDSTs). A mixed integer linear programming model is presented to solve small problems with respect to the makespan criterion. Due to the strong NP-hardness of the research problem, an effective and efficient meta...

This paper presents a cloud theory-based iterated greedy (CTIG) algorithm for solving the no-wait flowshop scheduling problem (NWFSP) with the objective of minimizing the sum of makespan and total weighted tardiness. The performance of the proposed CTIG algorithm is evaluated by comparing its computational results to those of the best-to-date meta-...

The no-wait flowline manufacturing cell scheduling problem with sequence-dependent family setup times and the objective of minimizing makespan is NP-hard in the strong sense even in the two-machine case. This work proposes an efficient matheuristic for solving this problem to optimality in a reasonable computational time. To demonstrate the effecti...

The no-wait flowshop scheduling problem with hard due date constraints is critical to operations in many industries, such as plastic, chemical, and pharmaceutical manufacturing. However, to date there is a lack of effective optimization algorithms for this NP-hard problem. This work develops a new mixed integer linear programming (MILP) model and a...

This study investigates no-wait flowshop scheduling problems with sequence-independent and sequence-dependent setup times aimed at minimizing the makespan. We propose an efficient two-phase matheuristic, which can optimally solve all tested instances of three existing benchmark problem sets and a new generated large-sized test problem set, with up...

The rapid growth of distributed manufacturing in industry today has recently attracted significant research attention that has focused on distributed scheduling problems. This work studied the distributed mixed no-idle flowshop scheduling problem using makespan as an optimality criterion. To the best of the authors’ knowledge, this is the first pap...

This work investigates the system testing scheduling problem (STSP), using one of the largest computer manufacturing companies in the world as a case study. A mixed integer linear programming (MILP) model and a restricted simulated annealing (RSA) heuristic which applies two rules to eliminate ineffective job moves to minimize makespan in the STSP...

Proportionate permutation flowshop (PPF) is a class of flowshop problems that has appeared in the literature since the early 1980s. However, no research has been conducted on PPF with variable maintenance activities (VMAs). To remedy this research gap, this study proposed optimization algorithms for six PPFs with equal- and unequal-duration VMAs, a...

Modeling and simulation are widely used in many business domains, such as logistics, manufacturing, warehouses, and hospitals. This research used discrete event simulation (DES) combined with agent-based simulation (ABS) to improve draftees' physical examination service by reducing their process waiting time. A computer simulation was developed to...

This paper presents an optimization model for determining the optimal time-varying numbers of cashiers and pharmacists in a large hospital. The objective of this model is to minimize the weighted sum of the waiting cost incurred by patients and the operating costs incurred by the hospital. A point-wise fluid-based approximation approach is adopted...

The trend of globalization has recently seen the study of distributed scheduling problems. This study attempts to solve the distributed hybrid flowshop scheduling problem with multiprocessor tasks, and is the first attempt to address this problem. To solve this strongly NP-hard problem, a mixed integer linear programming formulation and self-tuning...

This work addresses four single-machine scheduling problems (SMSPs) with learning effects and variable maintenance activity. The processing times of the jobs are simultaneously determined by a decreasing function of their corresponding scheduled positions and the sum of the processing times of the already processed jobs. Maintenance activity must s...

This paper studies the distributed blocking flow shop scheduling problem (DBFSP) using metaheuristics. A mixed integer programming model for solving the problem is proposed, and then three versions of the hybrid iterated greedy algorithm (HIG <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> , HI...

This study examines the uniform parallel-machine scheduling problem in which the objective aims to minimize the total resource consumption (TRC) with a bounded makespan. A matheuristic is proposed to deal with this strongly NP-hard problem. The performance of the proposed matheuristic is compared with that of the state-of-the-art particle swarm opt...

This paper investigates the Distributed No-idle Permutation Flowshop Scheduling Problem (DNIPFSP) with the objective of minimizing the makespan, which has not been discussed in any previous study. This study presents an Iterated Reference Greedy (IRG) algorithm for effectively solving this problem. The performance of the proposed IRG algorithm is c...

Printed circuit boards (PCBs) are composite structures consisting of FR-4, solder mask, and Cu materials. When heated during reflow, these materials exhibit different levels of expansion because of their dissimilar thermal expansion coefficients. Currently, the shadow moiré method is the primary means for measuring PCB warpage. However, applying th...

This paper investigates the multiskilled worker training and assignment (MWT&A) problem of the seru production system (SPS), which is a new type of assembly line configured as multiple assembly cells, or so-called serus. The configuration of the SPS emphasises production efficiency and flexibility, achieved by multiskilled workers (MWs) able to cop...

This paper presents a rolling horizon-based framework for real-time relief distribution in the aftermath of disasters. This framework consists of two modules. One is a state estimation and prediction module, which predicts relief demands and delivery times. The other is a relief distribution module, which solves for optimal relief distribution flow...

This study addresses the single-machine scheduling problem with a common due window (CDW) that has a constant size and position. The objective is to minimise the total weighted earliness–tardiness penalties for jobs completed out of the CDW. To determine a schedule as close to optimum as possible, this study develops a dynamic dispatching rule and...

This paper studies the no-wait flowshop scheduling problem with total flow time criterion, which is NP-complete in the strong sense. A self-adaptive ruin-and-recreate (SR&R) algorithm is proposed to solve this complex problem. The performance of the proposed SR&R algorithm is compared with that of the best available heuristics and the SR&R algorith...

This paper presents the distributed no-wait flowshop scheduling problem (DNFSP), which is the first attempt in the literature to solve this key problem faced by the manufacturing industry. A mixed integer programming (MIP) mathematical model and an iterated cocktail greedy (ICG) algorithm are developed for solving this problem of how to minimize th...

This paper deals with four single-machine scheduling problems (SMSPs) with a variable machine maintenance. The objectives of the four SMSPs are to minimize mean lateness, maximum tardiness, total flow time and mean tardiness, respectively. These four SMSPs are important in the literature and in practice. This study proposes an exact algorithm with...

This paper studies the scheduling problem of minimising total weighted earliness and tardiness penalties on identical parallel machines against a restrictive common due date. This problem is NP-hard in the strong sense and arises in many just-in-time production environments. A fast ruin-and-recreate (FR&R) algorithm is proposed to obtain high-quali...

A high resistance measuring system (HRMS) is used to measure the surface insulation resistance (SIR) values of the printed circuit board (PCB), and monitor whether a momentary circuit short and/or the case of current slow leakage occur, which will affect the electrical properties of electronic components. This study constructs a dynamic parameter d...

Many hospitals are currently paying more attention to patient satisfaction since it is an important service quality index. Many Asian countries’ healthcare systems have a mixed-type registration, accepting both walk-in patients and scheduled patients. This complex registration system causes a long patient waiting time in outpatient clinics. Differe...

The no-wait flowshop scheduling problem (NWFSP) with makespan minimization is a well-known strongly NP-hard problem with applications in various industries. This study formulates this problem as an asymmetric traveling salesman problem, and proposes two matheuristics to solve it. The performance of each of the proposed matheuristics is compared wit...

This paper addresses the two-machine flowshop scheduling problem with uncertain job processing times. It is assumed that in the realization of a schedule, job processing times may take any values from their corresponding intervals given before scheduling. The objective is to determine a robust schedule with the minimum makespan of the restricted wo...

The order acceptance and scheduling (OAS) problem is important in make-to-order production systems in which production capacity is limited and order delivery requirements are applied. This study proposes a multi-initiator simulated annealing (MSA) algorithm to maximize the total net revenue for the permutation flowshop scheduling problem with order...

This work proposes a high-performance algorithm for solving the multi-objective unrelated parallel machine scheduling problem. The proposed approach is based on the iterated Pareto greedy (IPG) algorithm but exploits the accessible Tabu list (TL) to enhance its performance. To demonstrate the superior performance of the proposed Tabu-enhanced itera...

This study considers the problem of job scheduling on unrelated parallel machines. A multi-objective multi-point simulated annealing (MOMSA) algorithm was proposed for solving this problem by simultaneously minimising makespan, total weighted completion time and total weighted tardiness. To assess the performance of the proposed heuristic and compa...

This research addresses a single machine scheduling problem with uncertain processing times and sequence-dependent setup times represented by intervals. Our objective is to obtain a robust schedule with the minimum absolute deviation from the optimal makespan in the worst-case scenario. The problem is reformulated as a robust traveling salesman pro...

Berth allocation is the forefront operation performed when ships arrive at a port and is a critical task in container port optimization. Minimizing the time ships spend at berths constitutes an important objective of berth allocation problems. This study focuses on the discrete dynamic berth allocation problem (discrete DBAP), which aims to minimiz...

The personnel task scheduling problem is a subject of commercial interest which has been investigated since the 1950s. This paper proposes an effective and efficient three-phase algorithm for solving the shift minimization personnel task scheduling problem (SMPTSP). To illustrate the increased efficacy of the proposed algorithm over an existing alg...

The multi-objective reentrant hybrid flowshop scheduling problem (RHFSP) exhibits significance in many industrial applications, but appears under-studied in the literature. In this study, an iterated Pareto greedy (IPG) algorithm is proposed to solve a RHFSP with the bi-objective of minimising makespan and total tardiness. The performance of the pr...

The efficiency of wafer sorting scheduling is of particular importance in semiconductor fabrication, especially in the face of strong industry competition. This paper presents a novel hybrid artificial immune system (HAIS) algorithm for solving the wafer sorting scheduling problem, aimed at minimizing the total setup time and the number of testers...

Minimizing makespan in permutation flowshops is one of the most frequently investigated problems in scheduling theory. The NEH heuristic is commonly regarded as the best current constructive heuristic for solving this NP-hard problem. In this paper, we propose a novel constructive heuristic with an effective tie-breaking strategy to improve the sch...

The distributed permutation flowshop scheduling problem (DPFSP) is a newly proposed topic in the shop scheduling field, which has important application in globalised and multi-plant environments. This study presents a modified iterated greedy (MIG) algorithm for this problem to minimise the maximum completion time among all the factories. Compared...

In this study, a bi-objective multi-start simulated-annealing algorithm (BMSA) is presented for permutation flowshop scheduling problems with the objectives of minimizing the makespan and total flowtime of jobs. To evaluate the performance of the BMSA, computational experiments were conducted on the well-known benchmark problem set provided by Tail...

The blocking flowshop scheduling problem has a strong industrial background but is under-represented in the research literature. In this study, a revised artificial immune system (RAIS) algorithm based on the features of artificial immune systems and the annealing process of simulated annealing algorithms was presented to minimize the makespan in a...

The order acceptance and scheduling (OAS) problem is an important topic for make-to-order production systems with limited production capacity and tight delivery requirements. This paper proposes a new algorithm based on Artificial Bee Colony (ABC) for solving the single machine OAS problem with release dates and sequence-dependent setup times. The...

Liriope spicata is a well-known herb in traditional Chinese medicine, and its root has been clinically demonstrated to be effective in the treatment of metabolic and neural disorders. The constituents isolated from Liriope have also recently been shown to possess anticancer activity, although the mechanism of which remains largely unknown. Here, we...

This study considers the problem of scheduling jobs on unrelated parallel machines with machine-dependent and job sequence-dependent setup times. In this study, a restricted simulated annealing (RSA) algorithm which incorporates a restricted search strategy is presented to minimize the makespan. The proposed RSA algorithm can effective reduce the s...

Intrusion detection system (IDS) is to monitor the attacks occurring in the computer or networks. Anomaly intrusion detection plays an important role in IDS to detect new attacks by detecting any deviation from the normal profile. In this paper, an intelligent algorithm with feature selection and decision rules applied to anomaly intrusion detectio...

The permutation flowshop scheduling problem with the objective of mini-mizing total flow time is known as a NP-hard problem, even for the two-machine cases. Because of the computational complexity of this problem, a multi-start simulated anneal-ing (MSA) heuristic, which adopts a multi-start hill climbing strategy in the simulated annealing (SA) he...

In a real-world manufacturing environment featuring a variety of uncertainties, production schedules for manufacturing systems often cannot be executed exactly as they are developed. In these environments, schedule robustness that guarantees the best worst-case performance is a more appropriate criterion in developing schedules, although most exist...

Flowshop manufacturing cell scheduling problems (FMCSPs) with sequence-dependent family setup times (SDFSTs) have become a key area in the field of scheduling. Though the need to consider multiple criteria in real-world scheduling is widely recognised, most of the currently available algorithms for FMCSPs with SDFSTs only deal with the optimisation...

This paper examines the no-wait flowshop manufacturing cell scheduling problem (FMCSP) with sequence-dependent family setup times. To the best of our knowledge, the present study is among the first to investigate FMSCPs with no-wait consideration, though it is a necessary production constraint in many real-world applications. In view of the strongl...

This study deals with the unrelated parallel machine scheduling problem with sequence- and machine-dependent setup times under due date constraints, a core topic for numerous industrial applications. In view of the computational complexity, an artificial bee colony (ABC) algorithm is presented to minimize the total tardiness. The performance of the...

One lead free solder candidate, Sn-Ag-Cu305 (Sn96.5/Ag3.0/Cu0.5), has come into widespread use as a replacement for traditional tin-lead solder (Sn63/Pb37). However, the price of silver has increased dramatically in recent years. This has increased manufacturing costs, impacting firm competitiveness. This paper evaluates the performance of the low...

The scheduling problem of multistage hybrid flowshop with multiprocessor tasks is a core topic for numerous industrial applications but under-represented in the research literature. In this study, a new hybrid immune algorithm based on the features of artificial immune systems and iterated greedy algorithms is presented to minimise the makespan of...

The flow-line manufacturing cell scheduling problem (FMCSP) with sequence dependent family setup times (SDFSTs) is a topic of great concern for many industrial applications, but under-represented in the research literature. In this study, a two-level iterated greedy (TLIG) heuristic is proposed to minimize makespan of this strongly NP-hard problem....

Purpose – The purpose of this paper is to comprehensively explore the effects of critical parameters on solder deposition and to establish a systematic approach for determining guidelines for solder paste inspection (SPI) workstations. Design/methodology/approach – This study explored the effects of process parameters, stencil and printed circuit...

In this paper, we consider an identical parallel machine scheduling problem with sequence-dependent setup times and job release dates. An improved iterated greedy heuristic with a sinking temperature is presented to minimize the maximum lateness. To verify the developed heuristic, computational experiments are conducted on a well-known benchmark pr...

Meta-heuristics that attempt to obtain (near) global optimal solutions of NP-hard combinatorial optimization problems generally require diversification to escape from local optimality. One way to achieve diversification is to utilize the multi-start hill climbing strategy. By combining the respective advantages of the multi-start hill climbing stra...